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Analytical Finite Element Matrix Elements and Global Matrix Assembly for Hierarchical 3-d Vector Basis Functions Within the Hybrid Finite Element Boundary Integral Method : Volume 12, Issue 1 (10/11/2014)

By Li, L.

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Book Id: WPLBN0004002725
Format Type: PDF Article :
File Size: Pages 11
Reproduction Date: 2015

Title: Analytical Finite Element Matrix Elements and Global Matrix Assembly for Hierarchical 3-d Vector Basis Functions Within the Hybrid Finite Element Boundary Integral Method : Volume 12, Issue 1 (10/11/2014)  
Author: Li, L.
Volume: Vol. 12, Issue 1
Language: English
Subject: Science, Advances, Radio
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Historic
Publication Date:
2014
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications

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Li, H., Wang, K., Eibert, T. F., & Li, L. (2014). Analytical Finite Element Matrix Elements and Global Matrix Assembly for Hierarchical 3-d Vector Basis Functions Within the Hybrid Finite Element Boundary Integral Method : Volume 12, Issue 1 (10/11/2014). Retrieved from http://www.ebooklibrary.org/


Description
Description: Technische Universität München, Lehrstuhl für Hochfrequenztechnik, Arcisstrasse 21, 80333 Munich, Germany. A hybrid higher-order finite element boundary integral (FE-BI) technique is discussed where the higher-order FE matrix elements are computed by a fully analytical procedure and where the gobal matrix assembly is organized by a self-identifying procedure of the local to global transformation. This assembly procedure applys to both, the FE part as well as the BI part of the algorithm. The geometry is meshed into three-dimensional tetrahedra as finite elements and nearly orthogonal hierarchical basis functions are employed. The boundary conditions are implemented in a strong sense such that the boundary values of the volume basis functions are directly utilized within the BI, either for the tangential electric and magnetic fields or for the asssociated equivalent surface current densities by applying a cross product with the unit surface normals. The self-identified method for the global matrix assembly automatically discerns the global order of the basis functions for generating the matrix elements. Higher order basis functions do need more unknowns for each single FE, however, fewer FEs are needed to achieve the same satisfiable accuracy. This improvement provides a lot more flexibility for meshing and allows the mesh size to raise up to Λ/3. The performance of the implemented system is evaluated in terms of computation time, accuracy and memory occupation, where excellent results with respect to precision and computation times of large scale simulations are found.

Summary
Analytical finite element matrix elements and global matrix assembly for hierarchical 3-D vector basis functions within the hybrid finite element boundary integral method

Excerpt
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