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Methods for solution of boundary value problems for regions with multiply connected boundaries

Traitak S.D.

#### Abstract:

Considering the outer Dirichlet problem for the Laplace equation in as an example, we make a comparative analysis of known analytical methods for solving boundary value problems for mediums containing non-intersecting inclusions. We study the possibility to employ the method of diffraction and the transform method. We proof the summation theorem for irreducible Cartesian tensors. Using this theorem, we reduce the boundary value problem under consideration to an infinite system of linear algebraic equations. It is shown that the known method of induced forces results in the same system of equations.

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