def search():
k = 2
g = pcb.FourierHankel([-1,-1], [0], k)
bdytag = "BDY"
bnddata={bdytag:pcbd.dirichlet(g)}
bounds=np.array([[0,1],[0,1]],dtype='d')
npoints=np.array([200,200])
gmresits = []
params = []
conds = []
n = 6
meshinfo = tum.regularsquaremeshinfo(n, bdytag)
topology = pmm.Topology(meshinfo)
partition = pmm.BespokePartition(meshinfo, topology, lambda n: np.arange(meshinfo.nelements).reshape(n, -1))
mesh = pmm.MeshView(meshinfo, topology, partition)
mesh = pmo.overlappingPartitions(mesh)
problem = psp.Problem(mesh,k,bnddata)
npw = 7
basisrule = pcb.planeWaveBases(2,k,npw)
basisrule = pcbr.ReferenceBasisRule(pcbr.Dubiner(0))
nquad = 4
# mesh = pmo.overlappingPartitions(pmo.overlappingPartitions(mesh))
# problem = psp.Problem(mesh, k, bnddata)
dovolumes = True
compinfo = psc.ComputationInfo(problem, basisrule, nquad)
computation = psc.Computation(compinfo, pcp.HelmholtzSystem)
sold = computation.solution(psc.DirectOperator(), psc.DirectSolver(), dovolumes=dovolumes)
pom.output2dsoln(bounds, sold, npoints, show = False)
for x in np.arange(-10,10,2):#, 1E-6, 1]:# 1j, -0.1, -0.1j]:
for y in np.arange(-10,10,2):
q = x + 1j * y
perturbation = GeneralRobinPerturbation(compinfo, q)
op = psd.GeneralSchwarzOperator(PerturbedSchwarzWorker(perturbation, mesh))
callback = psi.ItCounter(100)
solver = psi.GMRESSolver('ctor', callback)
sol = computation.solution(op, solver, dovolumes=dovolumes)
nn = len(op.rhs())
M = np.hstack([op.multiply(xx).reshape(-1,1) for xx in np.eye(nn)])
conds.append(np.linalg.cond(M))
params.append(q)
gmresits.append(solver.callback.n)
print conds
print params
print gmresits
def planewavesoln(problem, npw):
k = problem.k
pw = pcb.planeWaveBases(2, k, nplanewaves=npw)
h = 4.0/40
alpha = 1 / (k*h)
beta = np.min([(k*h), 1])
computation = psc.Computation(problem, pw, pcp.HelmholtzSystem, 15, alpha = alpha, beta = beta)
solution = computation.solution(psc.DirectSolver().solve, dovolumes=False)
bounds=array([[-2,2],[-2,2]],dtype='d')
npoints=array([200,200])
pos.standardoutput(computation, solution, 20, bounds, npoints, mploutput = True)
def sourcesquareconvergence(Ns, Ps, NPWs, k = 20, polyonly = False):
condfile = open("hankelcondition%s.txt"%k, 'a')
fileroot="hankelsquare_k%s"%(k);
bounds=np.array([[0,1],[0,1]],dtype='d')
npoints=np.array([k * 10,k * 10], dtype=int)
origin = np.array([-0.2,-0.2])
g = pcb.FourierHankel(origin, [0], k)
rt = PlaneWaveFromSourceRule(origin)
condfile.write("Plane waves\n")
for npw in NPWs:
print "Number of plane waves ",npw
pw = pcb.planeWaveBases(2, k, npw)
fo = pof.ErrorFileOutput(fileroot + 'npw%s'%(npw), str(Ns), g, bounds, npoints)
for N in Ns:
solver = psc.DirectSolver(callback = lambda M: condfile.writelines("%s, %s, %s\n"%(npw, N, cond(M))))
sol = solvesquare(N, 1, g, pw, solver.solve, k, dovolumes=False)
fo.process(N, sol)
if not polyonly:
condfile.write("Polynomials + plane wave\n")
for pdeg in Ps:
print "polynomial degree ",pdeg
poly = pcbr.ReferenceBasisRule(pcbr.Dubiner(pdeg))
polyrt = pcb.ProductBasisRule(poly, rt)
fo = pof.ErrorFileOutput(fileroot + 'poly%srt'%(pdeg), str(Ns), g, bounds, npoints)
for N in Ns:
