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A parallel fictitious domain method for the three-dimensional Helmholtz equation. (English) Zbl 1035.65126

Summary: The application of a fictitious domain (domain embedding) method to the three-dimensional Helmholtz equation with absorbing boundary conditions is considered. The finite element discretization is performed by using locally fitted meshes, and an algebraic fictitious domain method with a separable preconditioner is used in the iterative solution of the resultant linear systems. Such a method is based on embedding the original domain into a larger one with a simple geometry. With this approach, it is possible to realize the GMRES iterations in a low-dimensional subspace and use the partial solution method to solve the linear systems with the preconditioner.

An efficient parallel implementation of the iterative algorithm is introduced. Results of numerical experiments demonstrate good scalability properties on distributed-memory parallel computers and the ability to solve high frequency acoustic scattering problems.

MSC:
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65F10Iterative methods for linear systems
65Y05Parallel computation (numerical methods)
65F35Matrix norms, conditioning, scaling (numerical linear algebra)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation