Stability of the Fast Multipole Method for Helmholtz Equation in Three Dimensions

Martin Nilsson

November 2003

Abstract:

Stability limits for the diagonal forms approximating the free space Green's function in Helmholtz' equation are derived. It is shown that while the original approximation of the Green's function is stable except for overflows, the diagonalized form becomes unstable due to errors from roundoff, interpolation, choice of quadrature rule and approximation of the translation operator. Numerical experiments validate the theoretical estimates.

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