def __init__(self, cfgfile, runid=None, cfg=None):
super().__init__(cfgfile, runid, cfg)
if PETSc.COMM_WORLD.getRank() == 0:
print("Creating solver objects.")
# create solver objects
# self.vlasov_solver = self.vlasov_object.PETScVlasovSolver(
self.vlasov_solver = PETScVlasovSolver(self.da1,
self.grid,
self.h0,
self.h1c,
self.h1h,
self.h2c,
self.h2h,
self.charge,
coll_freq=self.coll_freq)
self.vlasov_solver.set_moments(self.nc, self.uc, self.ec, self.ac,
self.nh, self.uh, self.eh, self.ah)
# initialise Jacobian
self.J = self.da1.createMat()
self.J.setOption(self.J.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.J.setUp()
# create nonlinear predictor solver
self.snes = PETSc.SNES().create()
self.snes.setType('ksponly')
self.snes.setFunction(self.vlasov_solver.function_snes_mult, self.fb)
self.snes.setJacobian(self.updateVlasovJacobian, self.J)
self.snes.setFromOptions()
self.snes.getKSP().setType('preonly')
self.snes.getKSP().getPC().setType('lu')
self.snes.getKSP().getPC().setFactorSolverPackage(
self.cfg['solver']['lu_package'])
# create Poisson matrix and object
self.poisson_matrix = self.dax.createMat()
self.poisson_matrix.setUp()
self.poisson_matrix.setNullSpace(self.p_nullspace)
self.poisson_solver = self.poisson_object.PETScPoissonSolver(
self.dax, self.grid.nx, self.grid.hx, self.charge)
self.poisson_solver.formMat(self.poisson_matrix)
# create linear Poisson solver
self.poisson_ksp = PETSc.KSP().create()
self.poisson_ksp.setFromOptions()
self.poisson_ksp.setOperators(self.poisson_matrix)
self.poisson_ksp.setType('preonly')
self.poisson_ksp.getPC().setType('lu')
self.poisson_ksp.getPC().setFactorSolverPackage(
self.cfg['solver']['lu_package'])
if PETSc.COMM_WORLD.getRank() == 0:
print("Run script initialisation done.")
print("")
def blocked_solve():
"""Blocked version"""
Jmat = create_matrix_block(J)
Fvec = create_vector_block(F)
snes = PETSc.SNES().create(MPI.COMM_WORLD)
snes.setTolerances(rtol=1.0e-15, max_it=10)
snes.getKSP().setType("preonly")
snes.getKSP().getPC().setType("lu")
problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs)
snes.setFunction(problem.F_block, Fvec)
snes.setJacobian(problem.J_block, J=Jmat, P=None)
u.interpolate(initial_guess_u)
p.interpolate(initial_guess_p)
x = create_vector_block(F)
scatter_local_vectors(x, [u.vector.array_r, p.vector.array_r],
[(u.function_space.dofmap.index_map,
u.function_space.dofmap.index_map_bs),
(p.function_space.dofmap.index_map,
p.function_space.dofmap.index_map_bs)])
x.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
snes.solve(None, x)
assert snes.getKSP().getConvergedReason() > 0
assert snes.getConvergedReason() > 0
return x.norm()
def help(args=None):
import sys, shlex
# program name
try:
prog = sys.argv[0]
except Exception:
prog = getattr(sys, 'executable', 'python')
# arguments
if args is None:
args = sys.argv[1:]
elif isinstance(args, str):
args = shlex.split(args)
else:
args = [str(a) for a in args]
# import and initialize
import petsc4py
petsc4py.init([prog, '-help'] + args)
from petsc4py import PETSc
# help dispatcher
COMM = PETSc.COMM_SELF
if 'vec' in args:
vec = PETSc.Vec().create(comm=COMM)
vec.setSizes(0)
vec.setFromOptions()
vec.destroy()
if 'mat' in args:
mat = PETSc.Mat().create(comm=COMM)
mat.setSizes([0, 0])
mat.setFromOptions()
mat.destroy()
if 'pc' in args:
pc = PETSc.PC().create(comm=COMM)
pc.setFromOptions()
pc.destroy()
if 'ksp' in args:
ksp = PETSc.KSP().create(comm=COMM)
ksp.setFromOptions()
ksp.destroy()
if 'snes' in args:
snes = PETSc.SNES().create(comm=COMM)
snes.setFromOptions()
snes.destroy()
if 'ts' in args:
ts = PETSc.TS().create(comm=COMM)
ts.setFromOptions()
ts.destroy()
if 'tao' in args:
tao = PETSc.TAO().create(comm=COMM)
tao.setFromOptions()
tao.destroy()
if 'dmda' in args:
dmda = PETSc.DMDA().create(comm=COMM)
dmda.setFromOptions()
dmda.destroy()
if 'dmplex' in args:
dmplex = PETSc.DMPlex().create(comm=COMM)
dmplex.setFromOptions()
dmplex.destroy()
def __init__(self, scheme):
self.model = scheme.model
self.res = scheme.space.interpolate([0],name="residual")
self.scheme = scheme
self.jacobian = linearOperator(self.scheme)
self.snes = PETSc.SNES().create()
self.snes.setFunction(self.f, self.res.as_petsc.duplicate())
self.snes.setUseMF(False)
self.snes.setJacobian(self.Df, self.jacobian.as_petsc, self.jacobian.as_petsc)
self.snes.getKSP().setType("cg")
self.snes.setFromOptions()
def test_nonlinear_pde_snes():
"""Test Newton solver for a simple nonlinear PDE"""
# Create mesh and function space
mesh = dolfinx.generation.UnitSquareMesh(MPI.COMM_WORLD, 12, 15)
V = function.FunctionSpace(mesh, ("Lagrange", 1))
u = function.Function(V)
v = TestFunction(V)
F = inner(5.0, v) * dx - ufl.sqrt(u * u) * inner(
grad(u), grad(v)) * dx - inner(u, v) * dx
def boundary(x):
"""Define Dirichlet boundary (x = 0 or x = 1)."""
return np.logical_or(x[0] < 1.0e-8, x[0] > 1.0 - 1.0e-8)
u_bc = function.Function(V)
u_bc.vector.set(1.0)
u_bc.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
bc = fem.DirichletBC(u_bc, fem.locate_dofs_geometrical(V, boundary))
# Create nonlinear problem
problem = NonlinearPDE_SNESProblem(F, u, bc)
u.vector.set(0.9)
u.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
b = dolfinx.cpp.la.create_vector(V.dofmap.index_map)
J = dolfinx.cpp.fem.create_matrix(problem.a_comp._cpp_object)
# Create Newton solver and solve
snes = PETSc.SNES().create()
snes.setFunction(problem.F, b)
snes.setJacobian(problem.J, J)
snes.setTolerances(rtol=1.0e-9, max_it=10)
snes.getKSP().setType("preonly")
snes.getKSP().setTolerances(rtol=1.0e-9)
snes.getKSP().getPC().setType("lu")
snes.getKSP().getPC().setFactorSolverType("superlu_dist")
snes.solve(None, u.vector)
assert snes.getConvergedReason() > 0
assert snes.getIterationNumber() < 6
# Modify boundary condition and solve again
u_bc.vector.set(0.5)
u_bc.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
snes.solve(None, u.vector)
assert snes.getConvergedReason() > 0
assert snes.getIterationNumber() < 6
def monolithic_solve():
"""Monolithic version"""
E = P * P
W = FunctionSpace(mesh, E)
U = Function(W)
dU = ufl.TrialFunction(W)
u0, u1 = ufl.split(U)
v0, v1 = ufl.TestFunctions(W)
F = inner((u0**2 + 1) * ufl.grad(u0), ufl.grad(v0)) * dx \
+ inner((u1**2 + 1) * ufl.grad(u1), ufl.grad(v1)) * dx \
- inner(f, v0) * ufl.dx - inner(g, v1) * dx
J = derivative(F, U, dU)
F, J = form(F), form(J)
u0_bc = Function(V0)
u0_bc.interpolate(bc_val_0)
u1_bc = Function(V1)
u1_bc.interpolate(bc_val_1)
bdofsW0_V0 = locate_dofs_topological((W.sub(0), V0), facetdim,
bndry_facets)
bdofsW1_V1 = locate_dofs_topological((W.sub(1), V1), facetdim,
bndry_facets)
bcs = [
dirichletbc(u0_bc, bdofsW0_V0, W.sub(0)),
dirichletbc(u1_bc, bdofsW1_V1, W.sub(1))
]
Jmat = create_matrix(J)
Fvec = create_vector(F)
snes = PETSc.SNES().create(MPI.COMM_WORLD)
snes.setTolerances(rtol=1.0e-15, max_it=10)
snes.getKSP().setType("preonly")
snes.getKSP().getPC().setType("lu")
problem = NonlinearPDE_SNESProblem(F, J, U, bcs)
snes.setFunction(problem.F_mono, Fvec)
snes.setJacobian(problem.J_mono, J=Jmat, P=None)
U.sub(0).interpolate(initial_guess_u)
U.sub(1).interpolate(initial_guess_p)
x = create_vector(F)
x.array = U.vector.array_r
snes.solve(None, x)
assert snes.getKSP().getConvergedReason() > 0
assert snes.getConvergedReason() > 0
return x.norm()
def __init__(self, problem, solution):
self.problem = problem
self.solution = solution
# Create SNES object
self.snes = PETSc.SNES().create(wrapping.get_mpi_comm(solution))
# ... and associate residual and jacobian
self.snes.setFunction(self.problem.residual_vector_eval, wrapping.to_petsc4py(self.problem.residual_vector))
self.snes.setJacobian(self.problem.jacobian_matrix_eval, wrapping.to_petsc4py(self.problem.jacobian_matrix))
# Set sensible default values to parameters
self._report = None
self.set_parameters({
"report": True
})
def help(args=None):
import sys, shlex
# program name
try:
prog = sys.argv[0]
except Exception:
prog = getattr(sys, 'executable', 'python')
if args is None:
args = sys.argv[1:]
elif isinstance(args, str):
args = shlex.split(args)
else:
args = [str(a) for a in args]
import petsc4py
petsc4py.init([prog, '-help'] + args)
from petsc4py import PETSc
COMM = PETSc.COMM_SELF
if 'vec' in args:
vec = PETSc.Vec().create(comm=COMM)
vec.setSizes(0)
vec.setFromOptions()
del vec
if 'mat' in args:
mat = PETSc.Mat().create(comm=COMM)
mat.setSizes([0, 0])
mat.setFromOptions()
del mat
if 'ksp' in args:
ksp = PETSc.KSP().create(comm=COMM)
ksp.setFromOptions()
del ksp
if 'pc' in args:
pc = PETSc.PC().create(comm=COMM)
pc.setFromOptions()
del pc
if 'snes' in args:
snes = PETSc.SNES().create(comm=COMM)
snes.setFromOptions()
del snes
if 'ts' in args:
ts = PETSc.TS().create(comm=COMM)
ts.setFromOptions()
del ts
if 'da' in args:
da = PETSc.DA().create(comm=COMM)
da.setFromOptions()
del da
def nested_solve():
"""Nested version"""
Jmat = create_matrix_nest(J)
assert Jmat.getType() == "nest"
Fvec = create_vector_nest(F)
assert Fvec.getType() == "nest"
snes = PETSc.SNES().create(MPI.COMM_WORLD)
snes.setTolerances(rtol=1.0e-15, max_it=10)
nested_IS = Jmat.getNestISs()
snes.getKSP().setType("gmres")
snes.getKSP().setTolerances(rtol=1e-12)
snes.getKSP().getPC().setType("fieldsplit")
snes.getKSP().getPC().setFieldSplitIS(["u", nested_IS[0][0]],
["p", nested_IS[1][1]])
ksp_u, ksp_p = snes.getKSP().getPC().getFieldSplitSubKSP()
ksp_u.setType("preonly")
ksp_u.getPC().setType('lu')
ksp_p.setType("preonly")
ksp_p.getPC().setType('lu')
problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs)
snes.setFunction(problem.F_nest, Fvec)
snes.setJacobian(problem.J_nest, J=Jmat, P=None)
u.interpolate(initial_guess_u)
p.interpolate(initial_guess_p)
x = create_vector_nest(F)
assert x.getType() == "nest"
for x_soln_pair in zip(x.getNestSubVecs(), (u, p)):
x_sub, soln_sub = x_soln_pair
soln_sub.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
soln_sub.vector.copy(result=x_sub)
x_sub.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
snes.solve(None, x)
assert snes.getKSP().getConvergedReason() > 0
assert snes.getConvergedReason() > 0
return x.norm()
def test_nonlinear_pde_snes():
"""Test Newton solver for a simple nonlinear PDE"""
# Create mesh and function space
mesh = create_unit_square(MPI.COMM_WORLD, 12, 15)
V = FunctionSpace(mesh, ("Lagrange", 1))
u = Function(V)
v = TestFunction(V)
F = inner(5.0, v) * dx - ufl.sqrt(u * u) * inner(
grad(u), grad(v)) * dx - inner(u, v) * dx
u_bc = Function(V)
u_bc.x.array[:] = 1.0
bc = dirichletbc(
u_bc,
locate_dofs_geometrical(
V, lambda x: np.logical_or(np.isclose(x[0], 0.0),
np.isclose(x[0], 1.0))))
# Create nonlinear problem
problem = NonlinearPDE_SNESProblem(F, u, bc)
u.x.array[:] = 0.9
b = la.create_petsc_vector(V.dofmap.index_map, V.dofmap.index_map_bs)
J = create_matrix(problem.a)
# Create Newton solver and solve
snes = PETSc.SNES().create()
snes.setFunction(problem.F, b)
snes.setJacobian(problem.J, J)
snes.setTolerances(rtol=1.0e-9, max_it=10)
snes.getKSP().setType("preonly")
snes.getKSP().setTolerances(rtol=1.0e-9)
snes.getKSP().getPC().setType("lu")
snes.solve(None, u.vector)
assert snes.getConvergedReason() > 0
assert snes.getIterationNumber() < 6
# Modify boundary condition and solve again
u_bc.x.array[:] = 0.6
snes.solve(None, u.vector)
assert snes.getConvergedReason() > 0
assert snes.getIterationNumber() < 6
def create(use_multigrid=False, use_newton=True):
snes = PETSc.SNES().create()
options = PETSc.Options()
options.clear()
if use_multigrid:
options.setValue('pc_type', 'gamg')
options.setValue('pc_gamg_reuse_interpolation', 'True')
else:
options.setValue('pc_type', 'ilu')
options.setValue('ksp_type', 'gmres')
if use_newton:
options.setValue('snes_type', 'newtonls')
else:
options.setValue('snes_type', 'ksponly')
options.setValue('ksp_atol', 1e-7)
snes.setFromOptions()
return snes
def cavity_flow2D(nx, ny, lidvelocity, grashof, prandtl):
# create application context
# and PETSc nonlinear solver
snes = PETSc.SNES().create()
da = PETSc.DMDA().create([nx,ny],dof=4, stencil_width=1, stencil_type='star')
# set up solution vector
F = da.createGlobalVec()
snes.setFunction(CavityFlow2D.formFunction, F,
args=(da, lidvelocity, prandtl, grashof))
x = da.createGlobalVec()
CavityFlow2D.formInitGuess(x, da, lidvelocity, prandtl, grashof)
snes.setDM(da)
snes.setFromOptions()
# solve the nonlinear problem
snes.solve(None, x)
return x
def test_nonlinear_pde_snes():
"""Test Newton solver for a simple nonlinear PDE"""
# Create mesh and function space
mesh = dolfin.generation.UnitSquareMesh(dolfin.MPI.comm_world, 12, 15)
V = dolfin.function.FunctionSpace(mesh, ("Lagrange", 1))
u = dolfin.function.Function(V)
v = function.TestFunction(V)
F = inner(2.0, v) * dx - ufl.sqrt(u * u) * inner(
grad(u), grad(v)) * dx - inner(u, v) * dx
def boundary(x):
"""Define Dirichlet boundary (x = 0 or x = 1)."""
