THE INFINITE BOUNDARY ELEMENT METHOD AND ITS APPLICATION TO A COMBINED FINITE BOUNDARY ELEMENT TECHNIQUE FOR UNBOUNDED FIELD PROBLEMS

Abstract
The boundary element method is a useful method for the analysis of field problems involving unbounded regions. Therefore, the method can be used advantageously in combination with the finite element method. This is sometimes called a combination method and it is suitable as a picture‐frame technique. Although this technique attains good accuracy, the matrix of the discretized equation is not banded, since it is a dense matrix. In this paper, we propose an infinite boundary element which divides the unbounded region radially. By the use of this element, the bandwidth of the discretized system matrix does not increase beyond that of the finite element region and its original matrix structure is maintained. The infinite boundary element can also be applied to homogeneous unbounded field problems, for which the Green's function of the mirror image is difficult to use. To illustrate the validity of the proposed technique, some numerical calculations are demonstrated and the results are compared with those of the usual combination method and the method using the hybrid‐type infinite element.

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