def diagonal_block(context,layers,layer_id,impedance):
"""Create a diagonal block associated with a given layer_id
"""
plc = layers[layer_id]['spaces']['l']
pwc = layers[layer_id]['spaces']['c']
k = layers[layer_id]['k']
kappa = layers[layer_id]['kappa']
if layer_id == 0:
I_00 = lib.createIdentityOperator(context,plc,pwc,plc,label="I00")
I_01 = lib.createIdentityOperator(context,pwc,pwc,plc,label="I01")
I_10 = lib.createIdentityOperator(context,plc,plc,pwc,label="I10")
K = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,plc,plc,pwc,k,label="K10")
S = 1./kappa*lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,pwc,plc,pwc,k,label="S11")
return lib.createBlockedBoundaryOperator(context,[[I_00,impedance*I_01],[-.5*I_10-K,S]])
else:
kf = layers[layers[layer_id]['father']]['k']
kappaf = layers[layers[layer_id]['father']]['kappa']
DD = (-kappaf*lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(context,plc,pwc,plc,kf,label="Df"+str(layer_id)+"_"+str(layer_id))
-kappa*lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(context,plc,pwc,plc,k,label="D"+str(layer_id)+"_"+str(layer_id)))
TT = (-lib.createModifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(context,pwc,pwc,plc,kf,label="Tf"+str(layer_id)+"_"+str(layer_id))
-lib.createModifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(context,pwc,pwc,plc,k,label="T"+str(layer_id)+"_"+str(layer_id)))
KK = (lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,plc,plc,pwc,kf,label="Kf"+str(layer_id)+"_"+str(layer_id))
+lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,plc,plc,pwc,k,label="K"+str(layer_id)+"_"+str(layer_id)))
SS = (-1./kappaf*lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,pwc,plc,pwc,kf,label="Sf"+str(layer_id)+"_"+str(layer_id))
-1./kappa*lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,pwc,plc,pwc,k,label="S"+str(layer_id)+"_"+str(layer_id)))
return lib.createBlockedBoundaryOperator(context,[[DD,TT],[KK,SS]])
def off_diagonal_block_same_layer(context,layers,id1,id2):
"""Off-diagonal interaction between two different layers. Returns a tuple of two operators.
"""
pwc_id1 = layers[id1]['spaces']['c']
plc_id1 = layers[id1]['spaces']['l']
pwc_id2 = layers[id2]['spaces']['c']
plc_id2 = layers[id2]['spaces']['l']
k = layers[layers[id1]['father']]['k']
kappa = layers[layers[id1]['father']]['kappa']
D = kappa*lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(context,plc_id2,pwc_id1,plc_id1,k)
T = lib.createModifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(context,pwc_id2,pwc_id1,plc_id1,k)
K = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,plc_id2,plc_id1,pwc_id1,k)
S = 1./kappa*lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,pwc_id2,plc_id1,pwc_id1,k)
D2 = lib.adjoint(D,pwc_id2)
T2 = lib.adjoint(K,pwc_id2)
K2 = lib.adjoint(T,plc_id2)
S2 = lib.adjoint(S,plc_id2)
op1 = lib.createBlockedBoundaryOperator(context,[[-D,-T],[K,-S]])
op2 = lib.createBlockedBoundaryOperator(context,[[-D2,-T2],[K2,-S2]])
return (op1,op2)
def off_diagonal_block_same_layer(context, layers, id1, id2):
"""Off-diagonal interaction between two different layers. Returns a tuple of two operators.
