def volumeStiffness(self):
''' The contribution of the volume terms to the stiffness matrix (should be zero if using Trefftz basis functions)'''
E = pms.ElementMatrices(self.problem.mesh)
L2K = self.weightedassembly.assemble([[E.I, E.Z],[E.Z, E.Z]])
H1 = self.volumeassembly.assemble([[E.Z,E.Z],[E.Z, E.I]])
AJ = pms.AveragesAndJumps(self.problem.mesh)
B = pms.sumfaces(self.problem.mesh, self.internalassembly.assemble([[AJ.Z,AJ.Z],[AJ.I,AJ.Z]]))
return H1 - L2K - B
def internalStiffness(self):
''' The contribution of the internal faces to the stiffness matrix'''
jk = 1j * self.problem.k
AJ = pms.AveragesAndJumps(self.problem.mesh)
B = self.problem.mesh.boundary # This is the integration by parts term that generally gets folded into the boundary data, but is more appropriate here
SI = self.internalassembly.assemble([[jk * self.alpha * AJ.JD, -AJ.AN - B],
[AJ.AD + B, -(self.beta / jk) * AJ.JN]])
SFSI = pms.sumfaces(self.problem.mesh,SI)
return SFSI
def stiffness(self):
delta = self.delta
dik = delta / (1j * self.k)
B = self.B
# The contribution of the boundary conditions
SB = self.bdyassembly.assemble([[(1-delta) * B, (1-delta)*B],
[-dik * B, -dik *B]])
# SB = self.bdyassembly.assemble([[-(1-delta) * B, (1-delta)*B],
# [dik * B, -dik *B]])
return pms.sumfaces(self.mesh,SB)
def getPerturbation(self):
return pms.sumfaces(self.mesh, self.internalassembly.assemble([[self.B, self.Z],
[self.B, self.Z]]))
