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Two notes on the implementation of wavelet Galerkin boundary element methods
(1997)SAM Research ReportWe report, in two notes, recent progress in the implementation of wavelet-based Galerkin BEM on polyhedra and study the performance.Report -
Wavelet Galerkin Algorithms for Boundary Integral Equations
(1997)SAM Research ReportThe implementation of a fast, wavelet-based Galerkin discretization of second kind integral equations on piecewise smooth surfaces $\Gamma\subset \R^3$ is described. It allows meshes consisting of triangles as well as quadrilaterals. The algorithm generates a sparse, approximate stiffness matrix with $N=O(N(log N)^2)$ nonvanishing entries in $O(N(\log N)^4)$ operations where N is the number of degrees of freedom on the boundary while ...Report -
Advanced boundary element algorithms
(1999)SAM Research ReportWe review recent algorithmic developments in the boundary element method (BEM) for large scale engineering calculations. Two classes of algorithms, the clustering and the wavelet-based schemes are compared. Both have $O(N(\log N)^a)$ complexity with some small $a \ge 0$ and allow in-core simulations with up to $N = O(10^6)$ DOF on the boundary on serial workstations. Clustering appears more robust for complex surfaces.Report -
Fast numerical solution of the linearized Molodensky problem
(1999)SAM Research ReportWhen standard boundary element methods (BEM) are used to solve the linearized vector Molodensky problem we are confronted with two problems: (i) the absence of $O(|x|^{-2})$ terms in the decay condition is not taken into account, since the single layer ansatz, which is commonly used as representation of the perturbation potential, is of the order $O(|x|^{-1})$ as $x \to \infty$. This implies that the standard theory of Galerkin BEM is not ...Report