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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)

- Sabine Zaglmayr
- 2006

This thesis deals with the higher-order Finite Element Method (FEM) for computational electromagnetics. The hp-version of FEM combines local mesh refinement (h) and local increase of the polynomial order of the approximation space (p). A key tool in the design and the analysis of numerical methods for electromagnetic problems is the de Rham Complex relating… (More)

- Manfred G Hofer, N. Finger, +4 authors Reinhard Lerch
- IEEE transactions on ultrasonics, ferroelectrics…
- 2006

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)

- Bernardo M. Rocha, Ferdinand Kickinger, +5 authors Gernot Plank
- IEEE Trans. Biomed. Engineering
- 2011

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)

- Martin Huber, Joachim Schöberl, Astrid Sinwel, Sabine Zaglmayr
- SIAM J. Scientific Computing
- 2009

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)

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)

- Sven Beuchler, Veronika Pillwein, Sabine Zaglmayr
- Numerische Mathematik
- 2012

This paper deals with conforming high-order finite element discretizations of the vectorvalued 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
- Domain Decomposition Methods in Science and…
- 2013

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)

1 FWF-Start Project Y-192 “3D hp-Finite Elements”, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, Austria sz@jku.at 2 Radon Institute for Computational and Applied Mathematics (RICAM), Altenbergerstraße 69, 4040 Linz, Austria joachim.schoeberl@oeaw.ac.at 3 Institute of Computational Mathematics, Johannes Kepler University Linz,… (More)

- Martin Eller, Stefan Reitzinger, Sebastian Schöps, Sabine Zaglmayr
- SIAM J. Scientific Computing
- 2017

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