"""
pwc_id1 = layers[id1]['spaces']['c']
plc_id1 = layers[id1]['spaces']['l']
pwc_id2 = layers[id2]['spaces']['c']
plc_id2 = layers[id2]['spaces']['l']
k = layers[layers[id1]['father']]['k']
kappa = layers[layers[id1]['father']]['kappa']
D = kappa * lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(
context, plc_id2, pwc_id1, plc_id1, k)
T = lib.createModifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(
context, pwc_id2, pwc_id1, plc_id1, k)
K = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context, plc_id2, plc_id1, pwc_id1, k)
S = 1. / kappa * lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
context, pwc_id2, plc_id1, pwc_id1, k)
D2 = lib.adjoint(D, pwc_id2)
T2 = lib.adjoint(K, pwc_id2)
K2 = lib.adjoint(T, plc_id2)
S2 = lib.adjoint(S, plc_id2)
op1 = lib.createBlockedBoundaryOperator(context, [[-D, -T], [K, -S]])
op2 = lib.createBlockedBoundaryOperator(context, [[-D2, -T2], [K2, -S2]])
return (op1, op2)
def off_diagonal_block_father_son(context,layers,father_id,son_id):
"""Off-diagonal interaction between two different layers. Returns a tuple of two operators.
"""
plc_father = layers[father_id]['spaces']['l']
pwc_father = layers[father_id]['spaces']['c']
plc_son = layers[son_id]['spaces']['l']
pwc_son = layers[son_id]['spaces']['c']
kf = layers[father_id]['k']
kappaf = layers[father_id]['kappa']
if father_id==0:
null_00 = lib.createNullOperator(context,plc_son,pwc_father,plc_father,label="Null_00")
null_01 = lib.createNullOperator(context,pwc_son,pwc_father,plc_father,label="Null_01")
Kf = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,plc_son,plc_father,pwc_father,kf,label="Kf0_"+str(son_id))
Sf = 1./kappaf*lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,pwc_son,plc_father,pwc_father,kf,label="Sf0_"+str(son_id))
op_father_son = lib.createBlockedBoundaryOperator(context,[[null_00,null_01],[Kf,-Sf]])
Ds = kappaf*lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(context,plc_father,pwc_son,plc_son,kf,label="Ds"+str(son_id)+"_0")
Ts = lib.adjoint(Kf,pwc_son)
Ks = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,plc_father,plc_son,pwc_son,kf,label="Ks"+str(son_id)+"_0")
Ss = lib.adjoint(Sf,plc_son)
op_son_father = lib.createBlockedBoundaryOperator(context,[[Ds,Ts],[-Ks,Ss]])
else:
Df = kappaf*lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(context,plc_son,pwc_father,plc_father,kf)
Tf = lib.createModifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(context,pwc_son,pwc_father,plc_father,kf)
Kf = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,plc_son,plc_father,pwc_father,kf)
Sf = 1./kappaf*lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,pwc_son,plc_father,pwc_father,kf)
op_father_son = lib.createBlockedBoundaryOperator(context,[[Df,Tf],[-Kf,Sf]])
Ds = lib.adjoint(Df,pwc_son)
Ts = lib.adjoint(Kf,pwc_son)
Ks = lib.adjoint(Tf,plc_son)
Ss = lib.adjoint(Sf,plc_son)
op_son_father = lib.createBlockedBoundaryOperator(context,[[Ds,Ts],[-Ks,Ss]])
return (op_father_son,op_son_father)
def solve_bvp(self,wavenumber,rhs):
from scipy.sparse.linalg import gmres
from bempp.tools import RealOperator
self._residuals[wavenumber] = []
def evaluate_residual(res):
self._residuals[wavenumber].append(res)
n = len(rhs[0])
rhs_dual = (self._mass_matrix*rhs[0].reshape(n,1)).ravel()
op_found_in_cache = False
if self._use_cache:
try:
op = self._boundary_operator_cache(wavenumber)
op_found_in_cache = True
except:
pass
if not op_found_in_cache:
pconsts = self._spaces[0]
context = self._context
op = (_bempplib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,pconsts,pconsts,pconsts,wavenumber).weakForm()+
.5*self._mass_matrix)
#prec = _bempplib.acaOperatorApproximateLuInverse(op,self._aca_lu_epsilon)
op = RealOperator(op)
#prec = RealOperator(prec)
if self._use_cache: self._boundary_operator_cache.insert(wavenumber,op)
rhs_dual_real = _np.hstack([_np.real(rhs_dual),_np.imag(rhs_dual)])
sol_real,info = gmres(op,rhs_dual_real,tol=self._gmres_tol,maxiter=self._gmres_max_iter,callback=evaluate_residual)
if info != 0:
raise Exception('GMRES did not converge for wavenumber '+str(wavenumber)+'.')
sol = sol_real[:n]+1j*sol_real[n:]
return [sol.ravel()]
def off_diagonal_block_father_son(context, layers, father_id, son_id):
"""Off-diagonal interaction between two different layers. Returns a tuple of two operators.
