Application Of The Proper Orthogonal Decomposition In Steady State Inverse Problems

Abstract

This chapter provides an overview of an inverse analysis technique for retrieving unknown boundary conditions. The first step of this approach is to solve a sequence of forward problems made unique, by defining the missing boundary condition as a function of some unknown parameters. Several combinations of values of these parameters that produce a sequence of solutions are considered. These combinations are then sampled at a predefined set of points. Proper Orthogonal Decomposition (POD) is used to produce a truncated sequence of orthogonal basis function. The solution of the forward problem is written as a linear combination of the basis vectors. The unknown coefficients of this combination are evaluated by minimizing the discrepancy between the measurements and the POD approximation of the field. The chapter also discusses numerical examples to show the robustness and numerical stability of the proposed scheme. © 2003 Elsevier B.V. All rights reserved