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arXiv · 1507.05925

Integral equation methods for elastance and mobility problems in two dimensions

Manas Rachh·Leslie Greengard
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Abstract

We present new integral representations in two dimensions for the elastance problem in electrostatics and the mobility problem in Stokes flow. These representations lead to resonance-free Fredholm integral equations of the second kind and well conditioned linear systems upon discretization. By coupling our integral equations with high order quadrature and fast multipole acceleration, large-scale problems can be solved with only modest computing resources. We also discuss some applications of these boundary value problems in applied physics.

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Manas Rachh, Leslie Greengard. 2015-07-21. Integral equation methods for elastance and mobility problems in two dimensions. https://doi.org/10.1137/15m103251x

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