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Multipole method for the Dirichlet problem on doubly connected domains of complex geometry: A general description of the method. (English. Russian original) Zbl 1004.65116
Comput. Math. Math. Phys. 40, No. 11, 1567-1581 (2000); translation from Zh. Vychisl. Mat. Mat. Fiz. 40, No. 11, 1633-1647 (2000).
The authors develop the basic principles of a new analytical-numerical method as applied to the Dirichlet problem for Laplace’s equation on plane doubly connected domains with complex boundaries. The method is characterized by an exponential rate of convergence and guarantees a high-accuracy computation of the solution and its derivatives up to complex boundary segments as well as capacity, intensity coefficients in corners, etc.

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation