Geodesic
Piecewise linear wavelet collocation, approximation of the boundary manifold, and quadrature
Electronic transactions on numerical analysis, Tome 12 (2001), pp. 149-192
In this paper we consider a piecewise linear wavelet collocation method for the solution of boundary integral equations of order r = 0, - 1 over a closed and smooth boundary manifold. The trial space is the space of all continuous and piecewise linear functions defined over a uniform triangular grid and the collocation points are the grid points. For the wavelet basis in the trial space we choose the three-point hierarchical basis together with a slight modification near the boundary points of the global patches of parametrization. We choose three, four, and six term linear combinations of Dirac delta functionals as wavelet basis in the space of test functionals.
Classification : 45L10, 65D32, 65R20, 65N38
Keywords: boundary integral equation of order 0 and -1, piecewise linear collocation, wavelet algorithm, approximation of parametrization, quadrature 
@article{ETNA_2001__12__a4,
     author = {Ehrich,  S. and Rathsfeld,  A.},
     title = {Piecewise linear wavelet collocation, approximation of the boundary manifold, and quadrature},
     journal = {Electronic transactions on numerical analysis},
     pages = {149--192},
     year = {2001},
     volume = {12},
     zbl = {1002.65144},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ETNA_2001__12__a4/}
}
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Ehrich,  S.; Rathsfeld,  A. Piecewise linear wavelet collocation, approximation of the boundary manifold, and quadrature. Electronic transactions on numerical analysis, Tome 12 (2001), pp. 149-192. http://geodesic.mathdoc.fr/item/ETNA_2001__12__a4/