A GMRES iterative solution of FEM‐BEM global systems in skin effect problems

Abstract

Purpose

This paper aims to extend an efficient method to solve the global system of linear algebraic equations in the hybrid finite element method – boundary element method (FEM‐BEM) solution of open‐boundary skin effect problems. The extension covers the cases in which the skin effect problem is set in a truncated domain in which no homogeneous Dirichlet conditions are imposed.

Design/methodology/approach

The extended method is based on use of the generalized minimal residual (GMRES) solver, which is applied virtually to the reduced system of equations in which the unknowns are the nodal values of the normal derivative of the magnetic vector potential on the fictitious truncation boundary. In each step of the GMRES algorithm the FEM equations are solved by means of the standard complex conjugate gradient solver, whereas the BEM equations are not solved but used to perform fast matrix‐by‐vector multiplications. The BEM equations are written in a non‐conventional way, by making the nodes for the potential non‐coinciding with the nodes for its normal derivative.

Findings

The paper shows that the method proposed is very competitive with respect to other methods to solve open‐boundary skin effect problems.

Originality/value

The paper illustrates a new method to solve efficiently skin effect problems in open boundary domains by means of the hybrid FEM‐BEM method.

Citation

Aiello, G., Alfonzetti, S., Borzì, G., Dilettoso, E. and Salerno, N. (2008), "A GMRES iterative solution of FEM‐BEM global systems in skin effect problems", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 27 No. 6, pp. 1286-1295. https://doi.org/10.1108/03321640810905765