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arXiv · 2210.09954

Decomposition and conformal mapping techniques for the quadrature of nearly singular integrals

William Mitchell·Abbie Natkin·Paige Robertson·Marika Sullivan·Xuechen Yu·Chenxin Zhu
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Abstract

Gauss-Legendre quadrature and the trapezoidal rule are powerful tools for numerical integration of analytic functions. For nearly singular problems, however, these standard methods become unacceptably slow. We discuss and generalize some existing methods for improving on these schemes when the location of the nearby singularity is known. We conclude with an application to some nearly singular surface integrals of viscous flow.

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William Mitchell, Abbie Natkin, Paige Robertson, Marika Sullivan, Xuechen Yu, Chenxin Zhu. 2022-10-18. Decomposition and conformal mapping techniques for the quadrature of nearly singular integrals. https://arxiv.org/abs/2210.09954

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