Irina Munteanu, Silvia Drobny, Thomas Weiland and Daniel Ioan
This paper presents a hybrid algorithm used, in conjunction with the Finite Integration Technique (FIT), for solving static and quasistatic electromagnetic field problems in…
Abstract
This paper presents a hybrid algorithm used, in conjunction with the Finite Integration Technique (FIT), for solving static and quasistatic electromagnetic field problems in nonlinear media. The hybrid technique is based on new theoretical results regarding the similarities between the Picard‐Banach fixed‐point (polarization) method and the Newton method. At each iteration, the solution is obtained as a linear combination of the old solution, and the new Picard‐Banach and Newton solutions. The numerical solutions are calculated through a “triangle” (bidimensional) minimization of the residual or of the energy functional. The goal of this combination is to increase the robustness of the iterative method, without losing the quadratic speed of convergence in the vicinity of the solution. The proposed method generalizes and unifies in a single algorithm the overrelaxed Picard‐Banach and the underrelaxed Newton methods.
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Irina Munteanu, Catalin Ciobotaru and Daniel Ioan
The numerical solution of electromagnetic field nonlinear problems requires successive building and solving of linear systems of equations. This is the most time–consuming part…
Abstract
The numerical solution of electromagnetic field nonlinear problems requires successive building and solving of linear systems of equations. This is the most time–consuming part, especially for large problems. Both fast linear solvers and efficient nonlinear iterative algorithms, are critical for the overall efficiency of the nonlinear electromagnetic field solver. This paper presents an analysis of a variety of techniques that can be efficiently used to reduce the solution time of nonlinear magnetic field equations in large finite element method (FEM) problems.