Abstract
The solution of inhomogeneous partial differential equations by boundary element methods requires the evaluation of volume potentials. A direct standard computation of the classical Newton potentials is possible but expensive. Here, a fast evaluation of the Newton potentials by using the fast multipole method is described and analyzed. In particular, an approximation by the fast multipole method is investigated and related error estimates are given. Furthermore, an indirect evaluation of the normal derivative of the Newton potential is presented. A numerical analysis is presented for all approaches mentioned above. Numerical results are presented for the Poisson equation and for the system of linear elastostatics.
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