A New Formulation for Solutions of Boundary Value Problems Using Domain-type Approximations and Local Integral Equations

Abstract

The boundary and domain-type approximations are discussed in boundary integral equation formulations for solution of boundary value problems. A new approach is proposed with using a domain-type approximation of the primary field and collocation of boundary conditions at boundary nodes and local integral representation of the primary field at interior nodes. Two kinds of the domain-type approximation are utilized. The proposed method is illustrated on potential problems in two dimensions.