Comparison of Methods for Solving Nonlinear Finite-Element Equations in Heat Transfer

摘要

We have derived two new techniques for solving the finite-element heat-transfer equations with highly nonlinear boundary conditions and material properties. When compared with the more commonly employed successive substitution and Newton-Raphson procedures, the new methods speed convergence rates and simultaneously increase the radius of convergence. We have observed reductions in computation time in excess of 80% when the new techniques are employed. The first method accelerates the standard Newton-Raphson approach when the degree of the nonlinearity is known (for example, radiation boundary conditions or a prescribed temperature dependence in the thermal conductivity). The second technique employs feedback to regulate the solution algorithm during execution. Comparisons of these techniques are given for several practical examples. (ERA citation 07:047686)