def poissonneumann(k,N,g,f, points):
tag = "B1"
elements = H1Elements(k)
quadrule = pyramidquadrature(k+1)
system = SymmetricSystem(elements, quadrule, lambda m: buildcubemesh(N,m,tag), [])
SM = system.systemMatrix(True)
S = SM[1:,:][:,1:] # the first basis fn is guaranteed to be associated with an external degree, so is a linear comb of all the others
F = 0 if f is None else system.loadVector(f)
G = 0 if g is None else system.boundaryLoad({tag:g}, squarequadrature(k+1), trianglequadrature(k+1), False)
U = numpy.concatenate((numpy.array([0]), spsolve(S, G[tag][1:]-F[1:])))[:,numpy.newaxis]
return system.evaluate(points, U, {}, 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)