return np.logical_or(x[:, 0] < 1.0e-8, x[:, 0] > 1.0 - 1.0e-8)
u_bc = function.Function(V)
u_bc.vector().set(1.0)
u_bc.vector().update_ghosts()
bc = fem.DirichletBC(V, u_bc, boundary)
# Create nonlinear problem
problem = NonlinearPDE_SNESProblem(F, u, bc)
u.vector().set(0.9)
u.vector().update_ghosts()
b = dolfin.cpp.la.PETScVector(V.dofmap().index_map())
J = dolfin.cpp.fem.init_matrix(problem.a_comp._cpp_object)
# Create Newton solver and solve
snes = PETSc.SNES().create()
snes.setFunction(problem.F, b.vec())
snes.setJacobian(problem.J, J.mat())
snes.setTolerances(rtol=1.0e-9, max_it=10)
snes.setFromOptions()
snes.getKSP().setTolerances(rtol=1.0e-9)
snes.solve(None, u.vector().vec())
assert snes.getConvergedReason() > 0
assert snes.getIterationNumber() < 6
def solver_setup(self):
# Create nonlinear solver
snes = PETSc.SNES().create(self.comm)
# Set options
snes.setOptionsPrefix(self.prefix)
self.set_petsc_options()
snes.setFunction(self.F, self.b)
snes.setJacobian(self.J, self.a)
# We set the bound (Note: they are passed as reference and not as values)
if self.monitor is not None:
snes.setMonitor(self.monitor)
if self.bounds is not None:
snes.setVariableBounds(self.lb.vector, self.ub.vector)
snes.setFromOptions()
return snes
def _setup_snes(self, pressure_mesh, residual_size):
# Creates the Jacobian matrix structure.
j_structure = _calculate_jacobian_mask(pressure_mesh.nx, pressure_mesh.ny, 3)
logger.info("Jacobian NNZ=%s" % (j_structure.nnz,))
csr = (j_structure.indptr, j_structure.indices, j_structure.data)
self._petsc_jacobian = PETSc.Mat().createAIJWithArrays(j_structure.shape, csr)
self._petsc_jacobian.assemble(assembly=self._petsc_jacobian.AssemblyType.FINAL_ASSEMBLY)
self._comm = PETSc.COMM_WORLD
self._dm = PETSc.DMShell().create(comm=self._comm)
self._dm.setMatrix(self._petsc_jacobian)
# residual vector
self._r = PETSc.Vec().createSeq(residual_size)
self._snes = PETSc.SNES().create(comm=self._comm)
self._snes.setFunction(self.residual_function_for_petsc, self._r)
self._snes.setDM(self._dm)
self._snes.setConvergenceHistory()
self._snes.setFromOptions()
self._snes.setUseFD(True)
self._snes.setMonitor(self._solver_monitor)
self._snes.ksp.setMonitor(self._linear_solver_monitor)
self._snes.setTolerances(rtol=1e-4, atol=1e-4, stol=1e-4, max_it=50)
dm = PETSc.DMDA().create(dim=3, sizes = (M,N,P), proc_sizes=(m,n,p),
boundary_type=(bx,by,bz), stencil_type=stype,
stencil_width = 1, dof = 1, comm = comm, setup = False)
dm.setFromOptions()
dm.setUp()
# steady state sine-Gordon (or NLS?!?) equation...
# prepare the g(x,y) term
mass = OptDB.getScalar("mass", 1.0)
sineGordon = sineGordon(dm, {"dx":0.1, "dy":0.1e+1, "dz":0.1e+1}, mass)
# prepare the initial conditions
rhs = dm.createGlobalVector()
# go do fun things with sine-Gordon
# set up the SNES context
snes = PETSc.SNES().create()
snes.setDM(dm)
snes.setFunction(sineGordon.rhs, rhs)
snes.setMonitor(sineGordon.monitor)
# check the interplay of -snes_mf, -snes_fd, and nothing at all!
# PETSc has a complicated defaults system, so we deal with it here
# Normally you do not need to do this as you are only likely to use one or the other
# option but in this example we want them all.
if (OptDB.hasName("snes_mf")):
mf=OptDB.getBool("snes_mf")
else:
mf=None
if (OptDB.hasName("snes_fd")):
fd=OptDB.getBool("snes_fd")
else:
def test_assembly_solve_block():
"""Solve a two-field nonlinear diffusion like problem with block matrix
approaches and test that solution is the same.
"""
mesh = dolfinx.generation.UnitSquareMesh(dolfinx.MPI.comm_world, 12, 11)
p = 1
P = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), p)
V0 = dolfinx.function.FunctionSpace(mesh, P)
V1 = V0.clone()
def bc_val_0(x):
return x[0]**2 + x[1]**2
def bc_val_1(x):
return numpy.sin(x[0]) * numpy.cos(x[1])
def initial_guess_u(x):
return numpy.sin(x[0]) * numpy.sin(x[1])
def initial_guess_p(x):
return -x[0]**2 - x[1]**3
def boundary(x):
return numpy.logical_or(x[0] < 1.0e-6, x[0] > 1.0 - 1.0e-6)
facetdim = mesh.topology.dim - 1
mf = dolfinx.MeshFunction("size_t", mesh, facetdim, 0)
mf.mark(boundary, 1)
bndry_facets = numpy.where(mf.values == 1)[0]
u_bc0 = dolfinx.function.Function(V0)
u_bc0.interpolate(bc_val_0)
u_bc1 = dolfinx.function.Function(V1)
u_bc1.interpolate(bc_val_1)
bdofs0 = dolfinx.fem.locate_dofs_topological(V0, facetdim, bndry_facets)
bdofs1 = dolfinx.fem.locate_dofs_topological(V1, facetdim, bndry_facets)
bcs = [
dolfinx.fem.dirichletbc.DirichletBC(u_bc0, bdofs0),
dolfinx.fem.dirichletbc.DirichletBC(u_bc1, bdofs1)
]
# Block and Nest variational problem
u, p = dolfinx.function.Function(V0), dolfinx.function.Function(V1)
du, dp = ufl.TrialFunction(V0), ufl.TrialFunction(V1)
v, q = ufl.TestFunction(V0), ufl.TestFunction(V1)
f = 1.0
g = -3.0
F = [
inner((u**2 + 1) * ufl.grad(u), ufl.grad(v)) * dx - inner(f, v) * dx,
inner((p**2 + 1) * ufl.grad(p), ufl.grad(q)) * dx - inner(g, q) * dx
]
J = [[derivative(F[0], u, du),
derivative(F[0], p, dp)],
[derivative(F[1], u, du),
derivative(F[1], p, dp)]]
# -- Blocked version
Jmat0 = dolfinx.fem.create_matrix_block(J)
Fvec0 = dolfinx.fem.create_vector_block(F)
snes = PETSc.SNES().create(dolfinx.MPI.comm_world)
snes.setTolerances(rtol=1.0e-15, max_it=10)
snes.getKSP().setType("preonly")
snes.getKSP().getPC().setType("lu")
snes.getKSP().getPC().setFactorSolverType("mumps")
problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs)
snes.setFunction(problem.F_block, Fvec0)
snes.setJacobian(problem.J_block, J=Jmat0, P=None)
u.interpolate(initial_guess_u)
p.interpolate(initial_guess_p)
x0 = dolfinx.fem.create_vector_block(F)
dolfinx.cpp.la.scatter_local_vectors(
x0, [u.vector.array_r, p.vector.array_r],
[u.function_space.dofmap.index_map, p.function_space.dofmap.index_map])
x0.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
snes.solve(None, x0)
assert snes.getKSP().getConvergedReason() > 0
assert snes.getConvergedReason() > 0
J0norm = Jmat0.norm()
F0norm = Fvec0.norm()
x0norm = x0.norm()
# -- Nested (MatNest)
Jmat1 = dolfinx.fem.create_matrix_nest(J)
Fvec1 = dolfinx.fem.create_vector_nest(F)
snes = PETSc.SNES().create(dolfinx.MPI.comm_world)
snes.setTolerances(rtol=1.0e-15, max_it=10)
nested_IS = Jmat1.getNestISs()
snes.getKSP().setType("fgmres")
snes.getKSP().setTolerances(rtol=1e-12)
snes.getKSP().getPC().setType("fieldsplit")
snes.getKSP().getPC().setFieldSplitIS(["u", nested_IS[0][0]],
["p", nested_IS[1][1]])
ksp_u, ksp_p = snes.getKSP().getPC().getFieldSplitSubKSP()
ksp_u.setType("preonly")
ksp_u.getPC().setType('lu')
ksp_u.getPC().setFactorSolverType('mumps')
ksp_p.setType("preonly")
ksp_p.getPC().setType('lu')
ksp_p.getPC().setFactorSolverType('mumps')
problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs)
snes.setFunction(problem.F_nest, Fvec1)
snes.setJacobian(problem.J_nest, J=Jmat1, P=None)
u.interpolate(initial_guess_u)
p.interpolate(initial_guess_p)
x1 = dolfinx.fem.create_vector_nest(F)
for x1_soln_pair in zip(x1.getNestSubVecs(), (u, p)):
x1_sub, soln_sub = x1_soln_pair
soln_sub.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
soln_sub.vector.copy(result=x1_sub)
x1_sub.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
snes.solve(None, x1)
assert snes.getKSP().getConvergedReason() > 0
assert snes.getConvergedReason() > 0
assert x1.getType() == "nest"
assert Jmat1.getType() == "nest"
assert Fvec1.getType() == "nest"
J1norm = nest_matrix_norm(Jmat1)
F1norm = Fvec1.norm()
x1norm = x1.norm()
assert J1norm == pytest.approx(J0norm, 1.0e-12)
assert F1norm == pytest.approx(F0norm, 1.0e-12)
assert x1norm == pytest.approx(x0norm, 1.0e-12)
# -- Monolithic version
E = P * P
W = dolfinx.function.FunctionSpace(mesh, E)
U = dolfinx.function.Function(W)
dU = ufl.TrialFunction(W)
u0, u1 = ufl.split(U)
v0, v1 = ufl.TestFunctions(W)
F = inner((u0**2 + 1) * ufl.grad(u0), ufl.grad(v0)) * dx \
+ inner((u1**2 + 1) * ufl.grad(u1), ufl.grad(v1)) * dx \
- inner(f, v0) * ufl.dx - inner(g, v1) * dx
J = derivative(F, U, dU)
u0_bc = dolfinx.function.Function(V0)
u0_bc.interpolate(bc_val_0)
u1_bc = dolfinx.function.Function(V1)
u1_bc.interpolate(bc_val_1)
bdofsW0_V0 = dolfinx.fem.locate_dofs_topological((W.sub(0), V0), facetdim,
bndry_facets)
bdofsW1_V1 = dolfinx.fem.locate_dofs_topological((W.sub(1), V1), facetdim,
bndry_facets)
bcs = [
dolfinx.fem.dirichletbc.DirichletBC(u0_bc, bdofsW0_V0, W.sub(0)),
dolfinx.fem.dirichletbc.DirichletBC(u1_bc, bdofsW1_V1, W.sub(1))
]
Jmat2 = dolfinx.fem.create_matrix(J)
Fvec2 = dolfinx.fem.create_vector(F)
snes = PETSc.SNES().create(dolfinx.MPI.comm_world)
snes.setTolerances(rtol=1.0e-15, max_it=10)
snes.getKSP().setType("preonly")
snes.getKSP().getPC().setType("lu")
snes.getKSP().getPC().setFactorSolverType("mumps")
problem = NonlinearPDE_SNESProblem(F, J, U, bcs)
snes.setFunction(problem.F_mono, Fvec2)
snes.setJacobian(problem.J_mono, J=Jmat2, P=None)
U.interpolate(lambda x: numpy.row_stack(
(initial_guess_u(x), initial_guess_p(x))))
x2 = dolfinx.fem.create_vector(F)
x2.array = U.vector.array_r
snes.solve(None, x2)
assert snes.getKSP().getConvergedReason() > 0
assert snes.getConvergedReason() > 0
J2norm = Jmat2.norm()
F2norm = Fvec2.norm()
x2norm = x2.norm()
assert J2norm == pytest.approx(J0norm, 1.0e-12)
assert F2norm == pytest.approx(F0norm, 1.0e-12)
assert x2norm == pytest.approx(x0norm, 1.0e-12)
def setUp(self):
snes = PETSc.SNES()
snes.create(PETSc.COMM_SELF)
if self.SNES_TYPE:
snes.setType(self.SNES_TYPE)
self.snes = snes
