SOLUTION OF THE 3D-HELMHOLTZ EQUATION IN EXTERIOR DOMAINS OF ARBITRARY SHAPE USING HP-FINITE-INFINITE ELEMENTS

This work is devoted to a convergence and performance study of finite- infinite element discretizations for the Helmholtz equation in exterio r domains of arbitrary shape. The proposed approximation applies to ar bitrary geometries, combining an hp-FE discretization between the obje ct and a surrounding sphere and an hp infinite element (IE) discretiza tion outside the sphere with a spectral-like representation (resulting from the separation of variables) in the ''radial'' direction. The de scribed approximation is an extension of our earlier work, which was r estricted to domains with separable geometry. The numerical experiment s are confined to these geometrical configurations: a sphere, a (finit e) cylinder, and a cylinder with spherical incaps, all within a trunca ting sphere. The sphere problem admits an exact solution and serves as a basis for the convergence study. Solutions to the other two problem s are compared with those obtained using the boundary element method. (C) 1998 Elsevier Science B.V. All rights reserved.