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Solution of 3D singular electrostatics problems using adaptive hp ‐FEM

Solution of 3D singular electrostatics problems using adaptive hp ‐FEM Purpose – This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp ‐FEM and to show the benefits of this approach. Numerical experiments are presented to demonstrate its superiority. Design/methodology/approach – Adaptive hp ‐FEM is used. In contrast with standard FEM, the automatic adaptivity procedure can choose from a variety of refinement candidates. An element with over estimated error can be refined in space, or its polynomial degree can be increased. Arbitrary level hanging nodes are allowed, so that no unnecessary refinements are performed in order to keep a mesh regular. Findings – Numerical solution of a singular electrostatic problem is presented. From the comparison it can be seen that the hp ‐FEM outperforms both the standard linear and quadratic elements significantly. The accuracy of an hp ‐FEM solution would be hard to attain by standard means due to the limited capacity of the computer memory. Originality/value – The paper describes results obtained from an original and innovative implementation of the adaptive hp ‐FEM. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic Engineering Emerald Publishing

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References (4)

Publisher
Emerald Publishing
Copyright
Copyright © 2008 Emerald Group Publishing Limited. All rights reserved.
ISSN
0332-1649
DOI
10.1108/03321640810878360
Publisher site
See Article on Publisher Site

Abstract

Purpose – This paper seeks to describe the solution of a simple electrostatic problem using an adaptive hp ‐FEM and to show the benefits of this approach. Numerical experiments are presented to demonstrate its superiority. Design/methodology/approach – Adaptive hp ‐FEM is used. In contrast with standard FEM, the automatic adaptivity procedure can choose from a variety of refinement candidates. An element with over estimated error can be refined in space, or its polynomial degree can be increased. Arbitrary level hanging nodes are allowed, so that no unnecessary refinements are performed in order to keep a mesh regular. Findings – Numerical solution of a singular electrostatic problem is presented. From the comparison it can be seen that the hp ‐FEM outperforms both the standard linear and quadratic elements significantly. The accuracy of an hp ‐FEM solution would be hard to attain by standard means due to the limited capacity of the computer memory. Originality/value – The paper describes results obtained from an original and innovative implementation of the adaptive hp ‐FEM.

Journal

COMPEL: The International Journal for Computation and Mathematics in Electrical and Electronic EngineeringEmerald Publishing

Published: Jul 11, 2008

Keywords: Simulation; Finite element analysis; Meshes; Electrostatics

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