def MagneticSetup(Magnetic, Lagrange, u0, p0, CGtol,params):
MO.PrintStr("Preconditioning Magnetic setup",3,"=")
# parameters['linear_algebra_backend'] = 'uBLAS'
if Magnetic.__str__().find("N1curl2") == -1:
C, P = HiptmairSetup.HiptmairMatrixSetupBoundary(Magnetic.mesh(), Magnetic.dim(), Lagrange.dim(),Magnetic.mesh().geometry().dim())
G, P = HiptmairSetup.HiptmairBCsetupBoundary(C,P,Magnetic.mesh())
else:
G = None
P = None
u = TrialFunction(Magnetic)
v = TestFunction(Magnetic)
p = TrialFunction(Lagrange)
q = TestFunction(Lagrange)
def boundary(x, on_boundary):
return on_boundary
bcp = DirichletBC(Lagrange, p0, boundary)
bcu = DirichletBC(Magnetic, u0, boundary)
tic()
ScalarLaplacian, b1 = assemble_system(inner(grad(p),grad(q))*dx,inner(p0,q)*dx,bcp)
VectorLaplacian, b2 = assemble_system(inner(grad(p),grad(q))*dx+inner(p,q)*dx,inner(p0,q)*dx,bcp)
del b1, b2
print ("{:40}").format("Hiptmair Laplacians BC assembled, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
tic()
VectorLaplacian = CP.Assemble(VectorLaplacian)
ScalarLaplacian = CP.Assemble(ScalarLaplacian)
print ("{:40}").format("PETSc Laplacians assembled, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
tic()
if params[0] == 0:
CurlCurlShift, b2 = assemble_system(params[1]*inner(curl(u),curl(v))*dx+inner(u,v)*dx,inner(u0,v)*dx,bcu)
else:
CurlCurlShift, b2 = assemble_system(params[0]*params[1]*inner(curl(u),curl(v))*dx+inner(u,v)*dx,inner(u0,v)*dx,bcu)
CurlCurlShift = CP.Assemble(CurlCurlShift)
print ("{:40}").format("Shifted Curl-Curl assembled, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
tic()
kspVector, kspScalar, kspCGScalar, diag = HiptmairSetup.HiptmairKSPsetup(VectorLaplacian, ScalarLaplacian, CurlCurlShift, CGtol)
del VectorLaplacian, ScalarLaplacian
print ("{:40}").format("Hiptmair Setup time:"), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
return [G, P, kspVector, kspScalar, kspCGScalar, diag, CurlCurlShift]
# ksp.setTolerances(1e-6)
ksp.setType('minres')
ksp.setOperators(A)
# OptDB = PETSc.Options()
# OptDB['pc_factor_mat_solver_package'] = 'mumps'
# OptDB["pc_factor_mat_ordering_type"] = "rcm"
pc = ksp.getPC()
pc.setType(PETSc.PC.Type.PYTHON)
ksp.setFromOptions()
CGtol = 1e-2
Hiptmairtol = 1e-3
tic()
kspVector, kspScalar, kspCGScalar, diag = HiptmairSetup.HiptmairKSPsetup(VectorLaplacian, ScalarLaplacian, Prec, CGtol)
del A, VectorLaplacian, ScalarLaplacian
print ("{:40}").format("Hiptmair Setup time:"), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
reshist = {}
def monitor(ksp, its, rnorm):
print rnorm
reshist[its] = rnorm
ksp.setMonitor(monitor)
pc.setPythonContext(MaxwellPrecond.Hiptmair(W, kspScalar, kspCGScalar, kspVector, G, P, Prec,Hiptmairtol))
scale = b.norm()
b = b/scale
start_time = time.time()
ksp.solve(b, x)
def MagneticSetup(Magnetic, Lagrange, u0, p0, CGtol):
MO.PrintStr("Preconditioning Magnetic setup", 3, "=")
parameters['linear_algebra_backend'] = 'uBLAS'
