Parallel Multigrid Methods and Coarse Grid LDLT Solver for Maxwell’s Eigenvalue Problem
We consider efficient numerical solution methods for Maxwell’s eigenvalue problem in bounded domains. A suitable finite element discretization with Nédélec elements on tetrahedra leads to large linear systems of equations, where the resulting matrices are symmetric but singular and where the kernel corresponds to divergence-free vector fields. The discretized eigenvalue problem is solved by a preconditioned iterative eigenvalue solver, using a modification of the LOBPCGmethod extended by a projection onto the divergence-free vector fields, where we use a multigrid preconditioner for a regularized Maxwell problem as well as for the solution of the projection problem. In both cases, a new parallel direct block LDL T decomposition is used for the solution of the coarse grid problem. LDL T
KeywordsParallel computing finite elements block LDLT decomposition Maxwell’s eigenvalue problem LOBPCG method multigrid preconditioner
The authors acknowledge the financial support from BMBF grant 01IH08014A within the joint research project ASIL (Advanced Solvers Integrated Library). We thank W. Koch (CST) for the construction of the accelerator configuration.
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