def foo():
NN = 2 * 4
parameters["form_compiler"]["quadrature_degree"] = -1
nn = int(2**(NN))
omega = 1
mesh = UnitSquareMesh(nn, nn)
order = 1
parameters['reorder_dofs_serial'] = False
Magnetic = FunctionSpace(mesh, "N1curl", order)
Lagrange = FunctionSpace(mesh, "CG", order)
W = Magnetic * Lagrange
Magnetic = None
#del Magnetic, Lagrange
Vdim = W.sub(0).dim()
Qdim = W.sub(1).dim()
Wdim = W.dim()
print "\n\nV: ", Vdim, "Q: ", Qdim, "W: ", Wdim, "\n\n"
parameters['reorder_dofs_serial'] = False
parameters['linear_algebra_backend'] = 'uBLAS'
dim = 2
#@print_memory
G, P = HiptmairSetup.HiptmairMatrixSetupBoundary(mesh,
W.sub(0).dim(),
W.sub(1).dim(), dim)
G, P = HiptmairSetup.HiptmairBCsetupBoundary(G, P, mesh)
a = 1
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]
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]
Magnetic = FunctionSpace(mesh, "N1curl", order)
Lagrange = FunctionSpace(mesh, "CG", order)
W = Magnetic*Lagrange
print ("{:40}").format("Function space setup, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
Vdim[xx-1] = Magnetic.dim()
Qdim[xx-1] = Lagrange.dim()
Wdim[xx-1] = W.dim()
print "\n\nV: ",Vdim[xx-1],"Q: ",Qdim[xx-1],"W: ",Wdim[xx-1],"\n\n"
parameters['reorder_dofs_serial'] = False
DimSave[xx-1] = Magnetic.dim()
print Magnetic.dim()
parameters['linear_algebra_backend'] = 'uBLAS'
C, P = HiptmairSetup.HiptmairMatrixSetupBoundary(mesh, Magnetic.dim(), Lagrange.dim(),dim)
G, P = HiptmairSetup.HiptmairBCsetupBoundary(C,P,mesh)
def boundary(x, on_boundary):
return on_boundary
bcb = DirichletBC(W.sub(0),u0, boundary)
bcr = DirichletBC(W.sub(1), p0, boundary)
bcs = [bcb,bcr]
(v,q) = TestFunctions(W)
(u,p) = TrialFunctions(W)
a11 = inner(curl(u),curl(v))*dx
a12 = inner(v,grad(p))*dx