def FluidLinearSetup(Pressure,mu):
MO.PrintStr("Preconditioning Fluid linear setup",3,"=","\n\n")
parameters['linear_algebra_backend'] = 'uBLAS'
p = TrialFunction(Pressure)
q = TestFunction(Pressure)
N = FacetNormal(Pressure.mesh())
h = CellSize(Pressure.mesh())
h_avg =avg(h)
alpha = 10.0
gamma =10.0
tic()
if Pressure.__str__().find("CG") == -1:
L = assemble(mu*(inner(grad(q), grad(p))*dx(Pressure.mesh()) \
- inner(avg(grad(q)), outer(p('+'),N('+'))+outer(p('-'),N('-')))*dS(Pressure.mesh()) \
- inner(outer(q('+'),N('+'))+outer(q('-'),N('-')), avg(grad(p)))*dS(Pressure.mesh()) \
+ alpha/h_avg*inner(outer(q('+'),N('+'))+outer(q('-'),N('-')),outer(p('+'),N('+'))+outer(p('-'),N('-')))*dS(Pressure.mesh()) \
- inner(outer(q,N), grad(p))*ds(Pressure.mesh()) \
- inner(grad(q), outer(p,N))*ds(Pressure.mesh()) \
+ gamma/h*inner(q,p)*ds(Pressure.mesh())))
else:
L = assemble(mu*(inner(grad(q), grad(p))*dx(Pressure.mesh())))
L = PETSc.Mat().createAIJ(size=L.sparray().shape,csr=(L.sparray().indptr, L.sparray().indices, L.sparray().data))
print ("{:40}").format("DG scalar Laplacian assemble, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
tic()
Q = assemble((1./mu)*inner(p,q)*dx)
Q = PETSc.Mat().createAIJ(size=Q.sparray().shape,csr=(Q.sparray().indptr, Q.sparray().indices, Q.sparray().data))
print ("{:40}").format("DG scalar mass matrix assemble, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
tic()
kspA, ksp = NSprecondSetup.PCDKSPlinear(Q, L)
print ("{:40}").format("Linear fluid precond setup, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
return [kspA,ksp], [L,Q]
def FluidLinearSetup(Pressure, mu, mesh):
MO.PrintStr("Preconditioning Fluid linear setup", 3, "=", "\n\n")
# parameters['linear_algebra_backend'] = 'uBLAS'
q = TrialFunction(Pressure)
p = TestFunction(Pressure)
tic()
L = assemble(mu * inner(grad(q), grad(p)) * dx,
form_compiler_parameters=ffc_options)
L = CP.Assemble(L)
print("{:40}").format("CG scalar Laplacian assemble, time: "), " ==> ", (
"{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
tic()
Q = assemble((1. / mu) * inner(p, q) * dx,
form_compiler_parameters=ffc_options)
Q = CP.Assemble(Q)
print(
"{:40}").format("DG scalar mass matrix assemble, time: "), " ==> ", (
"{:4f}").format(
toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
tic()
kspL, kspQ = NSprecondSetup.PCDKSPlinear(L, Q)
print("{:40}").format("Linear fluid precond setup, time: "), " ==> ", (
"{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(
time.strftime('%X %x %Z')[0:5])
return [kspL, kspQ], [L, Q]
def FluidLinearSetup(Pressure,mu,mesh, boundaries, domains):
MO.PrintStr("Preconditioning Fluid linear setup",3,"=","\n\n")
# parameters['linear_algebra_backend'] = 'uBLAS'
q = TrialFunction(Pressure)
p = TestFunction(Pressure)
dx = Measure('dx', domain=mesh, subdomain_data=domains)
ds = Measure('ds', domain=mesh, subdomain_data=boundaries)
N = FacetNormal(Pressure.mesh())
h = CellSize(Pressure.mesh())
h_avg =avg(h)
alpha = 10.0
gamma =10.0
tic()
if Pressure.__str__().find("CG") == -1:
L = assemble(mu*(jump(q)*jump(p)*dx(Pressure.mesh())))
else:
L = assemble(mu*(inner(grad(q), grad(p))*dx(Pressure.mesh())))# + inner(grad(q),N)*p*ds(2))
L = CP.Assemble(L)
print ("{:40}").format("CG scalar Laplacian assemble, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
tic()
Q = assemble((1./mu)*inner(p,q)*dx)
Q = CP.Assemble(Q)
print ("{:40}").format("DG scalar mass matrix assemble, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
tic()
kspA, ksp = NSprecondSetup.PCDKSPlinear(Q, L)
print ("{:40}").format("Linear fluid precond setup, time: "), " ==> ",("{:4f}").format(toc()), ("{:9}").format(" time: "), ("{:4}").format(time.strftime('%X %x %Z')[0:5])
return [kspA,ksp], [L,Q]
print MU
Mass = assemble(inner(pQ, qQ) * dx)
L = MU * (inner(grad(qQ), grad(pQ)) * dx(mesh))
# O = - dot(u_k, n)*pQ('+')*qQ*ds(mesh) - dot(u_k, n)*(pQ('+') - pQ('-'))*qQ('-')*dS(mesh)
pp = Function(Q)
fp = MU * inner(grad(qQ), grad(pQ)) * dx(mesh) + inner(
(u_k[0] * grad(pQ)[0] + u_k[1] * grad(pQ)[1]), qQ) * dx(mesh) + (
1 / 2) * div(u_k) * inner(pQ, qQ) * dx(mesh) - (1 / 2) * (
u_k[0] * n[0] + u_k[1] * n[1]) * inner(pQ, qQ) * ds(mesh)
Laplacian = assemble(L)
Laplacian = CP.Assemble(Laplacian)
Mass = CP.Assemble(Mass)
kspA, kspQ = NSprecondSetup.PCDKSPlinear(Mass, Laplacian)
u_is = PETSc.IS().createGeneral(range(W.sub(0).dim()))
p_is = PETSc.IS().createGeneral(
range(W.sub(0).dim(),
W.sub(0).dim() + W.sub(1).dim()))
# print L
SolutionTime = 0
while eps > tol and iter < maxiter:
iter += 1
x = Function(W)
uu = Function(W)
tic()
AA, bb = assemble_system(a, L1 - RHSform, bcs)
A, b = CP.Assemble(AA, bb)
