def Mult(self, x, y):
globals()['max_char_speed'] = 0.;
num_equation = globals()['num_equation']
# 1. Create the vector z with the face terms -<F.n(u), [w]>.
self.A.Mult(x, self.z);
# 2. Add the element terms.
# i. computing the flux approximately as a grid function by interpolating
# at the solution nodes.
# ii. multiplying this grid function by a (constant) mixed bilinear form for
# each of the num_equation, computing (F(u), grad(w)) for each equation.
xmat = mfem.DenseMatrix(x.GetData(), self.vfes.GetNDofs(), num_equation)
self.GetFlux(xmat, self.flux)
for k in range(num_equation):
fk = mfem.Vector(self.flux[k].GetData(), self.dim * self.vfes.GetNDofs())
o = k * self.vfes.GetNDofs()
zk = self.z[o: o+self.vfes.GetNDofs()]
self.Aflux.AddMult(fk, zk)
# 3. Multiply element-wise by the inverse mass matrices.
zval = mfem.Vector()
vdofs = mfem.intArray()
dof = self.vfes.GetFE(0).GetDof()
zmat = mfem.DenseMatrix()
ymat = mfem.DenseMatrix(dof, num_equation)
for i in range(self.vfes.GetNE()):
# Return the vdofs ordered byNODES
vdofs = mfem.intArray(self.vfes.GetElementVDofs(i))
self.z.GetSubVector(vdofs, zval)
zmat.UseExternalData(zval.GetData(), dof, num_equation)
mfem.Mult(self.Me_inv[i], zmat, ymat);
y.SetSubVector(vdofs, ymat.GetData())
def AssembleElementMatrix2(self, trial_fe, test_fe, Tr, elmat):
# Assemble the form (vec(v), grad(w))
# Trial space = vector L2 space (mesh dim)
# Test space = scalar L2 space
dof_trial = trial_fe.GetDof()
dof_test = test_fe.GetDof()
dim = trial_fe.GetDim()
self.shape.SetSize(dof_trial)
self.dshapedr.SetSize(dof_test, dim)
self.dshapedx.SetSize(dof_test, dim)
elmat.SetSize(dof_test, dof_trial * dim)
elmat.Assign(0.0)
maxorder = max(trial_fe.GetOrder(), test_fe.GetOrder())
intorder = 2 * maxorder
ir = mfem.IntRules.Get(trial_fe.GetGeomType(), intorder)
for i in range(ir.GetNPoints()):
ip = ir.IntPoint(i)
# Calculate the shape functions
trial_fe.CalcShape(ip, self.shape)
self.shape *= ip.weight
# Compute the physical gradients of the test functions
Tr.SetIntPoint(ip)
test_fe.CalcDShape(ip, self.dshapedr)
mfem.Mult(self.dshapedr, Tr.AdjugateJacobian(), self.dshapedx)
for d in range(dim):
for j in range(dof_test):
for k in range(dof_trial):
elmat[j, k + d *
dof_trial] += self.shape[k] * self.dshapedx[j, d]
bVarf.Finalize()
B = bVarf.SpMat()
B *= -1
BT = mfem.Transpose(B)
darcyOp = mfem.BlockOperator(block_offsets)
darcyOp.SetBlock(0, 0, M)
darcyOp.SetBlock(0, 1, BT)
darcyOp.SetBlock(1, 0, B)
MinvBt = mfem.Transpose(B)
Md = mfem.Vector(M.Height())
M.GetDiag(Md)
for i in range(Md.Size()):
MinvBt.ScaleRow(i, 1 / Md[i])
S = mfem.Mult(B, MinvBt)
invM = mfem.DSmoother(M)
invS = mfem.GSSmoother(S)
invM.iterative_mode = False
invS.iterative_mode = False
darcyPrec = mfem.BlockDiagonalPreconditioner(block_offsets)
darcyPrec.SetDiagonalBlock(0, invM)
darcyPrec.SetDiagonalBlock(1, invS)
maxIter = 500
rtol = 1e-6
atol = 1e-10
stime = clock()