Convergence enhancement for the vector finite element modeling of microwaves and antennas via differential evolution

A global optimization technique, based on the differential evolution algorithm is introduced to trace the optimal higherorder Whitney element, with respect to convergence, among a very wide class of parameter-dependent finite elements. Any tetrahedral element of this class provides exactly the same solution, but the convergence of the iterative solution method may significantly vary. Through the proposed comprehensive optimization procedure, the existence of optimal vector finite elements is revealed. The proposed method has been applied to obtain second-order elements utilized in three-dimensional microwave and antenna simulations. 2005 Elsevier GmbH. All rights reserved.

[1]  A. Bossavit.  Whitney forms: a class of finite elements for three-dimensional computations in electromagnetism , 1988 .

[2]  Gene H. Golub,et al.  Matrix computations , 1983 .

[3]  Shiwen Yang,et al.  Antenna‐array pattern nulling using a differential evolution algorithm , 2004 .

[4]  L. S. Andersen,et al.  Hierarchical tangential vector finite elements for tetrahedra , 1998 .

[5]  Rainer Storn,et al.  Differential Evolution – A Simple and Efficient Heuristic for global Optimization over Continuous Spaces , 1997, J. Glob. Optim..

[6]  Z. Ren,et al.  Solving 3D eddy current problems using second order nodal and edge elements , 2000 .

[7]  Anyong Qing,et al.  Electromagnetic inverse scattering of multiple two-dimensional perfectly conducting objects by the differential evolution strategy , 2003 .

[8]  Krzysztof A. Michalski,et al.  Electromagnetic imaging of circular–cylindrical conductors and tunnels using a differential evolution algorithm , 2000 .

[9]  Roberto D. Graglia,et al.  Higher order interpolatory vector bases for computational electromagnetics," Special Issue on "Advanced Numerical Techniques in Electromagnetics , 1997 .

[10]  Theodoros D. Tsiboukis,et al.  Development and implementation of second and third order vector finite elements in various 3-D electromagnetic field problems , 1997 .

[11]  Jin-Fa Lee,et al.  Tangential vector finite elements for electromagnetic field computation , 1991 .

[12]  J. P. Webb.  Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements , 1999 .