Title :
A discontinuous Galerkin method with Lagrange multipliers to solve vector electromagnetic problems in two dimensions
Author :
Xue, Ming-Feng ; Jin, Jian-Ming
Author_Institution :
Dept. of Electr. & Comput. Eng., Univ. of Illinois at Urbana-Champaign, Urbana, IL, USA
Abstract :
A discontinuous Galerkin method is formulated with plane wave basis functions and Lagrange multipliers to solve the vector curl-curl equation. This method was developed only for the scalar Helmholtz equation in both two-dimensional (2D) and three-dimensional (3D) cases. By defining vector plane waves and vector Lagrange multipliers within unstructured quadrilateral elements and along the element boundaries, this algorithm can be extended to solve 2D vector problems. Numerical results for wave propagation and scattering by perfect electric conducting (PEC) cylinders are presented to validate the proposed method.
Keywords :
Galerkin method; Helmholtz equations; electromagnetic wave propagation; electromagnetic wave scattering; 2D vector problems; 3D cases; Lagrange multipliers; PEC; discontinuous Galerkin method; element boundaries; perfect electric conducting cylinders; plane wave basis functions; scalar Helmholtz equation; three-dimensional cases; two-dimensional cases; unstructured quadrilateral elements; vector curl-curl equation; vector electromagnetic problems; wave propagation; wave scattering; Electric fields; Equations; Finite element methods; Mathematical model; Moment methods; Scattering; Vectors;
Conference_Titel :
Antennas and Propagation Society International Symposium (APSURSI), 2012 IEEE
Conference_Location :
Chicago, IL
Print_ISBN :
978-1-4673-0461-0
DOI :
10.1109/APS.2012.6349014
