Boundary element approach for identification of the external forces in the scalar wave equations

Abstract

An identification problem is discussed for the unknown external force of a deterministic distributed parameter system governed by a nonhomogeneous partial differential equation of hyperbolic type. The mathematical formulation is based on boundary element partition and a weighted residual expression corresponding to the given partial differential equation, both of which are fundamental ideas of the boundary element method. The unknown external force is identified from state observations taken at the points on the boundary by minimizing the sum of squares of differences between observations and estimates. Numerical examples are presented to illustrate the usefulness of the proposed identification method.