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Multi-Dimensional Quadrature of Singular and Discontinuous Functions

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Abstract

In many simulations of physical phenomena, discontinuous material coefficients and singular forces pose severe challenges for the numerical methods. The singularity of the problem can be reduced by using a numerical method based on a weak form of the equations. Such a method, combined with an interface tracking method to track the interfaces to which the discontinuities and singularities are confined, will require numerical quadrature with singular or discontinuous integrands. We introduce a class of numerical integration methods based on a regularization of the integrand. The methods can be of arbitrary high order of accuracy. Moment and regularity conditions control the overall accuracy.

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Authors and Affiliations

  1. Department of Numerical Analysis and Computer Science, Royal Institute of Technology, SE-100 44, Stockholm, Sweden

    Anna-Karin Tornberg

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  1. Anna-Karin Tornberg
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Tornberg, AK. Multi-Dimensional Quadrature of Singular and Discontinuous Functions. BIT Numerical Mathematics 42, 644–669 (2002). https://doi.org/10.1023/A:1021988001059

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