"""
plc_father = layers[father_id]['spaces']['l']
pwc_father = layers[father_id]['spaces']['c']
plc_son = layers[son_id]['spaces']['l']
pwc_son = layers[son_id]['spaces']['c']
kf = layers[father_id]['k']
kappaf = layers[father_id]['kappa']
if father_id == 0:
null_00 = lib.createNullOperator(context,
plc_son,
pwc_father,
plc_father,
label="Null_00")
null_01 = lib.createNullOperator(context,
pwc_son,
pwc_father,
plc_father,
label="Null_01")
Kf = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context,
plc_son,
plc_father,
pwc_father,
kf,
label="Kf0_" + str(son_id))
Sf = 1. / kappaf * lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
context,
pwc_son,
plc_father,
pwc_father,
kf,
label="Sf0_" + str(son_id))
op_father_son = lib.createBlockedBoundaryOperator(
context, [[null_00, null_01], [Kf, -Sf]])
Ds = kappaf * lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(
context,
plc_father,
pwc_son,
plc_son,
kf,
label="Ds" + str(son_id) + "_0")
Ts = lib.adjoint(Kf, pwc_son)
Ks = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context,
plc_father,
plc_son,
pwc_son,
kf,
label="Ks" + str(son_id) + "_0")
Ss = lib.adjoint(Sf, plc_son)
op_son_father = lib.createBlockedBoundaryOperator(
context, [[Ds, Ts], [-Ks, Ss]])
else:
Df = kappaf * lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(
context, plc_son, pwc_father, plc_father, kf)
Tf = lib.createModifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(
context, pwc_son, pwc_father, plc_father, kf)
Kf = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context, plc_son, plc_father, pwc_father, kf)
Sf = 1. / kappaf * lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context, pwc_son, plc_father, pwc_father, kf)
op_father_son = lib.createBlockedBoundaryOperator(
context, [[Df, Tf], [-Kf, Sf]])
Ds = lib.adjoint(Df, pwc_son)
Ts = lib.adjoint(Kf, pwc_son)
Ks = lib.adjoint(Tf, plc_son)
Ss = lib.adjoint(Sf, plc_son)
op_son_father = lib.createBlockedBoundaryOperator(
context, [[Ds, Ts], [-Ks, Ss]])
return (op_father_son, op_son_father)
def diagonal_block(context, layers, layer_id, impedance):
"""Create a diagonal block associated with a given layer_id
"""
plc = layers[layer_id]['spaces']['l']
pwc = layers[layer_id]['spaces']['c']
k = layers[layer_id]['k']
kappa = layers[layer_id]['kappa']
if layer_id == 0:
I_00 = lib.createIdentityOperator(context, plc, pwc, plc, label="I00")
I_01 = lib.createIdentityOperator(context, pwc, pwc, plc, label="I01")
I_10 = lib.createIdentityOperator(context, plc, plc, pwc, label="I10")
K = lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context, plc, plc, pwc, k, label="K10")
S = 1. / kappa * lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
context, pwc, plc, pwc, k, label="S11")
return lib.createBlockedBoundaryOperator(
context, [[I_00, impedance * I_01], [-.5 * I_10 - K, S]])
else:
kf = layers[layers[layer_id]['father']]['k']
kappaf = layers[layers[layer_id]['father']]['kappa']
DD = (
-kappaf *
lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(
context,
plc,
pwc,
plc,
kf,
label="Df" + str(layer_id) + "_" + str(layer_id)) -
kappa * lib.createModifiedHelmholtz3dHypersingularBoundaryOperator(
context,
plc,
pwc,
plc,
k,
label="D" + str(layer_id) + "_" + str(layer_id)))
TT = (-lib.createModifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(
context,
pwc,
pwc,
plc,
kf,
label="Tf" + str(layer_id) + "_" + str(layer_id)) -
lib.createModifiedHelmholtz3dAdjointDoubleLayerBoundaryOperator(
context,
pwc,
pwc,
plc,
k,
label="T" + str(layer_id) + "_" + str(layer_id)))
KK = (lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context,
plc,
plc,
pwc,
kf,
label="Kf" + str(layer_id) + "_" + str(layer_id)) +
