Efficient BEM Design Sensitivity Analysis of Two-Dimensional Steady-State Heat Conduction Problems for Fields with Small Circular Holes.

Abstract

In conventional design sensitivity analysis using the boundary element method, all boundaries must be discretized. Therefore, the size of the coefficient matrix of the resulting system of linear algebraic equations becomes quite large for a field with small circular holes. In this paper, we present an efficient sensitivity analysis approach for two-dimensional steady-state heat conduction problems. In the boundary element formulation, the temperature and the heat flux over the boundary of a circular hole are approximated by simple trigonometrical functions. Then, the boundary integral equation is differentiated directly with respect to a design variable. The resulting boundary integral equation relates the sensitivity coefficients of temperature and heat flux over the boundary. The effectiveness of the proposed approach is illustrated through several numerical examples.