def __init__(self,
problem_params,
dtype_u=petsc_data,
dtype_f=rhs_2comp_petsc_data):
"""
Initialization routine
Args:
problem_params: custom parameters for the example
dtype_u: PETSc data type (will be passed to parent class)
dtype_f: PETSc data type with 2 components (will be passed to parent class)
"""
# define the Dirichlet boundary
if 'comm' not in problem_params:
problem_params['comm'] = PETSc.COMM_WORLD
if 'sol_tol' not in problem_params:
problem_params['sol_tol'] = 1E-10
if 'sol_maxiter' not in problem_params:
problem_params['sol_maxiter'] = None
# these parameters will be used later, so assert their existence
essential_keys = ['nvars', 'Du', 'Dv', 'A', 'B']
for key in essential_keys:
if key not in problem_params:
msg = 'need %s to instantiate problem, only got %s' % (
key, str(problem_params.keys()))
raise ParameterError(msg)
# create DMDA object which will be used for all grid operations (boundary_type=3 -> periodic BC)
da = PETSc.DMDA().create(
[problem_params['nvars'][0], problem_params['nvars'][1]],
dof=2,
boundary_type=3,
stencil_width=1,
comm=problem_params['comm'])
# invoke super init, passing number of dofs, dtype_u and dtype_f
super(petsc_grayscott_multiimplicit,
self).__init__(init=da,
dtype_u=dtype_u,
dtype_f=dtype_f,
params=problem_params)
# compute dx, dy and get local ranges
self.dx = 100.0 / (self.params.nvars[0])
self.dy = 100.0 / (self.params.nvars[1])
(self.xs, self.xe), (self.ys, self.ye) = self.init.getRanges()
# compute discretization matrix A and identity
self.A = self.__get_A()
self.Id = self.__get_Id()
self.localX = self.init.createLocalVec()
# setup linear solver
self.ksp = PETSc.KSP()
self.ksp.create(comm=self.params.comm)
self.ksp.setType('cg')
pc = self.ksp.getPC()
pc.setType('none')
self.ksp.setInitialGuessNonzero(True)
self.ksp.setFromOptions()
self.ksp.setTolerances(rtol=self.params.lsol_tol,
atol=self.params.lsol_tol,
max_it=self.params.lsol_maxiter)
self.ksp_itercount = 0
self.ksp_ncalls = 0
# setup nonlinear solver
self.snes = PETSc.SNES()
self.snes.create(comm=self.params.comm)
# self.snes.getKSP().setType('cg')
# self.snes.setType('ngmres')
self.snes.setFromOptions()
self.snes.setTolerances(rtol=self.params.nlsol_tol,
atol=self.params.nlsol_tol,
stol=self.params.nlsol_tol,
max_it=self.params.nlsol_maxiter)
self.snes_itercount = 0
self.snes_ncalls = 0
def __init__(self, problem_params, dtype_u=petsc_data, dtype_f=rhs_2comp_petsc_data):
"""
Initialization routine
Args:
problem_params: custom parameters for the example
dtype_u: PETSc data type (will be passed to parent class)
dtype_f: PETSc data type with 2 components (will be passed to parent class)
"""
# define optional parameters
if 'comm' not in problem_params:
problem_params['comm'] = PETSc.COMM_WORLD
if 'lsol_tol' not in problem_params:
problem_params['lsol_tol'] = 1E-10
if 'nlsol_tol' not in problem_params:
problem_params['nlsol_tol'] = 1E-10
if 'lsol_maxiter' not in problem_params:
problem_params['lsol_maxiter'] = None
if 'nlsol_maxiter' not in problem_params:
problem_params['nlsol_maxiter'] = None
# these parameters will be used later, so assert their existence
essential_keys = ['nvars', 'lambda0', 'nu', 'interval']
for key in essential_keys:
if key not in problem_params:
msg = 'need %s to instantiate problem, only got %s' % (key, str(problem_params.keys()))
raise ParameterError(msg)
# create DMDA object which will be used for all grid operations
da = PETSc.DMDA().create([problem_params['nvars']], dof=1, stencil_width=1, comm=problem_params['comm'])
# invoke super init, passing number of dofs, dtype_u and dtype_f
super(petsc_fisher_multiimplicit, self).__init__(init=da, dtype_u=dtype_u, dtype_f=dtype_f,
params=problem_params)
# compute dx and get local ranges
self.dx = (self.params.interval[1] - self.params.interval[0]) / (self.params.nvars - 1)
(self.xs, self.xe) = self.init.getRanges()[0]
# compute discretization matrix A and identity
self.A = self.__get_A()
self.localX = self.init.createLocalVec()
# setup linear solver
self.ksp = PETSc.KSP()
self.ksp.create(comm=self.params.comm)
self.ksp.setType('cg')
pc = self.ksp.getPC()
pc.setType('ilu')
self.ksp.setInitialGuessNonzero(True)
self.ksp.setFromOptions()
self.ksp.setTolerances(rtol=self.params.lsol_tol, atol=self.params.lsol_tol,
max_it=self.params.lsol_maxiter)
self.ksp_itercount = 0
self.ksp_ncalls = 0
# setup nonlinear solver
self.snes = PETSc.SNES()
self.snes.create(comm=self.params.comm)
if self.params.nlsol_maxiter <= 1:
self.snes.setType('ksponly')
self.snes.getKSP().setType('cg')
pc = self.snes.getKSP().getPC()
pc.setType('ilu')
# self.snes.setType('ngmres')
self.snes.setFromOptions()
self.snes.setTolerances(rtol=self.params.nlsol_tol, atol=self.params.nlsol_tol, stol=self.params.nlsol_tol,
max_it=self.params.nlsol_maxiter)
self.snes_itercount = 0
self.snes_ncalls = 0
self.F = self.init.createGlobalVec()
self.J = self.init.createMatrix()
def __init__(self, cfgfile):
'''
Constructor
'''
# stencil = 1
stencil = 2
# load run config file
cfg = Config(cfgfile)
# set some PETSc options
OptDB = PETSc.Options()
# OptDB.setValue('snes_lag_preconditioner', 5)
OptDB.setValue('snes_atol', cfg['solver']['petsc_residual'])
OptDB.setValue('snes_rtol', 1E-16)
OptDB.setValue('snes_stol', 1E-18)
OptDB.setValue('snes_max_it', 10)
OptDB.setValue('ksp_atol', cfg['solver']['petsc_residual'] * 1E-1)
OptDB.setValue('ksp_rtol', 1E-10)
OptDB.setValue('ksp_max_it', 10)
# OptDB.setValue('ksp_convergence_test', 'skip')
OptDB.setValue('snes_monitor', '')
OptDB.setValue('ksp_monitor', '')
# timestep setup
self.ht = cfg['grid']['ht'] # timestep size
self.nt = cfg['grid']['nt'] # number of timesteps
self.nsave = cfg['io']['nsave'] # save only every nsave'th timestep
# grid setup
nx = cfg['grid']['nx'] # number of points in x
ny = cfg['grid']['ny'] # number of points in y
Lx = cfg['grid']['Lx'] # spatial domain in x
x1 = cfg['grid']['x1'] #
x2 = cfg['grid']['x2'] #
Ly = cfg['grid']['Ly'] # spatial domain in y
y1 = cfg['grid']['y1'] #
y2 = cfg['grid']['y2'] #
self.nx = nx
self.ny = ny
if x1 != x2:
Lx = x2-x1
else:
x1 = 0.0
x2 = Lx
if y1 != y2:
Ly = y2-y1
else:
y1 = 0.0
y2 = Ly
self.hx = Lx / nx # gridstep size in x
self.hy = Ly / ny # gridstep size in y
if PETSc.COMM_WORLD.getRank() == 0:
print()
print("nt = %i" % (self.nt))
print("nx = %i" % (self.nx))
print("ny = %i" % (self.ny))
print()
print("ht = %e" % (self.ht))
print("hx = %e" % (self.hx))
print("hy = %e" % (self.hy))
print()
print("Lx = %e" % (Lx))
print("Ly = %e" % (Ly))
print()
self.time = PETSc.Vec().createMPI(1, PETSc.DECIDE, comm=PETSc.COMM_WORLD)
self.time.setName('t')
if PETSc.COMM_WORLD.getRank() == 0:
self.time.setValue(0, 0.0)
# create DA with single dof
self.da1 = PETSc.DA().create(dim=2, dof=1,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=stencil,
stencil_type='box')
# create DA (dof = 4 for Bx, By, Vx, Vy)
self.da4 = PETSc.DA().create(dim=2, dof=4,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=stencil,
stencil_type='box')
# create DA (dof = 5 for Bx, By, Vx, Vy, P)
self.da5 = PETSc.DA().create(dim=2, dof=5,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=stencil,
stencil_type='box')
# create DA for x grid
self.dax = PETSc.DA().create(dim=1, dof=1,
sizes=[nx],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# create DA for y grid
self.day = PETSc.DA().create(dim=1, dof=1,
sizes=[ny],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# initialise grid
self.da1.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.da4.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.da5.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.dax.setUniformCoordinates(xmin=x1, xmax=x2)
self.day.setUniformCoordinates(xmin=y1, xmax=y2)
# create solution and RHS vector
self.f = self.da5.createGlobalVec()
self.x = self.da5.createGlobalVec()
self.b = self.da5.createGlobalVec()
# create global RK4 vectors
self.Y = self.da5.createGlobalVec()
self.X0 = self.da5.createGlobalVec()
self.X1 = self.da5.createGlobalVec()
self.X2 = self.da5.createGlobalVec()
self.X3 = self.da5.createGlobalVec()
self.X4 = self.da5.createGlobalVec()
# create local RK4 vectors
self.localX0 = self.da5.createLocalVec()
self.localX1 = self.da5.createLocalVec()
self.localX2 = self.da5.createLocalVec()
self.localX3 = self.da5.createLocalVec()
self.localX4 = self.da5.createLocalVec()
# self.localP = self.da1.createLocalVec()
# create vectors for magnetic and velocity field
self.Bx = self.da1.createGlobalVec()
self.By = self.da1.createGlobalVec()
self.Vx = self.da1.createGlobalVec()
self.Vy = self.da1.createGlobalVec()
self.P = self.da1.createGlobalVec()
# create local vectors for initialisation of pressure
self.localBx = self.da1.createLocalVec()
self.localBy = self.da1.createLocalVec()
self.localVx = self.da1.createLocalVec()
self.localVy = self.da1.createLocalVec()
# set variable names
self.Bx.setName('Bx')
self.By.setName('By')
self.Vx.setName('Vx')
self.Vy.setName('Vy')
self.P.setName('P')
# create Matrix object
self.petsc_matrix = PETScMatrix (self.da1, self.da5, nx, ny, self.ht, self.hx, self.hy)
self.petsc_jacobian = PETScJacobian(self.da1, self.da5, nx, ny, self.ht, self.hx, self.hy)
self.petsc_function = PETScFunction(self.da1, self.da5, nx, ny, self.ht, self.hx, self.hy)
# self.petsc_jacobian_4d = PETSc_MHD_NL_Jacobian_Matrix.PETScJacobian(self.da1, self.da5, nx, ny, self.ht, self.hx, self.hy)
# initialise matrix
self.A = self.da5.createMat()