C, P = HiptmairSetup.HiptmairMatrixSetupBoundary(
Magnetic.mesh(), Magnetic.dim(), Lagrange.dim(),
Magnetic.mesh().geometry().dim())
G, P = HiptmairSetup.HiptmairBCsetupBoundary(C, P, Magnetic.mesh())
u = TrialFunction(Magnetic)
v = TestFunction(Magnetic)
p = TrialFunction(Lagrange)
q = TestFunction(Lagrange)
def boundary(x, on_boundary):
return on_boundary
bcp = DirichletBC(Lagrange, p0, boundary)
bcu = DirichletBC(Magnetic, u0, boundary)
tic()
ScalarLaplacian, b1 = assemble_system(
inner(grad(p), grad(q)) * dx,
inner(p0, q) * dx, bcp)
VectorLaplacian, b2 = assemble_system(
inner(grad(p), grad(q)) * dx + inner(p, q) * dx,
inner(p0, q) * dx, bcp)
del b1, b2
print("{:40}"
).format("Hiptmair Laplacians BC assembled, time: "), " ==> ", (
"{:4f}").format(
toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
tic()
VectorLaplacian = PETSc.Mat().createAIJ(
size=VectorLaplacian.sparray().shape,
csr=(VectorLaplacian.sparray().indptr,
VectorLaplacian.sparray().indices,
VectorLaplacian.sparray().data))
ScalarLaplacian = PETSc.Mat().createAIJ(
size=ScalarLaplacian.sparray().shape,
csr=(ScalarLaplacian.sparray().indptr,
ScalarLaplacian.sparray().indices,
ScalarLaplacian.sparray().data))
print("{:40}").format("PETSc Laplacians assembled, time: "), " ==> ", (
"{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
tic()
CurlCurlShift, b2 = assemble_system(
inner(curl(u), curl(v)) * dx + inner(u, v) * dx,
inner(u0, v) * dx, bcu)
CurlCurlShift = PETSc.Mat().createAIJ(size=CurlCurlShift.sparray().shape,
csr=(CurlCurlShift.sparray().indptr,
CurlCurlShift.sparray().indices,
CurlCurlShift.sparray().data))
print("{:40}").format("Shifted Curl-Curl assembled, time: "), " ==> ", (
"{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
tic()
kspVector, kspScalar, kspCGScalar, diag = HiptmairSetup.HiptmairKSPsetup(
VectorLaplacian, ScalarLaplacian, CurlCurlShift, CGtol)
del VectorLaplacian, ScalarLaplacian
print("{:40}").format("Hiptmair Setup time:"), " ==> ", ("{:4f}").format(
toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
return [G, P, kspVector, kspScalar, kspCGScalar, diag, CurlCurlShift]
VectorLaplacian.sparray().indices,
VectorLaplacian.sparray().data))
ScalarLaplacian = PETSc.Mat().createAIJ(
size=ScalarLaplacian.sparray().shape,
csr=(ScalarLaplacian.sparray().indptr,
ScalarLaplacian.sparray().indices,
ScalarLaplacian.sparray().data))
print "PETSc Laplacians assembled, time: ", toc()
ksp = PETSc.KSP().create()
ksp.setTolerances(1e-6)
ksp.setType('cg')
ksp.setOperators(A, A)
pc = ksp.getPC()
pc.setType(PETSc.PC.Type.PYTHON)
kspVector, kspScalar, diag = HiptmairSetup.HiptmairKSPsetup(
VectorLaplacian, ScalarLaplacian, A)
del A, VectorLaplacian, ScalarLaplacian
pc.setPythonContext(
HiptmairPrecond.GSvector(G, P, kspVector, kspScalar, diag))
scale = b.norm()
b = b / scale
tic()
ksp.solve(b, x)
TimeSave[xx - 1] = toc()
x = x * scale
print ksp.its
print TimeSave[xx - 1]
ItsSave[xx - 1] = ksp.its
print " \n\n\n\n"
import pandas as pd