Efficient Boundary Element Method for a focused domain

An efficient Boundary Element Method for focused domain is developed. In this method, whole boundaries are divided into near boundaries which are near to the focused domain and far boundaries which are sufficiently far from it. We set up boundary integral equations and express these integrals which contain unknown quantities on the far boundaries as low order multipole moments, approximately. Thus the number of unknowns and boundary integral equations set up are decreased drastically by this method, and enables us to compute them efficiently. When unknown quantities are required only in a specific domain, especially on large-scale boundary value problems, this method enables us to compute them efficiently. The capability of this method is verified with some numerical experiments.