self.A.setOption(self.A.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.A.setUp()
# create jacobian
self.J = self.da5.createMat()
self.J.setOption(self.J.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.J.setUp()
# create nonlinear solver
self.snes = PETSc.SNES().create()
self.snes.setFunction(self.petsc_function.snes_mult, self.f)
self.snes.setJacobian(self.updateJacobian, self.J)
self.snes.setFromOptions()
self.snes.getKSP().setType('preonly')
# self.snes.getKSP().setType('gmres')
self.snes.getKSP().getPC().setType('lu')
# self.snes.getKSP().getPC().setFactorSolverPackage('superlu_dist')
self.snes.getKSP().getPC().setFactorSolverPackage('mumps')
self.ksp = None
# set initial data
(xs, xe), (ys, ye) = self.da1.getRanges()
coords = self.da1.getCoordinatesLocal()
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
if cfg['initial_data']['magnetic_python'] != None:
init_data = __import__("runs." + cfg['initial_data']['magnetic_python'], globals(), locals(), ['magnetic_x', 'magnetic_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Bx_arr[i,j] = init_data.magnetic_x(coords[i,j][0], coords[i,j][1] + 0.5 * self.hy, Lx, Ly)
By_arr[i,j] = init_data.magnetic_y(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1], Lx, Ly)
else:
Bx_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
By_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
if cfg['initial_data']['velocity_python'] != None:
init_data = __import__("runs." + cfg['initial_data']['velocity_python'], globals(), locals(), ['velocity_x', 'velocity_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Vx_arr[i,j] = init_data.velocity_x(coords[i,j][0], coords[i,j][1] + 0.5 * self.hy, Lx, Ly)
Vy_arr[i,j] = init_data.velocity_y(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1], Lx, Ly)
else:
Vx_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
Vy_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
if cfg['initial_data']['pressure_python'] != None:
init_data = __import__("runs." + cfg['initial_data']['pressure_python'], globals(), locals(), ['pressure', ''], 0)
x_arr = self.da5.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 0] = Vx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 1] = Vy_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 2] = Bx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 3] = By_arr[xs:xe, ys:ye]
self.da1.globalToLocal(self.Bx, self.localBx)
self.da1.globalToLocal(self.By, self.localBy)
self.da1.globalToLocal(self.Vx, self.localVx)
self.da1.globalToLocal(self.Vy, self.localVy)
Bx_arr = self.da1.getVecArray(self.localBx)
By_arr = self.da1.getVecArray(self.localBy)
Vx_arr = self.da1.getVecArray(self.localVx)
Vy_arr = self.da1.getVecArray(self.localVy)
P_arr = self.da1.getVecArray(self.P)
for i in range(xs, xe):
for j in range(ys, ye):
P_arr[i,j] = init_data.pressure(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1] + 0.5 * self.hy, Lx, Ly)
# P_arr[i,j] = init_data.pressure(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1] + 0.5 * self.hy, Lx, Ly) \
# + 0.5 * (0.25 * (Bx_arr[i,j] + Bx_arr[i+1,j])**2 + 0.25 * (By_arr[i,j] + By_arr[i,j+1])**2)
# P_arr[i,j] = init_data.pressure(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1] + 0.5 * self.hy, Lx, Ly) \
# + 0.5 * (0.25 * (Vx_arr[i,j] + Vx_arr[i+1,j])**2 + 0.25 * (Vy_arr[i,j] + Vy_arr[i,j+1])**2)
# P_arr[i,j] = init_data.pressure(coords[i,j][0] + 0.5 * self.hx, coords[i,j][1] + 0.5 * self.hy, Lx, Ly) \
# + 0.5 * (0.25 * (Vx_arr[i,j] + Vx_arr[i+1,j])**2 + 0.25 * (Vy_arr[i,j] + Vy_arr[i,j+1])**2) \
# - 1.0 * (0.25 * (Bx_arr[i,j] + Bx_arr[i+1,j])**2 + 0.25 * (By_arr[i,j] + By_arr[i,j+1])**2)
# copy distribution function to solution vector
x_arr = self.da5.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 4] = P_arr [xs:xe, ys:ye]
# update solution history
self.petsc_matrix.update_history(self.x)
self.petsc_jacobian.update_history(self.x)
self.petsc_function.update_history(self.x)
# create HDF5 output file
self.hdf5_viewer = PETSc.ViewerHDF5().create(cfg['io']['hdf5_output'],
mode=PETSc.Viewer.Mode.WRITE,
comm=PETSc.COMM_WORLD)
self.hdf5_viewer.pushGroup("/")
# write grid data to hdf5 file
coords_x = self.dax.getCoordinates()
coords_y = self.day.getCoordinates()
coords_x.setName('x')
coords_y.setName('y')
self.hdf5_viewer(coords_x)
self.hdf5_viewer(coords_y)
# write initial data to hdf5 file
self.hdf5_viewer.setTimestep(0)
self.save_hdf5_vectors()
def run(self):
OptDB = PETSc.Options()
OptDB.setValue('ksp_monitor', '')
OptDB.setValue('snes_monitor', '')
# OptDB.setValue('snes_lag_preconditioner', 3)
# OptDB.setValue('snes_ls', 'basic')
# initialise matrix
self.A = self.da2.createMat()
self.A.setOption(self.A.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.A.setUp()
self.A.setNullSpace(self.nullspace)
# initialise Jacobian
self.J = self.da2.createMat()
self.J.setOption(self.J.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.J.setUp()
self.J.setNullSpace(self.nullspace)
# create Jacobian, Function, and linear Matrix objects
# self.petsc_jacobian_mf = PETScJacobianMatrixFree(self.da1, self.da2, self.dax,
# self.h0, self.vGrid,
# self.nx, self.nv, self.ht, self.hx, self.hv,
# self.charge, coll_freq=self.coll_freq)
self.petsc_solver = PETScSolver(self.da1,
self.da2,
self.dax,
self.h0,
self.vGrid,
self.nx,
self.nv,
self.ht,
self.hx,
self.hv,
self.charge,
coll_freq=self.coll_freq)
# self.petsc_function = PETScFunction(self.da1, self.da2, self.dax,
# self.h0, self.vGrid,
# self.nx, self.nv, self.ht, self.hx, self.hv,
# self.charge, coll_freq=self.coll_freq)
#
# self.petsc_matrix = PETScMatrix(self.da1, self.da2, self.dax,
# self.h0, self.vGrid,
# self.nx, self.nv, self.ht, self.hx, self.hv,
# self.charge)#, coll_freq=self.coll_freq)
# self.poisson_ksp = PETSc.KSP().create()
# self.poisson_ksp.setFromOptions()
# self.poisson_ksp.setOperators(self.poisson_A)
# self.poisson_ksp.setType('cg')
# self.poisson_ksp.getPC().setType('none')
# # self.poisson_ksp.setType('preonly')
# # self.poisson_ksp.getPC().setType('lu')
# # self.poisson_ksp.getPC().setFactorSolverPackage(self.solver_package)
# copy external potential
self.petsc_solver.update_external(self.p_ext)
# self.petsc_matrix.update_external(self.p_ext)
# update solution history
self.petsc_solver.update_history(self.x)
# self.petsc_matrix.update_history(self.f, self.h1, self.p, self.n, self.nu, self.ne, self.u, self.e, self.a)
# initialise matrixfree Jacobian
# self.Jmf = PETSc.Mat().createPython([self.x.getSizes(), self.b.getSizes()],
# context=self.petsc_jacobian_mf,
# comm=PETSc.COMM_WORLD)
# self.Jmf.setUp()
# # create linear solver
# self.snes_linear = PETSc.SNES().create()
# self.snes_linear.setType('ksponly')
# self.snes_linear.setFunction(self.petsc_matrix.snes_mult, self.b)
# self.snes_linear.setJacobian(self.updateMatrix, self.A)
# self.snes_linear.setFromOptions()
# # self.snes_linear.getKSP().setType('gmres')
# # self.snes_linear.getKSP().getPC().setType('bjacobi')
# # self.snes_linear.getKSP().getPC().setFactorSolverPackage(self.solver_package)
# self.snes_linear.getKSP().setType('preonly')
# self.snes_linear.getKSP().getPC().setType('lu')
# self.snes_linear.getKSP().getPC().setFactorSolverPackage(self.solver_package)
# create nonlinear solver
self.snes = PETSc.SNES().create()
self.snes.setFunction(self.petsc_solver.function_snes_mult, self.b)
# self.snes.setJacobian(self.updateJacobian, self.Jmf, self.J)
self.snes.setJacobian(self.updateJacobian, self.J)
self.snes.setFromOptions()
# self.snes.getKSP().setType('gmres')
# self.snes.getKSP().getPC().setType('bjacobi')
self.snes.getKSP().setType('preonly')
self.snes.getKSP().getPC().setType('lu')
self.snes.getKSP().getPC().setFactorSolverPackage(self.solver_package)
# self.snes_nsp = PETSc.NullSpace().create(vectors=(self.x_nvec,))
# self.snes.getKSP().setNullSpace(self.snes_nsp)
for itime in range(1, self.nt + 1):
current_time = self.ht * itime
if PETSc.COMM_WORLD.getRank() == 0:
localtime = time.asctime(time.localtime(time.time()))
print("\nit = %4d, t = %10.4f, %s" %
(itime, current_time, localtime))
print
self.time.setValue(0, current_time)
# calculate external field and copy to matrix, jacobian and function
self.calculate_external(current_time)
# self.petsc_jacobian_mf.update_external(self.p_ext)
self.petsc_solver.update_external(self.p_ext)
# self.petsc_jacobian.update_external(self.p_ext)
# self.petsc_function.update_external(self.p_ext)
# self.petsc_matrix.update_external(self.p_ext)
self.x.copy(self.xh)
self.petsc_solver.function_mult(self.x, self.b)
prev_norm = self.b.norm()
if PETSc.COMM_WORLD.getRank() == 0:
print(
" Previous Step: funcnorm = %24.16E"
% (prev_norm))
# calculate initial guess via RK4
# self.initial_guess_rk4()
# calculate initial guess via Gear
self.initial_guess_gear(itime)
# check if residual went down
# self.petsc_function.mult(self.x, self.b)
# ig_norm = self.b.norm()
#
# if ig_norm > prev_norm:
# self.xh.copy(self.x)
# calculate initial guess via linear solver
# self.initial_guess()
# nonlinear solve
self.snes.solve(None, self.x)
# output some solver info
if PETSc.COMM_WORLD.getRank() == 0:
print(
" Nonlin Solver: %5i iterations, funcnorm = %24.16E" %
(self.snes.getIterationNumber(),
self.snes.getFunctionNorm()))
print()
if self.snes.getConvergedReason() < 0:
if PETSc.COMM_WORLD.getRank() == 0:
print()
print("Solver not converging... %i" %
(self.snes.getConvergedReason()))
print()
