def PGsolver(world, ABase, f,k):
NWorldFine = world.NWorldFine
NWorldCoarse = world.NWorldCoarse
NCoarseElement = world.NCoarseElement
boundaryConditions = world.boundaryConditions
NpFine = np.prod(NWorldFine+1)
NpCoarse = np.prod(NWorldCoarse+1)
#interpolant
IPatchGenerator = lambda i, N: interp.L2ProjectionPatchMatrix(i, N, NWorldCoarse, NCoarseElement, boundaryConditions)
#Coefficient (need flatten form)
aCoef = coef.coefficientFine(NWorldCoarse, NCoarseElement, ABase)
pglod = pg_pert.PerturbedPetrovGalerkinLOD(aCoef, world, k, IPatchGenerator, 0)
pglod.originCorrectors(clearFineQuantities=False)
KFull = pglod.assembleMsStiffnessMatrix()
MFull = fem.assemblePatchMatrix(NWorldCoarse, world.MLocCoarse)
free = util.interiorpIndexMap(NWorldCoarse)
bFull = MFull*f
KFree = KFull[free][:,free]
bFree = bFull[free]
xFree = sparse.linalg.spsolve(KFree, bFree)
basis = fem.assembleProlongationMatrix(NWorldCoarse, NCoarseElement)
basisCorrectors = pglod.assembleBasisCorrectors()
modifiedBasis = basis - basisCorrectors
xFull = np.zeros(NpCoarse)
xFull[free] = xFree
uLodCoarse = xFull
uLodFine = modifiedBasis*xFull
return uLodCoarse, uLodFine
NWorldCoarse = world.NWorldCoarse
NCoarseElement = world.NCoarseElement
boundaryConditions = world.boundaryConditions
NpFine = np.prod(NWorldFine+1)
NpCoarse = np.prod(NWorldCoarse+1)
#interpolant
IPatchGenerator = lambda i, N: interp.L2ProjectionPatchMatrix(i, N, NWorldCoarse, NCoarseElement, boundaryConditions)
#old Coefficient (need flatten form)
Aold = coef.coefficientFine(NWorldCoarse, NCoarseElement, ABase)
for k in range(1,6):
print(('<<<<<<<<<<<<<<<< ' + str(k) + ' >>>>>>>>>>>>>>>>'))
pglod = pg_pert.PerturbedPetrovGalerkinLOD(Aold, world, k, IPatchGenerator, 1)
pglod.originCorrectors(clearFineQuantities=False)
#new Coefficient
ANew = R2.flatten()
Anew = coef.coefficientFine(NWorldCoarse, NCoarseElement, ANew)
# tolerance = 0
vis, eps = pglod.updateCorrectors(Anew, 0,clearFineQuantities=False, Computing = False)
elemente = np.arange(np.prod(NWorldCoarse))
if k==5:
plt.figure("Error indicator")
plt.plot(elemente,eps,label="e_{u,T}")
plt.ylabel('$e_{u,T}$')
#fine-fem
f_fine = np.ones(NpFine)
uFineFem, AFine, MFine = femsolver.solveFine(world, ABase, f_fine, None,
boundaryConditions)
#PGLOD
#interpolant
IPatchGenerator = lambda i, N: interp.L2ProjectionPatchMatrix(
i, N, NWorldCoarse, NCoarseElement, boundaryConditions)
#Coefficient (need flatten form)
aCoef = coef.coefficientFine(NWorldCoarse, NCoarseElement, ABase)
k = 4
pglod = pg_pert.PerturbedPetrovGalerkinLOD(aCoef, world, k, IPatchGenerator, 2)
pglod.originCorrectors(clearFineQuantities=False)
KFull = pglod.assembleMsStiffnessMatrix()
MFull = fem.assemblePatchMatrix(NWorldCoarse, world.MLocCoarse)
free = util.interiorpIndexMap(NWorldCoarse)
bFull = MFull * f
KFree = KFull[free][:, free]
bFree = bFull[free]
xFree = sparse.linalg.spsolve(KFree, bFree)
basis = fem.assembleProlongationMatrix(NWorldCoarse, NCoarseElement)
basisCorrectors = pglod.assembleBasisCorrectors()
