Marvin Fleck, Richards Grzhibovskis, and Sergej Rjasanow

A New Fundamental Solution Method Based on the Adaptive Cross Approximation

abstract:
A new adaptive Fundamental Solution Method (FSM) for the approximate solution of scalar elliptic boundary value problems is presented. The construction of the basis functions is based on the Adaptive Cross Approximation (ACA) of the fundamental solutions of the corresponding elliptic operator. An algorithm for an immediate computer implementation of the method is formulated. A series of numerical examples for the Laplace and Helmholtz equations in three dimensions illustrates the efficiency of the method. Extensions of the method to elliptic systems are discussed.

Mathematics Subject Classification: 65N80, 65N12, 65N35

Key words and phrases: Fundamental solution method, adaptive cross approximation, collocation, condition numbers