# if PETSc.COMM_WORLD.getRank() == 0:
# mat_viewer = PETSc.Viewer().createDraw(size=(800,800), comm=PETSc.COMM_WORLD)
# mat_viewer(self.J)
#
# print
# input('Hit any key to continue.')
# print
# update data vectors
self.copy_x_to_data()
# update history
self.petsc_solver.update_history(self.x)
# self.petsc_matrix.update_history(self.f, self.h1, self.p, self.n, self.nu, self.ne, self.u, self.e, self.a)
self.arakawa_gear.update_history(self.f, self.h1)
# save to hdf5
self.save_to_hdf5(itime)
# # some solver output
phisum = self.p.sum()
#
#
if PETSc.COMM_WORLD.getRank() == 0:
# print(" Solver")
print(" sum(phi) = %24.16E" % (phisum))
def __init__(self, cfgfile):
'''
Constructor
'''
# load run config file
cfg = Config(cfgfile)
# timestep setup
self.ht = cfg['grid']['ht'] # timestep size
self.nt = cfg['grid']['nt'] # number of timesteps
self.nsave = cfg['io']['nsave'] # save only every nsave'th timestep
# grid setup
nx = cfg['grid']['nx'] # number of points in x
ny = cfg['grid']['ny'] # number of points in y
Lx = cfg['grid']['Lx'] # spatial domain in x
x1 = cfg['grid']['x1'] #
x2 = cfg['grid']['x2'] #
Ly = cfg['grid']['Ly'] # spatial domain in y
y1 = cfg['grid']['y1'] #
y2 = cfg['grid']['y2'] #
if x1 != x2:
Lx = x2-x1
else:
x1 = 0.0
x2 = Lx
if y1 != y2:
Ly = y2-y1
else:
y1 = 0.0
y2 = Ly
self.hx = Lx / nx # gridstep size in x
self.hy = Ly / ny # gridstep size in y
self.time = PETSc.Vec().createMPI(1, PETSc.DECIDE, comm=PETSc.COMM_WORLD)
self.time.setName('t')
if PETSc.COMM_WORLD.getRank() == 0:
self.time.setValue(0, 0.0)
# set some PETSc options
OptDB = PETSc.Options()
OptDB.setValue('ksp_rtol', cfg['solver']['petsc_residual'])
# OptDB.setValue('snes_rtol', 1E-2)
# OptDB.setValue('ksp_max_it', 100)
OptDB.setValue('ksp_max_it', 200)
# OptDB.setValue('ksp_max_it', 1000)
# OptDB.setValue('ksp_max_it', 2000)
# OptDB.setValue('ksp_monitor', '')
# OptDB.setValue('log_info', '')
# OptDB.setValue('log_summary', '')
# create DA with single dof
self.da1 = PETSc.DA().create(dim=2, dof=1,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=1,
stencil_type='box')
# create DA (dof = 5 for Bx, By, Vx, Vy, P)
self.da4 = PETSc.DA().create(dim=2, dof=5,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=1,
stencil_type='box')
# create DA for x grid
self.dax = PETSc.DA().create(dim=1, dof=1,
sizes=[nx],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# create DA for y grid
self.day = PETSc.DA().create(dim=1, dof=1,
sizes=[ny],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# initialise grid
self.da1.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.da4.setUniformCoordinates(xmin=x1, xmax=x2,
ymin=y1, ymax=y2)
self.dax.setUniformCoordinates(xmin=x1, xmax=x2)
self.day.setUniformCoordinates(xmin=y1, xmax=y2)
# create solution and RHS vector
self.dx = self.da4.createGlobalVec()
self.x = self.da4.createGlobalVec()
self.b = self.da4.createGlobalVec()
self.f = self.da4.createGlobalVec()
self.Pb = self.da1.createGlobalVec()
self.localX = self.da4.createLocalVec()
# create global RK4 vectors
self.X1 = self.da4.createGlobalVec()
self.X2 = self.da4.createGlobalVec()
self.X3 = self.da4.createGlobalVec()
self.X4 = self.da4.createGlobalVec()
# create local RK4 vectors
self.localX1 = self.da4.createLocalVec()
self.localX2 = self.da4.createLocalVec()
self.localX3 = self.da4.createLocalVec()
self.localX4 = self.da4.createLocalVec()
# create vectors for magnetic and velocity field
self.Bx = self.da1.createGlobalVec()
self.By = self.da1.createGlobalVec()
self.Vx = self.da1.createGlobalVec()
self.Vy = self.da1.createGlobalVec()
self.P = self.da1.createGlobalVec()
# set variable names
self.x.setName('solver_x')
self.b.setName('solver_b')
self.Bx.setName('Bx')
self.By.setName('By')
self.Vx.setName('Vx')
self.Vy.setName('Vy')
self.P.setName('P')
# create Matrix object
self.petsc_matrix = PETScSolver (self.da1, self.da4, nx, ny, self.ht, self.hx, self.hy)
self.petsc_function = PETScFunction(self.da1, self.da4, nx, ny, self.ht, self.hx, self.hy)
self.petsc_jacobian = PETScJacobian(self.da1, self.da4, nx, ny, self.ht, self.hx, self.hy)
# create sparse matrix
self.J = PETSc.Mat().createPython([self.dx.getSizes(), self.b.getSizes()], comm=PETSc.COMM_WORLD)
self.J.setPythonContext(self.petsc_jacobian)
self.J.setUp()
# create nonlinear solver
self.snes = PETSc.SNES().create()
self.snes.setFunction(self.petsc_function.snes_mult, self.f)
self.snes.setJacobian(self.updateJacobian, self.J)
# self.snes.setUseMF()
self.snes.setFromOptions()
self.snes.getKSP().setType('gmres')
self.snes.getKSP().getPC().setType('none')
# create Preconditioner matrix and solver
self.pc_mat = PETScPreconditioner(self.da1, self.da4, self.P, nx, ny, self.ht, self.hx, self.hy)
# create sparse matrix
self.pc_A = PETSc.Mat().createPython([self.x.getSizes(), self.b.getSizes()], comm=PETSc.COMM_WORLD)
self.pc_A.setPythonContext(self.pc_mat)
self.pc_A.setUp()
# create linear solver and preconditioner
self.pc_ksp = PETSc.KSP().create()
self.pc_ksp.setFromOptions()
self.pc_ksp.setOperators(self.pc_A)
self.pc_ksp.setType(cfg['solver']['petsc_ksp_type'])
self.pc_ksp.setInitialGuessNonzero(True)
self.pc_pc = self.pc_ksp.getPC()
self.pc_pc.setType('none')
# create Poisson matrix and solver
self.poisson_mat = PETScPoissonSolver(self.da1, self.da4, self.x,
nx, ny, self.ht, self.hx, self.hy)
self.poisson_A = PETSc.Mat().createPython([self.P.getSizes(), self.Pb.getSizes()], comm=PETSc.COMM_WORLD)
self.poisson_A.setPythonContext(self.poisson_mat)
self.poisson_A.setUp()
self.poisson_ksp = PETSc.KSP().create()
self.poisson_ksp.setFromOptions()
self.poisson_ksp.setOperators(self.poisson_A)
self.poisson_ksp.setType(cfg['solver']['petsc_ksp_type'])
# self.poisson_ksp.setInitialGuessNonzero(True)
self.poisson_pc = self.poisson_ksp.getPC()
self.poisson_pc.setType('none')
# create Arakawa solver object
# self.mhd_rk4 = PETScRK4(self.da4, nx, ny, self.ht, self.hx, self.hy)
# set initial data
(xs, xe), (ys, ye) = self.da1.getRanges()
coords = self.da1.getCoordinateDA().getVecArray(self.da1.getCoordinates())
# print
# print(self.hx)
# print(coords[1,0][0] - coords[0,0][0])
# print
# print(self.hy)
# print(coords[0,1][1] - coords[0,0][1])
# print
# print(Lx)
# print(coords[-1,0][0]+self.hx)
# print
# print(Ly)
# print(coords[0,-1][1]+self.hy)
# print
x_arr = self.da4.getVecArray(self.x)
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
P_arr = self.da1.getVecArray(self.P)
if cfg['initial_data']['magnetic_python'] != None:
init_data = __import__("runs." + cfg['initial_data']['magnetic_python'], globals(), locals(), ['magnetic_x', 'magnetic_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Bx_arr[i,j] = init_data.magnetic_x(coords[i,j][0], coords[i,j][1], Lx, Ly)
By_arr[i,j] = init_data.magnetic_y(coords[i,j][0], coords[i,j][1], Lx, Ly)
else:
Bx_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
By_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
if cfg['initial_data']['velocity_python'] != None:
init_data = __import__("runs." + cfg['initial_data']['velocity_python'], globals(), locals(), ['velocity_x', 'velocity_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Vx_arr[i,j] = init_data.velocity_x(coords[i,j][0], coords[i,j][1], Lx, Ly)
Vy_arr[i,j] = init_data.velocity_y(coords[i,j][0], coords[i,j][1], Lx, Ly)
else:
Vx_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
Vy_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
if cfg['initial_data']['pressure_python'] != None:
init_data = __import__("runs." + cfg['initial_data']['pressure_python'], globals(), locals(), ['pressure', ''], 0)
for i in range(xs, xe):
for j in range(ys, ye):
P_arr[i,j] = init_data.pressure(coords[i,j][0], coords[i,j][1], Lx, Ly) #+ 0.5 * (Bx_arr[i,j]**2 + By_arr[i,j]**2)
# copy distribution function to solution vector
x_arr[xs:xe, ys:ye, 0] = Bx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 1] = By_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 2] = Vx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 3] = Vy_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 4] = P_arr [xs:xe, ys:ye]
# update solution history
self.petsc_matrix.update_history(self.x)
self.petsc_function.update_history(self.x)
self.petsc_jacobian.update_history(self.x)
# create HDF5 output file
self.hdf5_viewer = PETSc.Viewer().createHDF5(cfg['io']['hdf5_output'],
mode=PETSc.Viewer.Mode.WRITE,
comm=PETSc.COMM_WORLD)
self.hdf5_viewer.HDF5PushGroup("/")
# write grid data to hdf5 file
coords_x = self.dax.getCoordinates()
coords_y = self.day.getCoordinates()
coords_x.setName('x')
coords_y.setName('y')
self.hdf5_viewer(coords_x)
self.hdf5_viewer(coords_y)
# write initial data to hdf5 file
self.hdf5_viewer.HDF5SetTimestep(0)
self.hdf5_viewer(self.time)
# self.hdf5_viewer(self.x)
# self.hdf5_viewer(self.b)
self.hdf5_viewer(self.Bx)
self.hdf5_viewer(self.By)
self.hdf5_viewer(self.Vx)
self.hdf5_viewer(self.Vy)
self.hdf5_viewer(self.P)
def __init__(self, cfgfile, runid=None, cfg=None):
super(viVlasov1Drunscript, self).__init__(cfgfile, runid, cfg)
if PETSc.COMM_WORLD.getRank() == 0:
print("Creating solver objects.")
# create solver objects
# self.vlasov_solver = PETScVlasovSolver(
self.vlasov_solver = self.vlasov_object.PETScVlasovSolver(
self.cfg,
self.da1,
self.dax,
self.grid,
self.h0,
self.h1c,
self.h1h,
self.h2c,
self.h2h,
self.pc_int,
self.charge,
coll_freq=self.coll_freq,
coll_drag=self.coll_drag,
coll_diff=self.coll_diff)
self.vlasov_solver.set_moments(self.nc, self.uc, self.ec, self.ac,
self.nh, self.uh, self.eh, self.ah)
# initialise matrixfree Jacobian
self.Jmf.setPythonContext(self.vlasov_solver)
self.Jmf.setUp()
# create nonlinear predictor solver
self.snes = PETSc.SNES().create()
self.snes.setType('ksponly')
self.snes.setFunction(self.vlasov_solver.function_snes_mult, self.fb)
self.snes.setJacobian(self.updateVlasovJacobian, self.Jmf)
self.snes.setFromOptions()
self.snes.getKSP().setType('gmres')
self.snes.getKSP().getPC().setType('none')
# create Poisson matrix and object
self.poisson_matrix = self.dax.createMat()
self.poisson_matrix.setUp()
self.poisson_matrix.setNullSpace(self.p_nullspace)
self.poisson_solver = self.poisson_object.PETScPoissonSolver(
self.dax, self.grid.nx, self.grid.hx, self.charge)
self.poisson_solver.formMat(self.poisson_matrix)
self.poisson_mf = PETSc.Mat().createPython(
[self.pc_int.getSizes(),
self.pb.getSizes()],
context=self.poisson_solver,
comm=PETSc.COMM_WORLD)
self.poisson_mf.setUp()
# create linear Poisson solver
self.poisson_ksp = PETSc.KSP().create()
self.poisson_ksp.setFromOptions()
self.poisson_ksp.setTolerances(rtol=1E-13)
self.poisson_ksp.setOperators(self.poisson_mf, self.poisson_matrix)
self.poisson_ksp.setType('cg')
# self.poisson_ksp.setType('bcgs')
# self.poisson_ksp.setType('ibcgs')
# self.poisson_ksp.getPC().setType('hypre')
self.poisson_ksp.getPC().setType('lu')
self.poisson_ksp.getPC().setFactorSolverPackage('superlu_dist')
if PETSc.COMM_WORLD.getRank() == 0:
print("Run script initialisation done.")
print("")
def test_assembly_solve_taylor_hood_nl(mesh):
"""Assemble Stokes problem with Taylor-Hood elements and solve."""