solver = psc.DirectSolver(callback = lambda M: condfile.write("%s, %s, %s\n"%(pdeg, N, cond(M))))
sol = solvesquare(N, pdeg, g, polyrt, solver.solve, k)
fo.process(N, sol)
if polyonly:
condfile.write("Polynomials only\n")
for pdeg in Ps:
print "polynomial degree ",pdeg
poly = pcbr.ReferenceBasisRule(pcbr.Dubiner(pdeg))
fo = pof.ErrorFileOutput(fileroot + 'poly%srt'%(pdeg), str(Ns), g, bounds, npoints)
for N in Ns:
solver = psc.DirectSolver(callback = lambda M: condfile.write("%s, %s, %s\n"%(pdeg, N, cond(M))))
sol = solvesquare(N, pdeg, g, poly, solver.solve, k)
fo.process(N, sol)
condfile.close()
from numpy import array,sqrt
k = 20
n = 6
g = pcb.FourierHankel([-1,-1], [0], k)
bdytag = "BDY"
bnddata={bdytag:pcbd.dirichlet(g)}
bounds=array([[0,1],[0,1]],dtype='d')
npoints=array([200,200])
mesh = tum.regularsquaremesh(n, bdytag)
#print mesh.nodes
#print mesh.elements
problem = psp.Problem(mesh, k, bnddata)
basisrule = pcb.planeWaveBases(2,k,9)
nquad = 10
system = pcp.HelmholtzSystem
compinfo = psc.ComputationInfo(problem, basisrule, 10)
computation = psc.Computation(compinfo, system)
solblockdiagonal = computation.solution(psi.DiagonalBlockOperator(mesh), psi.GMRESSolver('ctor', psi.ItCounter()))
soldomaindecomp = computation.solution(psd.SchwarzOperator(mesh), psi.GMRESSolver('ctor', psi.ItCounter()))
mortarrule = pcbr.ReferenceBasisRule(pcbr.Legendre1D(6))
s = -1j*k
mc = psm.MortarComputation(problem, basisrule, mortarrule, nquad, system, system.boundaryclass, s)
solmortar = mc.solution(psi.GMRESSolver('ctor'), psi.ItCounter(5))
#solbrutal = computation.solution(psd.DomainDecompOperator(mesh), psi.GMRESSolver('ctor'))
#print "DD solve"
from numpy import array,sqrt
k = 10
direction=array([[1.0,1.0]])/sqrt(2)
g = pcb.PlaneWaves(direction, k)
bnddata={11:pcbd.zero_dirichlet(),
10:pcbd.generic_boundary_data([-1j*k,1],[-1j*k,1],g=g)}
bounds=array([[-2,2],[-2,2]],dtype='d')
npoints=array([200,200])
with puf.pushd('../../examples/2D'):
mesh = pmm.gmshMesh('squarescatt.msh',dim=2)
problem = psp.Problem(mesh, k, bnddata)
compinfo = psc.ComputationInfo(problem, pcb.planeWaveBases(2,k,11), 5)
computation = psc.Computation(compinfo, pcp.HelmholtzSystem)
#solbrutal = computation.solution(psi.BrutalSolver(np.complex, psi.DomainDecompOperator(mesh)).solve)
soldd = computation.solution(psd.SchwarzOperator(mesh), psi.GMRESSolver(np.complex))
solindirect = computation.solution(psi.BlockPrecondOperator(mesh), psi.GMRESSolver(np.complex))
soldirect = computation.solution(psc.DirectOperator(), psc.DirectSolver())
#print np.max(np.abs(soldirect.x - solbrutal.x))
print np.max(np.abs(soldirect.x - solindirect.x))
print np.max(np.abs(soldirect.x - soldd.x))
#solindirect = computation.solution(psi.IndirectSolver().solve)
#print solindirect.x[0:20]
#pos.standardoutput(computation, soldirect, 20, bounds, npoints, 'soundsoft')
import pypwdg.setup.problem as psp
import pypwdg.setup.computation as psc
import pypwdg.core.physics as pcp
import pypwdg.output.solution as pos
import pypwdg.raytrace.control as prc
import pypwdg.parallel.main
import pypwdg.output.mploutput as pom
from numpy import array,sqrt
k = 20
direction=array([[1.0,1.0]])/sqrt(2)
g = pcb.PlaneWaves(direction, k)
nq = 11
bnddata={11:pcbd.zero_dirichlet(),
10:pcbd.generic_boundary_data([-1j*k,1],[-1j*k,1],g=g)}
bounds=array([[-2,2],[-2,2]],dtype='d')
npoints=array([500,500])
mesh = pmm.gmshMesh('squarescatt.msh',dim=2)
problem = psp.Problem(mesh, k, bnddata)
computation = psc.DirectComputation(problem, pcb.planeWaveBases(2,k,12), nq, pcp.HelmholtzSystem, alpha=0.5, beta=0.0, delta=0.0)
solution = computation.solution()
pos.standardoutput(solution, 20, bounds, npoints, 'soundsoft')
pom.outputMeshPartition(bounds, npoints, mesh, 3)
pom.output2dsoln(bounds, solution, npoints, plotmesh=False)
import pypwdg.setup as ps
import pypwdg.core.bases as pcb
import pypwdg.mesh.mesh as pmm
import pypwdg.core.boundary_data as pcbd
import pypwdg.parallel.main
from numpy import array
import math
k = 10
g = pcb.PlaneWaves(array([[1,0,0]])/math.sqrt(1), k)
bnddata={82:pcbd.zero_impedance(k), 83:pcbd.dirichlet(g) }
bounds=array([[-2,2],[-2,2],[-2,2]],dtype='d')
npoints=array([200,200,200])
mesh = pmm.gmshMesh('scattmesh.msh',dim=3)
bases = pcb.planeWaveBases(mesh, k, 3)
problem=ps.Problem(mesh,k,16, bnddata)
solution = ps.Computation(problem, bases).solve()
solution.writeSolution(bounds,npoints,fname='scattmesh.vti')
problem.writeMesh(fname='scattmesh.vtu',scalars=solution.combinedError())
import pypwdg.core.bases as pcb
import pypwdg.mesh.mesh as pmm
import pypwdg.core.boundary_data as pcbd
import pypwdg.setup.problem as psp
import pypwdg.setup.computation as psc
import pypwdg.core.physics as pcp
import pypwdg.output.solution as pos
import pypwdg.parallel.main
from numpy import array,sqrt
k = 60
direction=array([[1.0,1.0]])/sqrt(2)
g = pcb.PlaneWaves(direction, k)
bnddata={13:pcbd.zero_dirichlet(),
12:pcbd.generic_boundary_data([-1j*k,1],[-1j*k,1],g=g)}
bounds=array([[-2,2],[-2,2]],dtype='d')
npoints=array([300,300])
mesh = pmm.gmshMesh('circscatt.msh',dim=2)
problem = psp.Problem(mesh, k, bnddata)
quadpoints = 30
computation = psc.Computation(problem, pcb.planeWaveBases(2,k,30), pcp.HelmholtzSystem, quadpoints)
#computation = psc.Computation(problem, pcb.FourierBesselBasisRule(range(-4,5)), pcp.HelmholtzSystem, quadpoints)
solution = computation.solution(psc.DirectSolver().solve)
pos.standardoutput(computation, solution, 30, bounds, npoints, 'circle')
import pypwdg.setup as ps
import pypwdg.core.bases as pcb
import pypwdg.mesh.mesh as pmm
import pypwdg.core.boundary_data as pcbd
import pypwdg.parallel.main
from numpy import array
k = 10
direction = array([[1.0, 0]])
g = pcb.PlaneWaves(direction, k)
bnddata = {
21: pcbd.zero_dirichlet(),
18: pcbd.generic_boundary_data([-1j * k, 1], [-1j * k, 1], g),
20: pcbd.generic_boundary_data([-1j * k, 1], [-1j * k, 1], g),
19: pcbd.zero_dirichlet(),
}
bounds = array([[0, 5], [0, 1]], dtype="d")
npoints = array([501, 101])
mesh = pmm.gmshMesh("2dhole.msh", dim=2)
bases = pcb.planeWaveBases(mesh, k, nplanewaves=15)
problem = ps.Problem(mesh, k, 20, bnddata)
solution = ps.Computation(problem, bases).solve()
solution.writeSolution(bounds, npoints, fname="2dhole.vti")
problem.writeMesh(fname="2dhole.vtu", scalars=solution.combinedError())