Multipole fast algorithm for the least-squares approach of the method of fundamental solutions for threedimensional harmonic problems. Numerical Methods for Partial Differential Equations


In this article we describe an improvement in the speed of computation for the least-squares method of fundamental solutions (MFS) by means of Greengard and Rokhlin’s FMA. Iterative solution of the linear system of equations is performed for the equations given by the least-squares formulation of the MFS. The results of applying the method to test problems from potential theory with a number of boundary points in the order of 80,000 show that the method can achieve fast solutions for the potential and its directional derivatives. The results show little loss of accuracy and a major reduction in the memory requirements compared to the direct solution method of the least squares problem with storage of the full MFS matrix. The method can be extended to the solution of overdetermined systems of equations arising from boundary integral methods with a large number of boundary integration points. © 2003 Wiley Periodicals, Inc. Nume

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