def initialize(self,evaluation_points=None):
self._evaluation_points = evaluation_points
self._space = _bempplib.createRaviartThomas0VectorSpace(self._context,self._grid)
self._identity = _bempplib.createMaxwell3dIdentityOperator(self._context,self._space,self._space,self._space).weakForm()
if self._operator_cache:
self._boundary_operator_cache = _tools.OperatorCache(self._operator_cache_tol)
self._potential_operator_cache = _tools.OperatorCache(self._operator_cache_tol)
def solve_bvp(self,wave_number,rhs):
self._residuals[wave_number] = []
def evaluate_residual(res):
self._residuals[wave_number].append(res)
k_ext = 1.0j*wave_number * _np.sqrt(self._eps_ext * self._mu_ext)
k_int = 1.0j*wave_number * _np.sqrt(self._eps_int * self._mu_int)
rho = (k_int * self._mu_ext) / (k_ext * self._mu_int)
op_found_in_cache = False
if self._operator_cache:
try:
op,prec = self._boundary_operator_cache(wave_number)
op_found_in_cache = True
except:
pass
if not op_found_in_cache:
context = self._context
space = self._space
slpOpExt = _bempplib.createMaxwell3dSingleLayerBoundaryOperator(
context, space, space, space, k_ext, "SLP_ext")
dlpOpExt = _bempplib.createMaxwell3dDoubleLayerBoundaryOperator(
context, space, space, space, k_ext, "DLP_ext")
slpOpInt = _bempplib.createMaxwell3dSingleLayerBoundaryOperator(
context, space, space, space, k_int, "SLP_int")
dlpOpInt = _bempplib.createMaxwell3dDoubleLayerBoundaryOperator(
context, space, space, space, k_int, "DLP_int")
idOp = _bempplib.createMaxwell3dIdentityOperator(
context, space, space, space, "Id")
# Form the left- and right-hand-side operators
lhsOp00 = -(slpOpExt + rho * slpOpInt)
lhsOp01 = lhsOp10 = dlpOpExt + dlpOpInt
lhsOp11 = slpOpExt + (1. / rho) * slpOpInt
lhsOp = _bempplib.createBlockedBoundaryOperator(
context, [[lhsOp00, lhsOp01], [lhsOp10, lhsOp11]])
precTol = self._aca_lu_delta
invLhsOp00 = _bempplib.acaOperatorApproximateLuInverse(
lhsOp00.weakForm().asDiscreteAcaBoundaryOperator(), precTol)
invLhsOp11 = _bempplib.acaOperatorApproximateLuInverse(
lhsOp11.weakForm().asDiscreteAcaBoundaryOperator(), precTol)
prec = _bempplib.discreteBlockDiagonalPreconditioner([invLhsOp00, invLhsOp11])
op = lhsOp
# Construct the grid functions representing the traces of the incident field
incDirichletTrace = _bempplib.createGridFunction(
context, space, space, coefficients=rhs[0])
incNeumannTrace = 1./(1j*k_ext)*_bempplib.createGridFunction(
context, space, space, coefficients=rhs[1])
self._inc_dirichlet_traces[wave_number] = incDirichletTrace
self._inc_neumann_traces[wave_number] = incNeumannTrace
# Construct the right-hand-side grid function
rhs = [idOp * incNeumannTrace, idOp * incDirichletTrace]
solver = _bempplib.createDefaultIterativeSolver(op)
solver.initializeSolver(_bempplib.defaultGmresParameterList(self._gmres_tol), prec)
# Solve the equation
solution = solver.solve(rhs)
print solution.solverMessage()
# Extract the solution components in the form of grid functions
extDirichletTrace = solution.gridFunction(0)
extNeumannTrace = solution.gridFunction(1)
if self._operator_cache: self._boundary_operator_cache.insert(wave_number,(op,prec))
scatt_dirichlet_ext_fun = extDirichletTrace - self._inc_dirichlet_traces[wave_number]
print "Dirichlet Error "+str(scatt_dirichlet_ext_fun.L2Norm()/extDirichletTrace.L2Norm())
scatt_neumann_ext_fun = extNeumannTrace - self._inc_neumann_traces[wave_number]
print "Neumann Error "+str(scatt_neumann_ext_fun.L2Norm()/extNeumannTrace.L2Norm())
return [extDirichletTrace.coefficients(),extNeumannTrace.coefficients()]