lib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context,
plc,
plc,
pwc,
k,
label="K" + str(layer_id) + "_" + str(layer_id)))
SS = (-1. / kappaf *
lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
context,
pwc,
plc,
pwc,
kf,
label="Sf" + str(layer_id) + "_" + str(layer_id)) - 1. /
kappa * lib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
context,
pwc,
plc,
pwc,
k,
label="S" + str(layer_id) + "_" + str(layer_id)))
return lib.createBlockedBoundaryOperator(context, [[DD, TT], [KK, SS]])
options = blib.createAssemblyOptions()
aca_options = blib.createAcaOptions()
aca_options.eps = 1E-5
options.switchToAca(aca_options)
context = blib.createContext(strategy, options)
# Create the spaces
sphere1_plc = blib.createPiecewiseLinearContinuousScalarSpace(context, sphere1)
sphere2_plc = blib.createPiecewiseLinearContinuousScalarSpace(context, sphere2)
sphere3_plc = blib.createPiecewiseLinearContinuousScalarSpace(context, sphere3)
# Now create the operators
slp11 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
context, sphere1_plc, sphere1_plc, sphere1_plc, w1)
dlp11 = blib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context, sphere1_plc, sphere1_plc, sphere1_plc, w1)
id11 = blib.createIdentityOperator(context, sphere1_plc, sphere1_plc,
sphere1_plc)
slp22_w1 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
context, sphere2_plc, sphere2_plc, sphere2_plc, w1)
dlp22_w1 = blib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context, sphere2_plc, sphere2_plc, sphere2_plc, w1)
slp22_w2 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
context, sphere2_plc, sphere2_plc, sphere2_plc, w2)
dlp22_w2 = blib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(
context, sphere2_plc, sphere2_plc, sphere2_plc, w2)
id22 = blib.createIdentityOperator(context, sphere2_plc, sphere2_plc,
sphere2_plc)
slp12 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(
options = blib.createAssemblyOptions() aca_options = blib.createAcaOptions() aca_options.eps=1E-5 options.switchToAca(aca_options) context = blib.createContext(strategy, options) # Create the spaces sphere1_plc = blib.createPiecewiseLinearContinuousScalarSpace(context,sphere1) sphere2_plc = blib.createPiecewiseLinearContinuousScalarSpace(context,sphere2) sphere3_plc = blib.createPiecewiseLinearContinuousScalarSpace(context,sphere3) # Now create the operators slp11 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,sphere1_plc,sphere1_plc,sphere1_plc,w1) dlp11 = blib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,sphere1_plc,sphere1_plc,sphere1_plc,w1) id11 = blib.createIdentityOperator(context,sphere1_plc,sphere1_plc,sphere1_plc) slp22_w1 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,sphere2_plc,sphere2_plc,sphere2_plc,w1) dlp22_w1 = blib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,sphere2_plc,sphere2_plc,sphere2_plc,w1) slp22_w2 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,sphere2_plc,sphere2_plc,sphere2_plc,w2) dlp22_w2 = blib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,sphere2_plc,sphere2_plc,sphere2_plc,w2) id22 = blib.createIdentityOperator(context,sphere2_plc,sphere2_plc,sphere2_plc) slp12 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,sphere2_plc,sphere1_plc,sphere1_plc,w1) dlp12 = blib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,sphere2_plc,sphere1_plc,sphere1_plc,w1) slp21 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,sphere1_plc,sphere2_plc,sphere2_plc,w1) dlp21 = blib.createModifiedHelmholtz3dDoubleLayerBoundaryOperator(context,sphere1_plc,sphere2_plc,sphere2_plc,w1) slp23 = blib.createModifiedHelmholtz3dSingleLayerBoundaryOperator(context,sphere3_plc,sphere2_plc,sphere2_plc,w2)
