General characteristics of the finite element and boundary element methods.

Abstract

Numerical methods can be characterized by the basis used, the criterion of fit used, and the approximations to the variational formulation which must be made to implement the numerical approximation. Finite element methods usually use a polynomial basis and the criterion of fit is a domain integral variational statement. The boundary element methods usually use a free‐space Green’s function as a basis. The criterion of it is usually a collocation method for satisfying a boundary integral equation for discrete specified boundary conditions. For both the finite element and boundary element methods, discretization, numerical mapping, and integration procedures are potential sources of significant error. The characteristics of structural acoustic applications of both the finite element and boundary element methods will be identified and contrasted to analytical methods. It will be demonstrated that numerical methods and analytical methods have different strengths and weaknesses and that the methods should be considered complementary.<ep;balance;l>