Boundary element approximation for Maxwell's eigenvalue problem. (1st July 2013)

• Record Type: Journal Article
• Authors: Wieners, Christian; Xin, Jiping
• Is Part Of: Mathematical methods in the applied sciences. Volume 36:Number 18(2013:Dec. 15)
• Page Start: 2524
• Page End: 2539
• Publication Date: 2013-07-01
• Subjects: Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.2772
• Languages: English
• ISSNs: 0170-4214

Abstract

<abstract abstract-type="main" id="mma2772-abs-0001"> <title> <x xml:space="preserve">Abstract</x> </title> <p id="mma2772-para-0001">We introduce a new method for computing eigenvalues of the Maxwell operator with boundary finite elements. On bounded domains with piecewise constant material coefficients, the Maxwell solution for fixed wave number can be represented by boundary integrals, which allows to reduce the eigenvalue problem to a nonlinear problem for determining the wave number along with boundary and interface traces. A Galerkin discretization yields a smooth nonlinear matrix eigenvalue problem that is solved by Newton's method or, alternatively, the contour integral method. Several numerical results including an application to the band structure computation of a photonic crystal illustrate the efficiency of this approach. Copyright © 2013 John Wiley &amp; Sons, Ltd.</p> </abstract>