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Kashirin, A. A.; Smagin, S. I.; Taltykina, M. Yu.

Mosaic-skeleton method as applied to the numerical solution of three-dimensional Dirichlet problems for the Helmholtz equation in integral form. (English. Russian original) Zbl 1353.65130

Comput. Math. Math. Phys. 56, No. 4, 612-625 (2016); translation from Zh. Vychisl. Mat. Mat. Fiz. 56, No. 4, 625-638 (2016).
The numerical solution of interior and exterior Helmholtz problems with Dirichlet boundary condition is considered in three dimensions. The problem at hand is reformulated as a first kind boundary integral equation which is approximated by a system of linear algebraic equations. This system is solved numerically by the iteration method. To speed up the solution procedure, the mosaic-skeleton method is used.
Reviewer: Andreas Kleefeld (Jülich)

Cited in 7 Documents

MSC:

65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65F10 Iterative numerical methods for linear systems

Keywords:

Dirichlet problem; Helmholtz equation; fast method; mosaic-skeleton method; incomplete cross approximation; boundary integral equation; iteration method
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References:

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