Abstract
A new approach to the integration of vertex singularities is described. This approach is based on a non-uniform subdivision of the region of integration and the technique fits well to the subdivision strategy used in many adaptive algorithms. A nice feature with this approach is that it can be used in any dimension and on any region of integration which can be subdivided into subregions of the same form. The strategy can be applied both to vertex singularities and internal point singularities. In the latter case this can be done without an initial subdivision of the region in order to put the singular point in a vertex. It turns out that the technique has excellent numerical stability properties.
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Dedicated to Carl-Erik Fröberg on the occasion of his 75th birthday.
This work was supported by The Norwegian Research Council for Science and the Humanities.
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Espelid, T.O. On integrating vertex singularities using extrapolation. BIT 34, 62–79 (1994). https://doi.org/10.1007/BF01935016
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DOI: https://doi.org/10.1007/BF01935016