Applications of a fast multipole Galerkin in boundary element method in linear elastostatics

Authors:
G. Of;O. Steinbach;W. L. Wendland
Affiliations:
Universität Stuttgart, Institut für Angewandte Analysis und Numerische Simulation, Pfaffenwaldring 57, 70569, Stuttgart, Germany;Institut für Mathematik D, TU Graz, Steyrergasse 30, 8010, Graz, Austria;Universität Stuttgart, Institut für Angewandte Analysis und Numerische Simulation, Pfaffenwaldring 57, 70569, Stuttgart, Germany
Venue:
Computing and Visualization in Science
Year:
2005

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Abstract

Boundary element methods provide a powerful tool for solving boundary value problems of linear elastostatics, especially in complicated three–dimensional structures. In contrast to the standard Galerkin approach leading to dense stiffness matrices, in fast boundary element methods such as the fast multipole method the application of matrix–vector products can be realized with almost linear complexity. Since all boundary integral operators of linear elastostatics can be reduced to those of the Laplacian, the discretization of the corresponding single and double layer potentials of the Laplace operator has to be employed only. This technique results in a fast multipole method which is an efficient tool for the simulation of elastic stress fields in engineering and industrial applications.