Numerical analysis of the exterior boundary value problem for the time-harmonic Maxwell equations by a boundary finite element method. II. The discrete problem

Abstract

Abstract. With the help of curved and mixed finite elements, we introduce an approximate surface on which the discrete problem is defined and construct surface currents and charges which approximate the solution of the continuous problem studied in a previous part. We study the existence and uniqueness of the solution of the discrete problem and give estimates for the error between currents, charges, corresponding fields and their calculated approximations.

A dual finite element complex on the barycentric refinement

“…Such finite element spaces on surfaces were considered in the context of integral equations for electromagnetism in Bendali [4]. For definitions of the functional spaces in the case of non-smooth surfaces we refer to Buffa-Ciarlet [11].…”

“…This work was started while the first author was a visitor at CMA, University of Oslo, May [24][25][26][27][28] 2004, and continued while the second author was a visitor at IMATI, CNR Pavia, October [4][5][6][7][8] 2004. We are grateful to both institutions for their kind hospitality.…”

“…In the boundary element method these are solved approximately by introducing finite-element spaces of vector fields on Γ. In particular, the most successful space for solving the so-called electric field integral equation consists of surface Raviart-Thomas vector fields constructed on a triangulation of Γ (see Bendali [4]). We denote by X 1 this space of divergence conforming vector fields.…”

Computational electromagnetics for multi-scale structures in circuits

“…This method treats the charge as an unknown and introduces an additional equation to relate the current and the charge [5]. The fmal matrix equation has the generalized saddle point form [6].…”

Iterative solution of a hybrid method for Maxwell's equations in the frequency domain

“…As basis functions f n the so called Rao-Wilton-Glisson (RWG) edge elements [10] are chosen. Other more accurate basis functions are discussed in Reference [11]. The currents are represented by…”