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Fast multipole method for the biharmonic equation in three dimensions. (English) Zbl 1103.65122
The first goal of the paper is to study the solutions of the biharmonic and the polyharmonic equation in 3 by use of special functions, in particular under the aspect of their behaviour under translations. Based on this, and on the fast multipole method for the Laplace equation, the authors develop a fast multipole method for the biharmonic equation. Its numerical implementation is tested with several examples.
MSC:
65N38Boundary element methods (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
35J40Higher order elliptic equations, boundary value problems
31B30Biharmonic and polyharmonic equations and functions (higher-dimensional)