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- W2041275405 abstract "The implementation of a fast, wavelet-based Galerkin discretization of second kind integral equations on piecewise smooth surfaces $Gammasubset IR^3$ is described. It allows meshes consisting of triangles as well as quadrilaterals. The algorithm generates a sparse, approximate stiffness matrix with $cN=O(N(log N)^2)$ nonvanishing entries in O(N(log N)4) operations, where N is the number of degrees of freedom on the boundary, whileessentially retaining the asymptotic convergence rate of the full Galerkin scheme. A new proof of the matrix-compression estimates is given based on derivative-free kernel estimates. The condition number of the sparse stiffness matrices is bounded independently of the meshwidth. The data structure containing the compressed stiffness matrix is described in detail: it requires $O(cN)$ memory and can be set up in $O(cN)$ operations. Numerical experiments show that the asymptotic performance estimates apply for moderate N. Problems with N=106 degrees of freedom were computed in core on a workstation. The impact of various parameters in the compression scheme on the performance and the accuracy of the algorithm is studied." @default.
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- W2041275405 date "1999-01-01" @default.
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- W2041275405 title "Wavelet Galerkin Algorithms for Boundary Integral Equations" @default.
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- W2041275405 doi "https://doi.org/10.1137/s1064827597329989" @default.
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