Newton and quasi‐Newton algorithms for non‐linear electromagnetic–thermal coupled problems
Johan Driesen, Kay Hameyer · COMPEL The International Journal for Computation and Mathematics in Electrical and Electronic Engineering · 2002
A general framework for the application of the Newton methods in non‐linear coupled electromagnetic‐thermal problems solved with the FEM on independent subproblem meshes is presented. The explicit derivation of the Jacobian matrix is outlined and discussed. A matrix‐free quasi‐Newton method, to be used along with linear system solvers built around Jacobian‐vector products is presented. This method does not require explicit derivatives and can be parallelised. The numerical aspects of these methods are discussed. The different Newton methods are demonstrated using a steady‐state conductive heating example problem.