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A summary of infinite element formulations for exterior Helmholtz problems. (English) Zbl 0943.65126
Summary: This work is devoted to a study and summary of different infinite element formulations for Helmholtz problems in arbitrary exterior domains. The theoretical setting for each of the different formulations is presented and related to the mathematical existence theory. The influence of a bilinear or a sesquilinear formulation is discussed as well as possible extensions to other elements. The implementation of the infinite element method incorporates the use of 2D and 3D \(hp\) finite elements and allows for \(hp\)-adaptive refinements. Numerical results show the computational efficiency of the coupled finite-infinite element methodology.

MSC:
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65Y20 Complexity and performance of numerical algorithms
Software:
HP90
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References:
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