def laplaceeigs(k,N,n):
import scipy.linalg as sl
tag = "B1"
elements = H1Elements(k)
quadrule = pyramidquadrature(k+1)
system = SymmetricSystem(elements, quadrule, lambda m: buildcubemesh(N, m, tag), [tag])
SM = system.systemMatrix(True)
S, SIBs, Gs = system.processBoundary(SM, {tag:lambda p: numpy.zeros((len(p),1))})
print S.shape
MM = system.systemMatrix(False)
M, _, _ = system.processBoundary(MM, {tag:lambda p: numpy.zeros((len(p),1))})
MLU = ssl.splu(M)
L = A = ssl.LinearOperator( M.shape, matvec=lambda x: MLU.solve(S* x), dtype=float)
return ssl.eigen(L, k=n, which='SM', return_eigenvectors=False)
def testSymmetry(self):
tag = "B1"
for k in range(1,3):
quadrule = pyramidquadrature(k+1)
for N in range(1,3):
for elements in [H1Elements(k), HcurlElements(k), HdivElements(k)]:
system = SymmetricSystem(elements, quadrule, lambda m: buildcubemesh(N, m, tag), [tag])
for deriv in [False, True]:
SM = system.systemMatrix(deriv)
g = lambda x: np.zeros((len(x),1))
S, SIBs, Gs = system.processBoundary(SM, {tag:g})
np.testing.assert_array_almost_equal(SM.todense(), SM.transpose().todense())
np.testing.assert_array_almost_equal(S.todense(), S.transpose().todense())
def laplacedirichlet(k, N, g, points):
tag = "B1"
elements = H1Elements(k)
quadrule = pyramidquadrature(k+1)
system = SymmetricSystem(elements, quadrule, lambda m: buildcubemesh(N, m, tag), [tag])
SM = system.systemMatrix(True)
S, SIBs, Gs = system.processBoundary(SM, {tag:g})
SG = SIBs[tag] * Gs[tag]
print S.shape
U = spsolve(S, -SG)[:,numpy.newaxis]
return system.evaluate(points, U, Gs, False)
def poissondirichlet(k,N,g,f, points):
tag = "B1"
elements = H1Elements(k)
quadrule = pyramidquadrature(k+1)
system = SymmetricSystem(elements, quadrule, lambda m: buildcubemesh(N, m, tag), [tag])
SM = system.systemMatrix(True)
S, SIBs, Gs = system.processBoundary(SM, {tag:g})
SG = SIBs[tag] * Gs[tag]
if f:
F = system.loadVector(f)
else: F = 0
print SM.shape, S.shape, SIBs[tag].shape, Gs[tag].shape, F.shape, SG.shape
t = Timer().start()
U = spsolve(S, -F-SG)[:,numpy.newaxis]
t.split("spsolve").show()
return system.evaluate(points, U, Gs, False)