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The goal of the presented work is the efficient computation of Maxwell boundary and eigenvalue problems using high order H(curl) finite elements. We discuss a systematic strategy for the realization of arbitrary order hierarchic H(curl)-conforming finite elements for triangular and tetrahedral element geometries. The shape functions are classified as… (More)

The aim of this paper is to discuss simulation methods of diffraction of electromagnetic waves on biperiodic structures. The region with complicated structures is discretised by Nédélec Finite Elements. In the unbounded homogeneous regions above and below, a plane wave expansion containing the exact far-field pattern is applied. A consistent coupling is… (More)

Many surface acoustic wave (SAW) devices consist of quasiperiodic structures that are designed by successive repetition of a base cell. The precise numerical simulation of such devices, including all physical effects, is currently beyond the capacity of high-end computation. Therefore, we have to restrict the numerical analysis to the periodic substructure.… (More)

Electrical activity in cardiac tissue can be described by the bidomain equations whose solution for large-scale simulations still remains a computational challenge. Therefore, improvements in the discrete formulation of the problem, which decrease computational and/or memory demands are highly desirable. In this study, we propose a novel technique for… (More)

This paper deals with conforming high-order finite element discretizations of the vector-valued function space H(div) in 2 and 3 dimensions. A new set of hierarchic basis functions on simplices with the following two main properties is introduced. When working with an affine, simplicial triangulation, first, the divergence of the basis functions is… (More)

- Sven Beuchler, Veronika Pillwein, Sabine Zaglmayr
- 2012

H(curl) conforming finite element discretizations are a powerful tool for the numerical solution of the system of Maxwell's equations in electrodynamics. In this paper we construct a basis for conforming high-order finite element discretizations of the function space H(curl) in 3 dimensions. We introduce a set of hierarchic basis functions on tetrahedra… (More)

- Manfred Hofer, Norman Finger, Sabine Zaglmayr, Joachim Schöberl, Günter Kovacs, Ulrich Langer +1 other
- 2002

In the design procedure of surface acoustic wave (SAW) devices simple models like Equivalent Circuit Models or the Coupling of Modes (COM) Model are used to achieve short calculation times. Therefore, these models can be used for iterative component optimization. However, they are subject to many simplifications and restrictions. In order to improve the… (More)

This paper considers the hp-finite element discretization of an elliptic boundary value problem using tetrahedral elements. The discretization uses a polynomial basis in which the number of nonzero entries per row is bounded independently of the polynomial degree. The authors present an algorithm which computes the nonzero entries of the stiffness matrix in… (More)

Surface acoustic wave filters are widely used for frequency filtering in telecommunications. These devices mainly consist of a piezoelectric substrate with periodically arranged electrodes on the surface. The periodic structure of the electrodes subdivides the frequency domain into stop-bands and pass-bands. This means only piezoelectric waves excited at… (More)

- Sven Beuchler, Veronika Pillwein, Sabine Zaglmayr, Bruno Buchberger, Bert Jüttler, Ulrich Langer +8 others
- 2010

This paper deals with conforming high-order finite element discretizations of the vector-valued function space H(div) in 2 and 3 dimensions. A new set of hierarchic basis functions on simplices with the following two main properties is introduced. Provided an affine simplicial triangulation, first, the divergence of the basis functions is L2-orthogonal, and… (More)

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