gdim = mesh.geometry.dim
P2 = VectorFunctionSpace(mesh, ("Lagrange", 2))
P1 = FunctionSpace(mesh, ("Lagrange", 1))
def boundary0(x):
"""Define boundary x = 0"""
return np.isclose(x[0], 0.0)
def boundary1(x):
"""Define boundary x = 1"""
return np.isclose(x[0], 1.0)
def initial_guess_u(x):
u_init = np.row_stack(
(np.sin(x[0]) * np.sin(x[1]), np.cos(x[0]) * np.cos(x[1])))
if gdim == 3:
u_init = np.row_stack((u_init, np.cos(x[2])))
return u_init
def initial_guess_p(x):
return -x[0]**2 - x[1]**3
u_bc_0 = Function(P2)
u_bc_0.interpolate(
lambda x: np.row_stack(tuple(x[j] + float(j) for j in range(gdim))))
u_bc_1 = Function(P2)
u_bc_1.interpolate(
lambda x: np.row_stack(tuple(np.sin(x[j]) for j in range(gdim))))
facetdim = mesh.topology.dim - 1
bndry_facets0 = locate_entities_boundary(mesh, facetdim, boundary0)
bndry_facets1 = locate_entities_boundary(mesh, facetdim, boundary1)
bdofs0 = locate_dofs_topological(P2, facetdim, bndry_facets0)
bdofs1 = locate_dofs_topological(P2, facetdim, bndry_facets1)
bcs = [dirichletbc(u_bc_0, bdofs0), dirichletbc(u_bc_1, bdofs1)]
u, p = Function(P2), Function(P1)
du, dp = ufl.TrialFunction(P2), ufl.TrialFunction(P1)
v, q = ufl.TestFunction(P2), ufl.TestFunction(P1)
F = [
inner(ufl.grad(u), ufl.grad(v)) * dx + inner(p, ufl.div(v)) * dx,
inner(ufl.div(u), q) * dx
]
J = [[derivative(F[0], u, du),
derivative(F[0], p, dp)],
[derivative(F[1], u, du),
derivative(F[1], p, dp)]]
P = [[J[0][0], None], [None, inner(dp, q) * dx]]
F, J, P = form(F), form(J), form(P)
# -- Blocked and monolithic
Jmat0 = create_matrix_block(J)
Pmat0 = create_matrix_block(P)
Fvec0 = create_vector_block(F)
snes = PETSc.SNES().create(MPI.COMM_WORLD)
snes.setTolerances(rtol=1.0e-15, max_it=10)
snes.getKSP().setType("minres")
snes.getKSP().getPC().setType("lu")
problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs, P=P)
snes.setFunction(problem.F_block, Fvec0)
snes.setJacobian(problem.J_block, J=Jmat0, P=Pmat0)
u.interpolate(initial_guess_u)
p.interpolate(initial_guess_p)
x0 = create_vector_block(F)
with u.vector.localForm() as _u, p.vector.localForm() as _p:
scatter_local_vectors(x0, [_u.array_r, _p.array_r],
[(u.function_space.dofmap.index_map,
u.function_space.dofmap.index_map_bs),
(p.function_space.dofmap.index_map,
p.function_space.dofmap.index_map_bs)])
x0.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
snes.solve(None, x0)
assert snes.getConvergedReason() > 0
# -- Blocked and nested
Jmat1 = create_matrix_nest(J)
Pmat1 = create_matrix_nest(P)
Fvec1 = create_vector_nest(F)
snes = PETSc.SNES().create(MPI.COMM_WORLD)
snes.setTolerances(rtol=1.0e-15, max_it=10)
nested_IS = Jmat1.getNestISs()
snes.getKSP().setType("minres")
snes.getKSP().setTolerances(rtol=1e-12)
snes.getKSP().getPC().setType("fieldsplit")
snes.getKSP().getPC().setFieldSplitIS(["u", nested_IS[0][0]],
["p", nested_IS[1][1]])
ksp_u, ksp_p = snes.getKSP().getPC().getFieldSplitSubKSP()
ksp_u.setType("preonly")
ksp_u.getPC().setType('lu')
ksp_p.setType("preonly")
ksp_p.getPC().setType('lu')
problem = NonlinearPDE_SNESProblem(F, J, [u, p], bcs, P=P)
snes.setFunction(problem.F_nest, Fvec1)
snes.setJacobian(problem.J_nest, J=Jmat1, P=Pmat1)
u.interpolate(initial_guess_u)
p.interpolate(initial_guess_p)
x1 = create_vector_nest(F)
for x1_soln_pair in zip(x1.getNestSubVecs(), (u, p)):
x1_sub, soln_sub = x1_soln_pair
soln_sub.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
soln_sub.vector.copy(result=x1_sub)
x1_sub.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
x1.set(0.0)
snes.solve(None, x1)
assert snes.getConvergedReason() > 0
assert nest_matrix_norm(Jmat1) == pytest.approx(Jmat0.norm(), 1.0e-12)
assert Fvec1.norm() == pytest.approx(Fvec0.norm(), 1.0e-12)
assert x1.norm() == pytest.approx(x0.norm(), 1.0e-12)
# -- Monolithic
P2_el = ufl.VectorElement("Lagrange", mesh.ufl_cell(), 2)
P1_el = ufl.FiniteElement("Lagrange", mesh.ufl_cell(), 1)
TH = P2_el * P1_el
W = FunctionSpace(mesh, TH)
U = Function(W)
dU = ufl.TrialFunction(W)
u, p = ufl.split(U)
du, dp = ufl.split(dU)
v, q = ufl.TestFunctions(W)
F = inner(ufl.grad(u), ufl.grad(v)) * dx + inner(p, ufl.div(v)) * dx \
+ inner(ufl.div(u), q) * dx
J = derivative(F, U, dU)
P = inner(ufl.grad(du), ufl.grad(v)) * dx + inner(dp, q) * dx
F, J, P = form(F), form(J), form(P)
bdofsW0_P2_0 = locate_dofs_topological((W.sub(0), P2), facetdim,
bndry_facets0)
bdofsW0_P2_1 = locate_dofs_topological((W.sub(0), P2), facetdim,
bndry_facets1)
bcs = [
dirichletbc(u_bc_0, bdofsW0_P2_0, W.sub(0)),
dirichletbc(u_bc_1, bdofsW0_P2_1, W.sub(0))
]
Jmat2 = create_matrix(J)
Pmat2 = create_matrix(P)
Fvec2 = create_vector(F)
snes = PETSc.SNES().create(MPI.COMM_WORLD)
snes.setTolerances(rtol=1.0e-15, max_it=10)
snes.getKSP().setType("minres")
snes.getKSP().getPC().setType("lu")
problem = NonlinearPDE_SNESProblem(F, J, U, bcs, P=P)
snes.setFunction(problem.F_mono, Fvec2)
snes.setJacobian(problem.J_mono, J=Jmat2, P=Pmat2)
U.sub(0).interpolate(initial_guess_u)
U.sub(1).interpolate(initial_guess_p)
x2 = create_vector(F)
x2.array = U.vector.array_r
snes.solve(None, x2)
assert snes.getConvergedReason() > 0
assert Jmat2.norm() == pytest.approx(Jmat0.norm(), 1.0e-12)
assert Fvec2.norm() == pytest.approx(Fvec0.norm(), 1.0e-12)
assert x2.norm() == pytest.approx(x0.norm(), 1.0e-12)
def __init__(self, cfgfile):
'''
Constructor
'''
super().__init__(cfgfile, mode="lu")
OptDB = PETSc.Options()
OptDB.setValue('ksp_monitor', '')
OptDB.setValue('snes_monitor', '')
# OptDB.setValue('log_info', '')
# OptDB.setValue('log_summary', '')
OptDB.setValue('snes_ls', 'basic')
# OptDB.setValue('snes_ls', 'quadratic')
OptDB.setValue('snes_rtol', self.cfg['solver']['petsc_snes_rtol'])
OptDB.setValue('snes_atol', self.cfg['solver']['petsc_snes_atol'])
OptDB.setValue('snes_stol', self.cfg['solver']['petsc_snes_stol'])
OptDB.setValue('snes_max_it',
self.cfg['solver']['petsc_snes_max_iter'])
OptDB.setValue('ksp_rtol', self.cfg['solver']['petsc_ksp_rtol'])
OptDB.setValue('ksp_atol', self.cfg['solver']['petsc_ksp_atol'])
OptDB.setValue('ksp_max_it', self.cfg['solver']['petsc_ksp_max_iter'])
# OptDB.setValue('mat_superlu_dist_matinput', 'DISTRIBUTED')
# OptDB.setValue('mat_superlu_dist_rowperm', 'NATURAL')
OptDB.setValue('mat_superlu_dist_colperm', 'PARMETIS')
OptDB.setValue('mat_superlu_dist_parsymbfact', 1)
# create Jacobian, Function, and linear Matrix objects
self.petsc_solver = PETScSolver(self.da1, self.da4, self.nx, self.ny,
self.ht, self.hx, self.hy)
# initialise linear matrix
self.M = self.da4.createMat()
self.M.setOption(PETSc.Mat.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.M.setUp()
# initialise Jacobian
self.Jac = self.da4.createMat()
self.Jac.setOption(PETSc.Mat.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.Jac.setUp()
# initialise matrixfree Jacobian
self.Jmf = PETSc.Mat().createPython(
[self.x.getSizes(), self.b.getSizes()],
context=self.petsc_solver,
comm=PETSc.COMM_WORLD)
self.Jmf.setUp()
# create nonlinear solver
self.snes = PETSc.SNES().create()
self.snes.setFunction(self.petsc_solver.snes_function, self.f)
self.snes.setJacobian(self.updateJacobian, self.Jmf, self.Jac)
self.snes.setFromOptions()
self.snes.getKSP().setType('preonly')
self.snes.getKSP().getPC().setType('lu')
self.snes.getKSP().getPC().setFactorSolverType(self.solver_package)
# update solution history
self.petsc_solver.update_previous(self.x)
def __init__(self, cfgfile):
'''
Constructor
'''
# load run config file
cfg = Config(cfgfile)
# timestep setup
self.ht = cfg['grid']['ht'] # timestep size
self.nt = cfg['grid']['nt'] # number of timesteps
self.nsave = cfg['io']['nsave'] # save only every nsave'th timestep
# grid setup
self.nx = cfg['grid']['nx'] # number of points in x
self.ny = cfg['grid']['ny'] # number of points in y
Lx = cfg['grid']['Lx'] # spatial domain in x
x1 = cfg['grid']['x1'] #
x2 = cfg['grid']['x2'] #
Ly = cfg['grid']['Ly'] # spatial domain in y
y1 = cfg['grid']['y1'] #
y2 = cfg['grid']['y2'] #
if x1 != x2:
Lx = x2 - x1
else:
x1 = 0.0
x2 = Lx
if y1 != y2:
Ly = y2 - y1
else:
y1 = 0.0
y2 = Ly
self.hx = Lx / self.nx # gridstep size in x
self.hy = Ly / self.ny # gridstep size in y
self.time = PETSc.Vec().createMPI(1,
PETSc.DECIDE,
comm=PETSc.COMM_WORLD)
self.time.setName('t')
if PETSc.COMM_WORLD.getRank() == 0:
self.time.setValue(0, 0.0)
OptDB = PETSc.Options()
OptDB.setValue('snes_rtol', cfg['solver']['petsc_snes_rtol'])
OptDB.setValue('snes_atol', cfg['solver']['petsc_snes_atol'])
OptDB.setValue('snes_stol', cfg['solver']['petsc_snes_stol'])
OptDB.setValue('snes_max_it', cfg['solver']['petsc_snes_max_iter'])
OptDB.setValue('ksp_rtol', cfg['solver']['petsc_ksp_rtol'])
OptDB.setValue('ksp_atol', cfg['solver']['petsc_ksp_atol'])
OptDB.setValue('ksp_max_it', cfg['solver']['petsc_ksp_max_iter'])
# OptDB.setValue('ksp_monitor', '')
# OptDB.setValue('snes_monitor', '')
#
# OptDB.setValue('log_info', '')
# OptDB.setValue('log_summary', '')
self.snes_rtol = cfg['solver']['petsc_snes_rtol']
self.snes_atol = cfg['solver']['petsc_snes_atol']
self.snes_max_iter = cfg['solver']['petsc_snes_max_iter']
# create DA with single dof
self.da1 = PETSc.DA().create(dim=2,
dof=1,
sizes=[self.nx, self.ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=2,
stencil_type='box')
# create DA (dof = 4 for A, J, P, O)
self.da4 = PETSc.DA().create(dim=2,
dof=4,
sizes=[self.nx, self.ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=2,
stencil_type='box')
# create DA for x grid
self.dax = PETSc.DA().create(dim=1,
dof=1,
sizes=[self.nx],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# create DA for y grid
self.day = PETSc.DA().create(dim=1,
dof=1,
sizes=[self.ny],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# initialise grid
self.da1.setUniformCoordinates(xmin=x1, xmax=x2, ymin=y1, ymax=y2)
self.da4.setUniformCoordinates(xmin=x1, xmax=x2, ymin=y1, ymax=y2)
self.dax.setUniformCoordinates(xmin=x1, xmax=x2)
self.day.setUniformCoordinates(xmin=y1, xmax=y2)
# create RHS vector
self.Ab = self.da1.createGlobalVec()
self.Ob = self.da1.createGlobalVec()
self.Pb = self.da1.createGlobalVec()
# create vectors for magnetic and velocity field
self.A = self.da1.createGlobalVec() # magnetic vector potential A
self.J = self.da1.createGlobalVec() # current density J
self.P = self.da1.createGlobalVec() # streaming function psi
self.O = self.da1.createGlobalVec() # vorticity omega
self.Bx = self.da1.createGlobalVec()
self.By = self.da1.createGlobalVec()
self.Vx = self.da1.createGlobalVec()
self.Vy = self.da1.createGlobalVec()
# set variable names
self.A.setName('A')
self.J.setName('J')
self.P.setName('P')
self.O.setName('O')
self.Bx.setName('Bx')
self.By.setName('By')
self.Vx.setName('Vx')
self.Vy.setName('Vy')
# create nullspace
self.poisson_nullspace = PETSc.NullSpace().create(constant=True)
# create jacobian and matrix objects
self.petsc_vorticity = PETScVorticity(self.da1, self.nx, self.ny,
self.ht, self.hx, self.hy)
self.petsc_ohmslaw = PETScOhmsLaw(self.da1, self.nx, self.ny, self.ht,
self.hx, self.hy)
self.petsc_poisson = PETScPoisson(self.da1, self.nx, self.ny, self.hx,
self.hy)
# initialise vorticity matrix
self.vorticity_matrix = self.da1.createMat()
self.vorticity_matrix.setOption(
self.vorticity_matrix.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.vorticity_matrix.setUp()
# initialise Ohms's law matrix
self.ohmslaw_matrix = self.da1.createMat()
self.ohmslaw_matrix.setOption(
self.ohmslaw_matrix.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.ohmslaw_matrix.setUp()
# initialise Poisson matrix
self.poisson_matrix = self.da1.createMat()
self.poisson_matrix.setOption(
self.poisson_matrix.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.poisson_matrix.setUp()
self.poisson_matrix.setNullSpace(self.poisson_nullspace)
# create nonlinear vorticity solver
self.vorticity_snes = PETSc.SNES().create()
self.vorticity_snes.setType('ksponly')
self.vorticity_snes.setFunction(self.petsc_vorticity.snes_mult,
self.Ob)
self.vorticity_snes.setJacobian(self.update_vorticity_jacobian,
self.vorticity_matrix)
self.vorticity_snes.setFromOptions()
# self.vorticity_snes.getKSP().setType('gmres')
self.vorticity_snes.getKSP().setType('preonly')
self.vorticity_snes.getKSP().getPC().setType('lu')
self.vorticity_snes.getKSP().getPC().setFactorSolverPackage(
solver_package)
# create nonlinear Ohms's law solver
self.ohmslaw_snes = PETSc.SNES().create()
self.ohmslaw_snes.setType('ksponly')
self.ohmslaw_snes.setFunction(self.petsc_ohmslaw.snes_mult, self.Ab)
self.ohmslaw_snes.setJacobian(self.update_ohmslaw_jacobian,
self.ohmslaw_matrix)
self.ohmslaw_snes.setFromOptions()
# self.ohmslaw_snes.getKSP().setType('gmres')
self.ohmslaw_snes.getKSP().setType('preonly')
self.ohmslaw_snes.getKSP().getPC().setType('lu')
self.ohmslaw_snes.getKSP().getPC().setFactorSolverPackage(
solver_package)
# create linear Poisson solver
self.poisson_ksp = PETSc.KSP().create()
self.poisson_ksp.setFromOptions()
self.poisson_ksp.setOperators(self.poisson_matrix)
self.poisson_ksp.setType('preonly')
self.poisson_ksp.getPC().setType('lu')
self.poisson_ksp.getPC().setFactorSolverPackage(solver_package)
# self.poisson_ksp.setNullSpace(self.poisson_nullspace)
self.petsc_poisson.formMat(self.poisson_matrix)
# create derivatives object
self.derivatives = PETScDerivatives(self.da1, self.nx, self.ny,
self.ht, self.hx, self.hy)
# get coordinate vectors
coords_x = self.dax.getCoordinates()
coords_y = self.day.getCoordinates()
# save x coordinate arrays
scatter, xVec = PETSc.Scatter.toAll(coords_x)
scatter.begin(coords_x, xVec, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
scatter.end(coords_x, xVec, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
xGrid = xVec.getValues(range(0, self.nx)).copy()
scatter.destroy()
xVec.destroy()
# save y coordinate arrays
scatter, yVec = PETSc.Scatter.toAll(coords_y)
scatter.begin(coords_y, yVec, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
scatter.end(coords_y, yVec, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
yGrid = yVec.getValues(range(0, self.ny)).copy()
scatter.destroy()
yVec.destroy()
# set initial data
(xs, xe), (ys, ye) = self.da1.getRanges()
A_arr = self.da1.getVecArray(self.A)
P_arr = self.da1.getVecArray(self.P)
init_data = __import__("runs." + cfg['initial_data']['python'],
globals(), locals(),
['magnetic_A', 'velocity_P'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
A_arr[i, j] = init_data.magnetic_A(xGrid[i], yGrid[j], Lx, Ly)
P_arr[i, j] = init_data.velocity_P(xGrid[i], yGrid[j], Lx, Ly)
# Fourier Filtering
self.nfourier = cfg['initial_data']['nfourier']
if self.nfourier >= 0:
# obtain whole A vector everywhere
scatter, Aglobal = PETSc.Scatter.toAll(self.A)
scatter.begin(self.A, Aglobal, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
scatter.end(self.A, Aglobal, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
petsc_indices = self.da1.getAO().app2petsc(
np.arange(self.nx * self.ny, dtype=np.int32))
Ainit = Aglobal.getValues(petsc_indices).copy().reshape(
(self.ny, self.nx))
scatter.destroy()
Aglobal.destroy()
# compute FFT, cut, compute inverse FFT
from scipy.fftpack import rfft, irfft
Afft = rfft(Ainit, axis=1)
Afft[:, 0] = 0.
