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 from 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 GIVIRES without any preconditioning takes little more than 1 hour. The accuracy obtained so far is not satisfactory yet and needs further investigation
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References
Greengard, L. and Rokhlin, V. (1997). A new version of the fast multipole method for the Laplace equation in three dimensions. Acta Numerica, 6: 229–269
Haagmans, R (1999). A synthetic earth model for use in geodesy. Submitted to Journal of Geodesy.
Hackbusch, W. and Novak, Z. (1989). On the fast matrix multiplication in the BEM by panel clustering. Numer. Math, 54: 463–491
Klees, R. (1997). Topics on the boundary value problems. In: F. Sansò and R. Rummel (eds.) Geodetic boundary value problems in view of the one centimeter geoid, Lecture Notes in Earth Sciences 65: 482–531, Springer, Berlin.
Klees, R., Lage, C., and Schwab, C. (1998a). Fast numerical solution of the vector Molodenski problem. DEOS Progress Letter, 98.1: 31–42.
Klees, R., Ritter, S., and Lehmann, R. (1998b). Integral equation formulations for geodetic mixed boundary value problems. DEOS Progress Letter, 98.2: 1–14.
Klees, R., Lage, C., and Schwab, C. (1999a). Research Report, Seminar fur Angewandte Mathematik, ETH Zürich.
Klees, R., Lage, C., and Schwab (1999b). Fast numerical solution of the vector Molodenski problem. In: Proc. IV Hotine-Marussi Symposium on Mathematical Geodesy, Trento, Italy.
Lage, C. (1999). Advanced boundary element algorithms. Research Report 99–11, Seminar fur Angewandte Mathematik, ETH Zürich
Lehmann, R. and Klees, R. (1999). Numerical solution of geodetic boundary value problems using a global reference field. Accepted for publication in Journal of Geodesy.
Saad, Y. and Schultz, M. (1986). GMRES: a generalized minimal residual algorithm for solving non-symmetric linear systems. SIAM J. Scientific and Statistical Computing 7: 856–869
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© 2000 SPringer-Verlag Berlin Heidelberg
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Klees, R., van Gelderen, M. (2000). On an O(N) algorithm for the solution of geodetic boundary value problems. In: Schwarz, KP. (eds) Geodesy Beyond 2000. International Association of Geodesy Symposia, vol 121. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59742-8_29
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DOI: https://doi.org/10.1007/978-3-642-59742-8_29
Publisher Name: Springer, Berlin, Heidelberg
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