SOLVING NONLINEAR STEADY-STATE POTENTIAL PROBLEMS IN INHOMOGENOUS BODIES USING THE BOUNDARY-ELEMENT METHOD

An efficient algorithm for solving nonlinear steady-state potential problems in multilayered media using the boundary-element method (BEM) is presented. Two sources of nonlinearity are considered: Solution-dependent material properties and nonlinear boundary conditions, The approach is based on Kirchhoff's transformation. Applying this transformation and a standard BEM technique results in a set of nonlinear equations. The final version of the developed nonlinear equations solver evolved from some simple iteration schemes that proved to be divergent or slowly convergent. The solver relies on the incremental loading concept and Aitken extrapolation. Numerical examples dealing with thermal analysis of industrial furnaces are included. A simple and efficient Kirchhoff's transformation and inverse transformation technique is described. © 1989 by Hemisphere Publishing Corporation.