Afft[:, self.nfourier + 1:] = 0.
A_arr = self.da1.getVecArray(self.A)
A_arr[:, :] = irfft(Afft).T[xs:xe, ys:ye]
# compute current and vorticity
self.derivatives.laplace_vec(self.A, self.J, -1.)
self.derivatives.laplace_vec(self.P, self.O, -1.)
J_arr = self.da1.getVecArray(self.J)
O_arr = self.da1.getVecArray(self.O)
# add perturbations
for i in range(xs, xe):
for j in range(ys, ye):
J_arr[i, j] += init_data.current_perturbation(
xGrid[i], yGrid[j], Lx, Ly)
O_arr[i, j] += init_data.vorticity_perturbation(
xGrid[i], yGrid[j], Lx, Ly)
# create HDF5 output file
self.hdf5_viewer = PETSc.ViewerHDF5().create(
cfg['io']['hdf5_output'],
mode=PETSc.Viewer.Mode.WRITE,
comm=PETSc.COMM_WORLD)
self.hdf5_viewer.pushGroup("/")
# write grid data to hdf5 file
coords_x = self.dax.getCoordinates()
coords_y = self.day.getCoordinates()
coords_x.setName('x')
coords_y.setName('y')
self.hdf5_viewer(coords_x)
self.hdf5_viewer(coords_y)
# write initial data to hdf5 file
self.save_to_hdf5(0)
def __init__(self, cfgfile, runid):
super().__init__(cfgfile, runid)
OptDB = PETSc.Options()
# OptDB.setValue('snes_ls', 'basic')
# OptDB.setValue('ksp_monitor', '')
# OptDB.setValue('snes_monitor', '')
# OptDB.setValue('log_info', '')
# OptDB.setValue('log_summary', '')
# initialise predictor Jacobian
self.J = self.da1.createMat()
self.J.setOption(self.J.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.J.setUp()
# create solver objects
self.vlasov_solver = PETScVlasovSolver(self.da1,
self.dax,
self.h0,
self.vGrid,
self.nx,
self.nv,
self.ht,
self.hx,
self.hv,
self.charge,
coll_freq=self.coll_freq)
# update solution history
self.vlasov_solver.update_history(self.f, self.p, self.p_ext, self.n,
self.u, self.e)
# create nonlinear predictor solver
self.snes = PETSc.SNES().create()
self.snes.setType('ksponly')
self.snes.setFunction(self.vlasov_solver.function_snes_mult, self.fb)
self.snes.setJacobian(self.updateVlasovJacobian, self.J)
self.snes.setFromOptions()
self.snes.getKSP().setType('gmres')
self.snes.getKSP().getPC().setType('none')
self.poisson_mf = PETSc.Mat().createPython(
[self.p.getSizes(), self.pb.getSizes()],
context=self.poisson_solver,
comm=PETSc.COMM_WORLD)
self.poisson_mf.setUp()
del self.poisson_ksp
OptDB.setValue('ksp_rtol', 1E-13)
self.poisson_ksp = PETSc.KSP().create()
self.poisson_ksp.setFromOptions()
self.poisson_ksp.setOperators(self.poisson_mf, self.poisson_matrix)
self.poisson_ksp.setType('cg')
# self.poisson_ksp.setType('bcgs')
# self.poisson_ksp.setType('ibcgs')
self.poisson_ksp.getPC().setType('hypre')
OptDB.setValue('ksp_rtol', self.cfg['solver']['petsc_ksp_rtol'])
def __init__(self, cfgfile):
'''
Constructor
'''
# stencil = 1
stencil = 2
# load run config file
cfg = Config(cfgfile)
self.cfg = cfg
cfg.set_petsc_options()
# timestep setup
self.ht = cfg['grid']['ht'] # timestep size
self.nt = cfg['grid']['nt'] # number of timesteps
self.nsave = cfg['io']['nsave'] # save only every nsave'th timestep
# grid setup
nx = cfg['grid']['nx'] # number of points in x
ny = cfg['grid']['ny'] # number of points in y
Lx = cfg['grid']['Lx'] # spatial domain in x
x1 = cfg['grid']['x1'] #
x2 = cfg['grid']['x2'] #
Ly = cfg['grid']['Ly'] # spatial domain in y
y1 = cfg['grid']['y1'] #
y2 = cfg['grid']['y2'] #
self.nx = nx
self.ny = ny
if x1 != x2:
Lx = x2 - x1
else:
x1 = 0.0
x2 = Lx
if y1 != y2:
Ly = y2 - y1
else:
y1 = 0.0
y2 = Ly
self.hx = Lx / nx # gridstep size in x
self.hy = Ly / ny # gridstep size in y
# friction, viscosity and resistivity
mu = cfg['initial_data']['mu'] # friction
nu = cfg['initial_data']['nu'] # viscosity
eta = cfg['initial_data']['eta'] # resistivity
de = cfg['initial_data']['de'] # electron skin depth
# self.update_jacobian = True
if PETSc.COMM_WORLD.getRank() == 0:
print()
print("nt = %i" % (self.nt))
print("nx = %i" % (self.nx))
print("ny = %i" % (self.ny))
print()
print("ht = %e" % (self.ht))
print("hx = %e" % (self.hx))
print("hy = %e" % (self.hy))
print()
print("Lx = %e" % (Lx))
print("Ly = %e" % (Ly))
print()
print("mu = %e" % (mu))
print("nu = %e" % (nu))
print("eta = %e" % (eta))
print()
self.time = PETSc.Vec().createMPI(1,
PETSc.DECIDE,
comm=PETSc.COMM_WORLD)
self.time.setName('t')
if PETSc.COMM_WORLD.getRank() == 0:
self.time.setValue(0, 0.0)
# create derivatives object
self.derivatives = MHD_Derivatives(nx, ny, self.ht, self.hx, self.hy)
# create DA with single dof
self.da1 = PETSc.DA().create(dim=2,
dof=1,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=stencil,
stencil_type='box')
# create DA (dof = 7 for Vx, Vy, Bx, By, Bix, Biy, P)
self.da7 = PETSc.DA().create(dim=2,
dof=7,
sizes=[nx, ny],
proc_sizes=[PETSc.DECIDE, PETSc.DECIDE],
boundary_type=('periodic', 'periodic'),
stencil_width=stencil,
stencil_type='box')
# create DA for x grid
self.dax = PETSc.DA().create(dim=1,
dof=1,
sizes=[nx],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# create DA for y grid
self.day = PETSc.DA().create(dim=1,
dof=1,
sizes=[ny],
proc_sizes=[PETSc.DECIDE],
boundary_type=('periodic'))
# initialise grid
self.da1.setUniformCoordinates(xmin=x1, xmax=x2, ymin=y1, ymax=y2)
self.da7.setUniformCoordinates(xmin=x1, xmax=x2, ymin=y1, ymax=y2)
self.dax.setUniformCoordinates(xmin=x1, xmax=x2)
self.day.setUniformCoordinates(xmin=y1, xmax=y2)
# create solution and RHS vector
self.f = self.da7.createGlobalVec()
self.x = self.da7.createGlobalVec()
self.b = self.da7.createGlobalVec()
# create global RK4 vectors
self.Y = self.da7.createGlobalVec()
self.X0 = self.da7.createGlobalVec()
self.X1 = self.da7.createGlobalVec()
self.X2 = self.da7.createGlobalVec()
self.X3 = self.da7.createGlobalVec()
self.X4 = self.da7.createGlobalVec()
# create local RK4 vectors
self.localX0 = self.da7.createLocalVec()
self.localX1 = self.da7.createLocalVec()
self.localX2 = self.da7.createLocalVec()
self.localX3 = self.da7.createLocalVec()
self.localX4 = self.da7.createLocalVec()
# self.localP = self.da1.createLocalVec()
# create vectors for magnetic and velocity field
self.Bix = self.da1.createGlobalVec()
self.Biy = self.da1.createGlobalVec()
self.Bx = self.da1.createGlobalVec()
self.By = self.da1.createGlobalVec()
self.Vx = self.da1.createGlobalVec()
self.Vy = self.da1.createGlobalVec()
self.P = self.da1.createGlobalVec()
self.xcoords = self.da1.createGlobalVec()
self.ycoords = self.da1.createGlobalVec()
# create local vectors for initialisation of pressure
self.localBix = self.da1.createLocalVec()
self.localBiy = self.da1.createLocalVec()
self.localBx = self.da1.createLocalVec()
self.localBy = self.da1.createLocalVec()
self.localVx = self.da1.createLocalVec()
self.localVy = self.da1.createLocalVec()
# set variable names
self.Bix.setName('Bix')
self.Biy.setName('Biy')
self.Bx.setName('Bx')
self.By.setName('By')
self.Vx.setName('Vx')
self.Vy.setName('Vy')
self.P.setName('P')
# create Matrix object
self.petsc_matrix = PETScMatrix(self.da1, self.da7, nx, ny, self.ht,
self.hx, self.hy, mu, nu, eta, de)
self.petsc_function = PETScFunction(self.da1, self.da7, nx, ny,
self.ht, self.hx, self.hy, mu, nu,
eta, de)
# initialise matrix
self.A = self.da7.createMat()
self.A.setOption(self.A.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.A.setUp()
# create jacobian
self.J = self.da7.createMat()
self.J.setOption(self.J.Option.NEW_NONZERO_ALLOCATION_ERR, False)
self.J.setUp()
# create nonlinear solver
self.snes = PETSc.SNES().create()
self.snes.setFunction(self.petsc_function.snes_mult, self.f)
self.snes.setJacobian(self.updateJacobian, self.J)
self.snes.setFromOptions()
# self.snes.getKSP().setInitialGuessNonzero(True)
# self.snes.getKSP().getPC().setReusePreconditioner(True)
self.ksp = None
# set initial data
(xs, xe), (ys, ye) = self.da1.getRanges()
# coords = self.da1.getCoordinatesLocal()
xc_arr = self.da1.getVecArray(self.xcoords)
yc_arr = self.da1.getVecArray(self.ycoords)
for i in range(xs, xe):
for j in range(ys, ye):
xc_arr[i, j] = x1 + i * self.hx
yc_arr[i, j] = y1 + j * self.hy
if cfg['io']['hdf5_input'] != None:
hdf5_filename = self.cfg["io"]["hdf5_input"]
if PETSc.COMM_WORLD.getRank() == 0:
print(" Input: %s" % hdf5_filename)
hdf5in = h5py.File(hdf5_filename,
"r",
driver="mpio",
comm=PETSc.COMM_WORLD.tompi4py())
# assert self.nx == hdf5in.attrs["grid.nx"]
# assert self.ny == hdf5in.attrs["grid.ny"]
# assert self.hx == hdf5in.attrs["grid.hx"]
# assert self.hy == hdf5in.attrs["grid.hy"]
# assert self.Lx == hdf5in.attrs["grid.Lx"]
# assert self.Ly == hdf5in.attrs["grid.Ly"]
#
# assert self.de == hdf5in.attrs["initial_data.skin_depth"]
timestep = len(hdf5in["t"][...].flatten()) - 1
hdf5in.close()
hdf5_viewer = PETSc.ViewerHDF5().create(
cfg['io']['hdf5_input'],
mode=PETSc.Viewer.Mode.READ,
comm=PETSc.COMM_WORLD)
hdf5_viewer.setTimestep(timestep)
self.Bix.load(hdf5_viewer)
self.Biy.load(hdf5_viewer)
self.Bx.load(hdf5_viewer)
self.By.load(hdf5_viewer)
self.Vx.load(hdf5_viewer)
self.Vy.load(hdf5_viewer)
self.P.load(hdf5_viewer)
hdf5_viewer.destroy()
# copy modified magnetic induction to solution vector
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
Bix_arr = self.da1.getVecArray(self.Bix)
Biy_arr = self.da1.getVecArray(self.Biy)
P_arr = self.da1.getVecArray(self.P)
x_arr = self.da7.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 0] = Vx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 1] = Vy_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 2] = Bx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 3] = By_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 4] = Bix_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 5] = Biy_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 6] = P_arr[xs:xe, ys:ye]
else:
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
xc_arr = self.da1.getVecArray(self.xcoords)
yc_arr = self.da1.getVecArray(self.ycoords)
if cfg['initial_data']['magnetic_python'] != None:
init_data = __import__(
"examples." + cfg['initial_data']['magnetic_python'],
globals(), locals(), ['magnetic_x', 'magnetic_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Bx_arr[i, j] = init_data.magnetic_x(
xc_arr[i, j], yc_arr[i, j] + 0.5 * self.hy,
self.hx, self.hy)
By_arr[i, j] = init_data.magnetic_y(
xc_arr[i, j] + 0.5 * self.hx, yc_arr[i, j],
self.hx, self.hy)
else:
Bx_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
By_arr[xs:xe, ys:ye] = cfg['initial_data']['magnetic']
if cfg['initial_data']['velocity_python'] != None:
init_data = __import__(
"examples." + cfg['initial_data']['velocity_python'],
globals(), locals(), ['velocity_x', 'velocity_y'], 0)
for i in range(xs, xe):
for j in range(ys, ye):
Vx_arr[i, j] = init_data.velocity_x(
xc_arr[i, j], yc_arr[i, j] + 0.5 * self.hy,
self.hx, self.hy)
Vy_arr[i, j] = init_data.velocity_y(
xc_arr[i, j] + 0.5 * self.hx, yc_arr[i, j],
self.hx, self.hy)
else:
Vx_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
Vy_arr[xs:xe, ys:ye] = cfg['initial_data']['velocity']
if cfg['initial_data']['pressure_python'] != None:
init_data = __import__(
"examples." + cfg['initial_data']['pressure_python'],
globals(), locals(), ['pressure', ''], 0)
# Fourier Filtering
from scipy.fftpack import rfft, irfft
nfourier_x = cfg['initial_data']['nfourier_Bx']
nfourier_y = cfg['initial_data']['nfourier_By']
if nfourier_x >= 0 or nfourier_y >= 0:
print("Fourier Filtering B")
# obtain whole Bx vector everywhere
scatter, Xglobal = PETSc.Scatter.toAll(self.Bx)
scatter.begin(self.Bx, Xglobal, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
scatter.end(self.Bx, Xglobal, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
petsc_indices = self.da1.getAO().app2petsc(
np.arange(self.nx * self.ny, dtype=np.int32))
BxTmp = Xglobal.getValues(petsc_indices).copy().reshape(
(self.ny, self.nx)).T
scatter.destroy()
Xglobal.destroy()
# obtain whole By vector everywhere
scatter, Xglobal = PETSc.Scatter.toAll(self.By)
scatter.begin(self.By, Xglobal, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
scatter.end(self.By, Xglobal, PETSc.InsertMode.INSERT,
PETSc.ScatterMode.FORWARD)
petsc_indices = self.da1.getAO().app2petsc(
np.arange(self.nx * self.ny, dtype=np.int32))
ByTmp = Xglobal.getValues(petsc_indices).copy().reshape(
(self.ny, self.nx)).T
scatter.destroy()
Xglobal.destroy()
if nfourier_x >= 0:
# compute FFT, cut, compute inverse FFT
BxFft = rfft(BxTmp, axis=1)
ByFft = rfft(ByTmp, axis=1)
BxFft[:, nfourier_x + 1:] = 0.
