Salvatore Alfonzetti, Giuseppe Borzì and Nunzio Salerno
The purpose of this paper is to improve the accuracy of the integral equation of the hybrid FEM‐RBCI (Finite Element Method‐Robin Boundary Condition Iteration) method for the…
Abstract
Purpose
The purpose of this paper is to improve the accuracy of the integral equation of the hybrid FEM‐RBCI (Finite Element Method‐Robin Boundary Condition Iteration) method for the numerical solution of two‐dimensional electromagnetic (or acoustic) scattering problems.
Design/methodology/approach
This accuracy improvement is achieved by selecting the integration curve as straight segments lying in the middle of the triangular finite elements. An accuracy improvement is obtained as compared with selecting the integration curve as constituted by element sides.
Findings
The improved FEM‐RBCI method described in this paper leads to accuracies of the numerical results which are better than those obtained by selecting the integration curve by element sides.
Originality/value
The paper presents results for a simple two‐dimensional structure: a dielectric circular cylinder.
Details
Keywords
Giovanni Aiello, Salvatore Alfonzetti, Giuseppe Borzì, Santi Agatino Rizzo and Nunzio Salerno
– The purpose of this paper is to compare the hybrid FEM-BEM and FEM-DBCI methods for the solution of open-boundary static and quasi-static electromagnetic field problems.
Abstract
Purpose
The purpose of this paper is to compare the hybrid FEM-BEM and FEM-DBCI methods for the solution of open-boundary static and quasi-static electromagnetic field problems.
Design/methodology/approach
After a brief review of the two methods (both coupling a differential equation for the interior problem with an integral equation for the exterior one), they are compared in terms of accuracy, memory and computing time requirements by means of a set of simple examples.
Findings
The comparison suggests that FEM-BEM is more accurate than FEM-DBCI but requires more computing time.
Practical implications
Then FEM-DBCI appears more appropriate for applications which require a shorter computing time, for example in the stochastic optimization of electromagnetic devices. Conversely, FEM-BEM is more appropriate in cases in which a high level of precision is required in a single computation.
Originality/value
Note that the FEM-BEM considered in this paper is a non standard one in which the nodes of the normal derivative on the truncation boundary are placed in positions different from those of the potential.
Details
Keywords
Giovanni Aiello, Salvatore Alfonzetti, Giuseppe Borzì, Emanuele Dilettoso and Nunzio Salerno
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…
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.