On an O(N) algorithm for the solution of geodetic boundary value problems

Abstract

We study a fast algorithm for the solution of geodetic boundary value problems. The algorithm uses basis functions that ideally localize in space. It can handle any smooth enough boundary surface and does not require spherical and constant radius approximation. It solves a problem with N unknowns in O(N) operations up to some logarithmic terms. A priori given satellite models can easily be taken into account without degrading the performance. Some numerical experiments based on a synthetic earth model show that the algorithm is suited for ultrahigh resolution global gravity field recovery fi om terrestrial data on any hardware platform including PC's. For N = 65538 unknowns the matrix assembly takes less than 1 hour, and the solution of the linear system of equations using GMRES without any preconditioning takes little more than 1 hour. The accuracy obtained so far is not satisfactory yet and needs further investigation.