The Multipole method for the Laplace equation in domains with polyhedral corners

Sergey L. Skorokhodov; Vladimir I. Vlasov

Sergey L. Skorokhodov Dorodnicyn Computing Centre of Russian Acad. Sci.
Vladimir I. Vlasov Dorodnicyn Computing Centre of Russian Acad. Sci.

Abstract

A new analytic-numerical method has been developed for solving the Laplace equation in domains with cones of arbitrary base, in particular with polyhedral corners. The solution is represented as an expansion involving singular functions (the Multipoles), which play the role of basic functions. The method enables to find these functions explicitly and to compute efficiently their singularity exponents. The method possesses exponential rate of convergence and provides precise computation of the solution, its derivatives and intensity factors at the edges and at the corner point. In addition, an asymptotic expansion of the solution near the edges of polyhedral corner has been obtained.

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References

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