Performance of the Alternating Direction Implicit Scheme With Recursive Sparsification for the Finite Element Time Domain Method

Author

de Moura, Alex Sander ; Silva, Elson J. ; Saldanha, Rodney R. ; Gomes Facco, Werley

Author_Institution

Dept. of Econ. Sci., Fed. Univ. of Juiz de Fora, Governador Valadares, Brazil

Volume

51

Issue

3

fYear

2015

fDate

Mar-15

Firstpage

1

Lastpage

4

Abstract

In this paper, we solve the ε and B mixed finite element time domain formulation using the alternating-direction implicit (ADI) scheme in time. To save computational cost, the algorithm is improved using a recursive sparsification procedure that approximates the inverse matrix needed to calculate the electric field. Although the method is unconditionally stable, we show that the numerical performance of the algorithm is strongly related to the time step. Numerical results demonstrated that for the same accuracy our approach is much faster than the ADI with Cholesky factorization.

Keywords

finite element analysis; ADI; Cholesky factorization; alternating direction implicit scheme; electric field calculation; finite element time domain formulation; finite element time domain method; inverse matrix approximation; numerical performance; recursive sparsification procedure; Accuracy; Approximation methods; Cavity resonators; Finite element analysis; Mathematical model; Sparse matrices; Time-domain analysis; Alternating-direction implicit (ADI); block matrix inversion; differential forms; finite element time domain (FETD); recursive sparsification;

fLanguage

English

Journal_Title

Magnetics, IEEE Transactions on

Publisher

ieee

ISSN

0018-9464

Type

jour

DOI

10.1109/TMAG.2014.2349942

Filename

7093555