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Solution of the 3D-Helmholtz equation in exterior domains of arbitrary shape using emhp/em-finite infinite elements

by K. Gerdes

(Report number 1996-21)

Abstract
This work is devoted to a convergence and performance study of finite-infinite element discretizations for the Helmholtz equation in exterior domains of arbitrary shape. The proposed approximation applies to arbitrary geometries, combining an emhp/em FE discretization between the object and a surrounding sphere and an {\em hp} Infinite Element (IE) discretization outside the sphere with a spectral-like representation (resulting from the separation of variables) in the "radial" direction. The described approximation is an extension of our earlier work, which was restricted to domains with separable geometry. The numerical experiments are confined to these geometrical configurations: a sphere, a (finite) cylinder, and a cylinder with spherical incaps, all within a truncating sphere. The sphere problem admits an exact solution and serves as a basis for the convergence study. Solutions to the other two problems are compared with those obtained using the Boundary Element Method.

Keywords:

@Techreport{G96_204,
  author = {K. Gerdes},
  title = {Solution of the 3D-Helmholtz equation in exterior domains of arbitrary shape using emhp/em-finite infinite elements},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {1996-21},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports1996/1996-21.pdf },
  year = {1996}
}

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