Cannot get eigenpair from Multimesh

variational formulation
1

Hi. I’m trying to use Multimesh to solve an eigenvalue problem with two overlapping domains. This domain is a square, with two subsquares that have an overlap.

The MWE is:

from dolfin import *

from mshr import Rectangle, generate_mesh

# Geometrical Data #

L = 1.5 # Side of the Rectangle

h = 1.0 # Height of the Rectangle

o = 0.2 # Total overlapping Area

b = L*(1-o)/2 # Non Overlapping Side of the Rectangle

# MESHES

omega = MultiMesh()

domain = Rectangle(Point(0., 0), Point(L, h))

domain_left = domain and Rectangle(Point(0., 0), Point(b+L*o, h))

omega_left = generate_mesh(domain_left, 15)

omega.add(omega_left)

domain_right = domain and Rectangle(Point(b, 0), Point(L, h))

omega_right = generate_mesh(domain_right, 15)

omega.add(omega_right)

omega.build()

# Boundaries

class DirichletBoundary(SubDomain):

    def inside(self, x, on_boundary):

        return on_boundary

# FUNCTION SPACES #

V = MultiMeshFunctionSpace(omega, "Lagrange", 1)

u = TrialFunction(V)

v = TestFunction(V)

# Bilinear Forms

k = inner(grad(u), grad(v))*dX

m = u*v*dX

# Assembly

K = PETScMatrix()

K = assemble_multimesh(form=k, tensor=K)

boundary = DirichletBoundary()

bc = MultiMeshDirichletBC(V, Constant(0,), boundary)

bc.apply(K)

M = PETScMatrix()

M = assemble_multimesh(form=m, tensor=M)

# EigenSolver

solver0 = SLEPcEigenSolver(K,M)

solver0.parameters['spectrum'] = 'smallest magnitude'

solver0.parameters['tolerance'] = 1e-6

solver0.parameters['problem_type'] = 'pos_gen_non_hermitian'

solver0.solve(0)

r, c, rx, cx = solver0.get_eigenpair(0)

print("Target Frequency: ", sqrt(r))`

I get the following error:

Traceback (most recent call last):
  File "/mnt/c/repos/Doutorado/FEniCS Scripts/SCHWARZ_MultiMesh.py", line 61, in <module>
    r, c, rx, cx = solver0.get_eigenpair(0)
RuntimeError: 

*** -------------------------------------------------------------------------
*** DOLFIN encountered an error. If you are not able to resolve this issue
*** using the information listed below, you can ask for help at
***
***     fenics-support@googlegroups.com
***
*** Remember to include the error message listed below and, if possible,
*** include a *minimal* running example to reproduce the error.
***
*** -------------------------------------------------------------------------
*** Error:   Unable to extract eigenpair from SLEPc eigenvalue solver.
*** Reason:  Requested eigenpair (0) has not been computed.
*** Where:   This error was encountered inside SLEPcEigenSolver.cpp.
*** Process: 0
*** 
*** DOLFIN version: 2019.2.0.dev0
*** Git changeset:  unknown
*** -------------------------------------------------------------------------
2

There are multiple issues here.
The first is that you are not using multimesh as they are intended to be used. See for instance:




You should also familiarize yourself with how to use multimesh, as there are many multimesh specific commands, see for instance