Tensor Structured Evaluation of Singular Volume Integrals
Jonas Ballani and Peter Meszmer
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Submission date: 03. Dec. 2012
published in: Computing and visualization in science, 15 (2012) 2, p. 75-86
DOI number (of the published article): 10.1007/s00791-013-0199-y
Keywords and phrases: singular integrals, tensor approximation, Hierarchical Tensor Format, Hierarchical Quadrature
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In this article, we introduce a new method for the accurate and fast computation of singular integrals over cuboids in three-dimensional space. Using a straightforward geometric parametrisation of the domain of integration, we interpret the integral as a smooth function on a high-dimensional parameter space. A standard interpolation scheme then leads to a high-dimensional tensor to which an approximation in the data-sparse hierarchical tensor format is applied. Once this approximation is available, the evaluation of an integral value becomes an easy task which does no longer require the treatment of singular terms. Numerical experiments illustrate the potential of the proposed approach for typical examples.