ByFft[:, nfourier_x + 1:] = 0.
BxTmp = irfft(BxFft, axis=1)
ByTmp = irfft(ByFft, axis=1)
if nfourier_y >= 0:
BxFft = rfft(BxTmp, axis=0)
ByFft = rfft(ByTmp, axis=0)
BxFft[nfourier_y + 1:, :] = 0.
ByFft[nfourier_y + 1:, :] = 0.
BxTmp = irfft(BxFft, axis=0)
ByTmp = irfft(ByFft, axis=0)
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Bx_arr[:, :] = BxTmp[xs:xe, ys:ye]
By_arr[:, :] = ByTmp[xs:xe, ys:ye]
Bx_arr = self.da1.getVecArray(self.Bx)
By_arr = self.da1.getVecArray(self.By)
Vx_arr = self.da1.getVecArray(self.Vx)
Vy_arr = self.da1.getVecArray(self.Vy)
x_arr = self.da7.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 0] = Vx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 1] = Vy_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 2] = Bx_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 3] = By_arr[xs:xe, ys:ye]
# compure generalised magnetic induction
self.da1.globalToLocal(self.Bx, self.localBx)
self.da1.globalToLocal(self.By, self.localBy)
self.da1.globalToLocal(self.Vx, self.localVx)
self.da1.globalToLocal(self.Vy, self.localVy)
Bx_arr = self.da1.getVecArray(self.localBx)
By_arr = self.da1.getVecArray(self.localBy)
Vx_arr = self.da1.getVecArray(self.localVx)
Vy_arr = self.da1.getVecArray(self.localVy)
Bix_arr = self.da1.getVecArray(self.Bix)
Biy_arr = self.da1.getVecArray(self.Biy)
for i in range(xs, xe):
for j in range(ys, ye):
Bix_arr[i,
j] = self.derivatives.Bix(Bx_arr[...], By_arr[...],
i - xs + 2, j - ys + 2,
de)
Biy_arr[i,
j] = self.derivatives.Biy(Bx_arr[...], By_arr[...],
i - xs + 2, j - ys + 2,
de)
# copy modified magnetic induction to solution vector
x_arr = self.da7.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 4] = Bix_arr[xs:xe, ys:ye]
x_arr[xs:xe, ys:ye, 5] = Biy_arr[xs:xe, ys:ye]
# compute pressure
self.da1.globalToLocal(self.Bix, self.localBix)
self.da1.globalToLocal(self.Biy, self.localBiy)
Bix_arr = self.da1.getVecArray(self.localBix)
Biy_arr = self.da1.getVecArray(self.localBiy)
P_arr = self.da1.getVecArray(self.P)
for i in range(xs, xe):
for j in range(ys, ye):
P_arr[i,j] = init_data.pressure(xc_arr[i,j] + 0.5 * self.hx, yc_arr[i,j] + 0.5 * self.hy, self.hx, self.hy) \
- 0.5 * 0.25 * (Bix_arr[i,j] + Bix_arr[i+1,j]) * (Bx_arr[i,j] + Bx_arr[i+1,j]) \
- 0.5 * 0.25 * (Biy_arr[i,j] + Biy_arr[i,j+1]) * (By_arr[i,j] + By_arr[i,j+1]) \
# - 0.5 * (0.25 * (Vx_arr[i,j] + Vx_arr[i+1,j])**2 + 0.25 * (Vy_arr[i,j] + Vy_arr[i,j+1])**2)
# copy pressure to solution vector
x_arr = self.da7.getVecArray(self.x)
x_arr[xs:xe, ys:ye, 6] = P_arr[xs:xe, ys:ye]
# update solution history
self.petsc_matrix.update_history(self.x)
self.petsc_function.update_history(self.x)
hdf5_filename = cfg['io']['hdf5_output']
if PETSc.COMM_WORLD.getRank() == 0:
print(" Output: %s" % hdf5_filename)
hdf5out = h5py.File(hdf5_filename,
"w",
driver="mpio",
comm=PETSc.COMM_WORLD.tompi4py())
for cfg_group in self.cfg:
for cfg_item in self.cfg[cfg_group]:
if self.cfg[cfg_group][cfg_item] != None:
value = self.cfg[cfg_group][cfg_item]
else:
value = ""
hdf5out.attrs[cfg_group + "." + cfg_item] = value
# if self.cfg["initial_data"]["python"] != None and self.cfg["initial_data"]["python"] != "":
# python_input = open("runs/" + self.cfg['initial_data']['python'] + ".py", 'r')
# python_file = python_input.read()
# python_input.close()
# else:
# python_file = ""
# hdf5out.attrs["initial_data.python_file"] = python_file
hdf5out.close()
# create HDF5 output file
self.hdf5_viewer = PETSc.ViewerHDF5().create(
hdf5_filename, mode=PETSc.Viewer.Mode.WRITE, comm=PETSc.COMM_WORLD)
self.hdf5_viewer.pushGroup("/")
# write grid data to hdf5 file
coords_x = self.dax.getCoordinates()
coords_y = self.day.getCoordinates()
coords_x.setName('x')
coords_y.setName('y')
self.hdf5_viewer(coords_x)
self.hdf5_viewer(coords_y)
# write initial data to hdf5 file
self.hdf5_viewer.setTimestep(0)
self.save_hdf5_vectors()
def main():
# 'linear;, 'quadratic' or 'cubic'
elementType = 'cubic'
# '2pt','3pt', '4pt'
quadratureRule = '4pt'
# meshType = 'uniform' or 'adaptive'
meshType = 'uniform'
# FIXME: generalize later
numAtoms = 1
if(numAtoms == 1):
# define number of elements
numberElements = 52
# define domain size in 1D
domainStart = -17.5
domainEnd = 17.5
#define parameters for adaptive Mesh
innerDomainSize = 8
innerMeshSize = 0.25
#read the external potental from matlab
if(meshType == 'uniform'):
pot = open('vpotOneAtomUniform52Elem.txt','r')
else :
pot = open('vpotOneAtomAdaptive52Elem.txt','r')
else:
# define number of elements
numberElements = 84
# define domain size in 1D
domainStart = -17.5
domainEnd = 17.5
#define parameters for adaptive Mesh
innerDomainSize = 16
innerMeshSize = 0.25
#read the external potental from matlab
if(meshType =='uniform'):
pot = open('vpot14AtomUniform84Elem.txt','r')
else :
pot = open('vpot14AtomAdaptive84Elem.txt','r')
# create FEM object
fem=FEM.FEM(numberElements,
quadratureRule,
elementType,
domainStart,
domainEnd,
innerDomainSize,
innerMeshSize,
meshType)
# mesh the domain in 1D
globalNodalCoordinates = fem.generateNodes()
# generate Adaptive Mesh
numberNodes = fem.numberNodes
#get number quadrature points
numberQuadraturePoints = fem.getNumberQuadPointsPerElement()
totalnumberQuadraturePoints = numberElements*numberQuadraturePoints
v= []
for line in pot:
v.append(float(line))
v = np.array(v)
data= np.reshape(v,(totalnumberQuadraturePoints,totalnumberQuadraturePoints,totalnumberQuadraturePoints))
# reducedRank
rankVeff = 5
reducedRank = (rankVeff, rankVeff, rankVeff)
#perform tensor decomposition of effective potential
time_tensorStart = time.clock()
#convert to a tensor
fTensor = tensor.tensor(data)
[a,b] = DTA.DTA(fTensor,reducedRank)
time_tensorEnd = time.clock()
print 'time elapsed for tensor decomposition of Veff (s)',time_tensorEnd-time_tensorStart
sigma_core = a.core
sigma = sigma_core.tondarray()
umat = a.u[0].real
vmat = a.u[1].real
wmat = a.u[2].real
sigma = sigma.real
sigma2D = sigma.reshape((rankVeff**2,rankVeff)) # done to reduce cost while contracting
functional = FunctionalRayleighQuotientSeparable.FEMFunctional(fem,
rankVeff,
sigma2D,
[umat,vmat,wmat])
# initial guess for psix, psiy, psiz
xx = globalNodalCoordinates
yy = xx.copy()
zz = xx.copy()
X, Y, Z = meshgrid2(xx,yy,zz)
psixyz = (1/np.sqrt(np.pi))*np.exp(-np.sqrt(X**2 + Y**2 + Z**2))
igTensor = tensor.tensor(psixyz)
# generate tensor decomposition of above guess of rank 1
time_tensorStart = time.clock()
rankIG = (1,1,1)
[Psi,Xi] = DTA.DTA(igTensor,rankIG)
time_tensorEnd = time.clock()
print 'time elapsed(s) for DTA of initial guess',time_tensorEnd-time_tensorStart
guessPsix = Psi.u[0].real
guessPsiy = Psi.u[1].real
guessPsiz = Psi.u[2].real
guessLM = 0.2
guessFields = np.concatenate((guessPsix[1:-1],guessPsiy[1:-1],guessPsiz[1:-1]))
#append the initial guess for lagrange multiplier
guessFields = np.append(guessFields,guessLM)
petsc = True
if (petsc == False):
t0 = time.clock()
print 'Method fsolve'
[result,infodict,ier,mesg] = scipy.optimize.fsolve(residual,guessFields,args=(functional),full_output=1,xtol=1.0e-8,maxfev=20000)
print 'Number of Function Evaluations: ',infodict['nfev']
print 'Ground State Energy: ',result[-1]
print 'numberElements ',numberElements
print mesg
t1 = time.clock()
print 'time elapsed(s) for minimization problem',t1-t0
else:
t0 = time.clock()
snes = PETSc.SNES().create()
pde = SeparableHamiltonian(functional)
n = len(guessFields)
F = PETSc.Vec().createSeq(n)
snes.setFunction(pde.residualPetsc,F)
snes.setUseMF()
snes.getKSP().setType('gmres')
snes.setFromOptions()
X = PETSc.Vec().createSeq(n)
pde.formInitGuess(snes, X,guessFields)
snes.solve(None, X)
print X[n-1]
t1 = time.clock()
print 'time elapsed(s) for minimization problem',t1-t0
result = pde.copySolution(X,guessFields)
