Efficient Boundary Element Method by multipole expansion and generalized inverse matrix for analysing target region (Applied for two-dementional elastostatic problems)

This paper presents Efficient Boundary Element Method for Analysing Target Region, which is developed by Yamagishi, et al. to efficiently compute unknown quantities only in a specific domain extended to 2 D elastostatic problems. In this method, whole boundaries are devided into Neighborhood Boundaries which are near to Target Region and Distant Boundaries which are sufficienty far from it. We set up boundary integral equations whose source points are placed on all the elements of the Neighborhood Boundaries and express these integrals which contain the unknown quantities on the Distant Boundaries as low order multipole moments by using a multipole expansion of the fundamental solution. Then, we set up boundary integral equations whose source points are placed near to Distant Boundaries by the increment of those multipole moments and express these integrals which contain the unknown quantities on the Distant Boundaries approximately as the multipole moments by using a generalized inverse matrix. Thus the number of unknowns and boundary integral equations set up are decreased drastically by this method. When unknown quantities are required only in a specific domain, especially on large-scale boundary value problems, this method enable us to compute them efficiently. The capability of this method extended to 2D elastostatic problems is verified with some numerical experiments.