A local iteration scheme for nonlinear two-dimensional steady-state heat conduction: A BEM approach
The 2D steady-state heat conduction equation with nonlinear boundary conditions and temperature dependent thermal conductivity is reduced to the Laplace equation with nonlinear boundary conditions by Kirchoff's transformation. Applying the boundary element method (BEM) to the last problem, the resulting matrix equation becomes nonlinear. The author proposes a local iterative scheme to reduce this matrix equation to a smaller one whose rank is the same as the number of boundary nodes with nonlinear boundary conditions. That's the point of the paper. Some numerical results obtained for a two-region problem as well as for some cavity problems where radiation determines the heat transfer are displayed. For these specific problems the results look well, in spite of the fact that nothing is proved.
scientific article; zbMATH DE number 580025
scientific article