TY - GEN

T1 - Numerical solution to Maxwell's equations in singular waveguides

AU - Assous, Franck

PY - 2007

Y1 - 2007

N2 - This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. The geometry is called singular, in the sense that its boundary can include reentrant corners or edges. The difficulties arise from the fact that those geometrical singularities generate, in their neighborhood, strong electromagnetic fields. Using some new theoretical and practical results on singular electromagnetic fields, we have built a method which allows to compute the time-dependent electromagnetic field. It is based on a splitting of the spaces of solutions into a two-term direct (orthogonal) sum. First, the subspace of regular fields, which coincides with the whole space of solutions, in the case of convex or smooth boundary. Second, a singular subspace, defined and characterized via the singularities of the Laplace operator. Numerical results are presented to illustrate how the frequency of the ingoing electromagnetic waves influences the singular solution in a L-shaped waveguide.

AB - This paper is devoted to the numerical solution of the instationary Maxwell equations in singular waveguides. The geometry is called singular, in the sense that its boundary can include reentrant corners or edges. The difficulties arise from the fact that those geometrical singularities generate, in their neighborhood, strong electromagnetic fields. Using some new theoretical and practical results on singular electromagnetic fields, we have built a method which allows to compute the time-dependent electromagnetic field. It is based on a splitting of the spaces of solutions into a two-term direct (orthogonal) sum. First, the subspace of regular fields, which coincides with the whole space of solutions, in the case of convex or smooth boundary. Second, a singular subspace, defined and characterized via the singularities of the Laplace operator. Numerical results are presented to illustrate how the frequency of the ingoing electromagnetic waves influences the singular solution in a L-shaped waveguide.

KW - Finite-element method

KW - Maxwell's equation

KW - Singular geometry

KW - Waveguide

UR - http://www.scopus.com/inward/record.url?scp=84888322902&partnerID=8YFLogxK

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AN - SCOPUS:84888322902

SN - 9789889867171

T3 - Lecture Notes in Engineering and Computer Science

SP - 2366

EP - 2371

BT - IMECS 2007 - International MultiConference of Engineers and Computer Scientists 2007

T2 - International MultiConference of Engineers and Computer Scientists 2007, IMECS 2007

Y2 - 21 March 2007 through 23 March 2007

ER -