Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1 One and Two Dimensional Elliptic and Maxwell Problems

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CRC Press, Oct 25, 2006 - Science - 398 pages
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Offering the only existing finite element (FE) codes for Maxwell equations that support hp refinements on irregular meshes, Computing with hp-ADAPTIVE FINITE ELEMENTS: Volume 1. One- and Two-Dimensional Elliptic and Maxwell Problems presents 1D and 2D codes and automatic hp adaptivity. This self-contained source discusses the theory and implementation of hp-adaptive FE methods, focusing on projection-based interpolation and the corresponding hp-adaptive strategy.

The book is split into three parts, progressing from simple to more advanced problems. Part I examines the hp elements for the standard 1D model elliptic problem. The author develops the variational formulation and explains the construction of FE basis functions. The book then introduces the 1D code (1Dhp) and automatic hp adaptivity. This first part ends with a study of a 1D wave propagation problem. In Part II, the book proceeds to 2D elliptic problems, discussing two model problems that are slightly beyond standard-level examples: 3D axisymmetric antenna problem for Maxwell equations (example of a complex-valued, indefinite problem) and 2D elasticity (example of an elliptic system). The author concludes with a presentation on infinite elements - one of the possible tools to solve exterior boundary-value problems. Part III focuses on 2D time-harmonic Maxwell equations. The book explains the construction of the hp edge elements and the fundamental de Rham diagram for the whole family of hp discretizations. Next, it explores the differences between the elliptic and Maxwell versions of the 2D code, including automatic hp adaptivity. Finally, the book presents 2D exterior (radiation and scattering) problems and sample solutions using coupled hp finite/infinite elements.

In Computing with hp-ADAPTIVE FINITE ELEMENTS, the information provided, including many unpublished details, aids in solving elliptic and Maxwell problems.
 

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Contents

Chapter 1 1D Model Elliptic Problem
3
Chapter 2 Galerkin Method
33
Chapter 3 1D hp Finite Element Method
41
Chapter 4 1D hp Code
57
Chapter 5 Mesh Refinements in 1D
71
Chapter 6 Automatic hp Adaptivity in 1D
95
Chapter 7 Wave Propagation Problems
117
Part II 2D Elliptic Problems
133
Chapter 15 Examples of Applications
241
Chapter 16 Exterior BoundaryValue Problems
259
Part III 2D Maxwell Problems
283
Chapter 17 2D Maxwell Equations
285
Chapter 18 Edge Elements and the de Rham Diagram
301
Chapter 19 2D Maxwell Code
323
Chapter 20 hp Adaptivity for Maxwell Equations
337
Chapter 21 Exterior Maxwell BoundaryValue Problems
351

Chapter 8 2D Elliptic BoundaryValue Problem
135
Chapter 9 Sobolev Spaces
149
Chapter 10 2D hp Finite Element Mehtod on Regular Meshes
163
Chapter 11 2D hp Code
185
Chapter 12 Geometric Modeling and Mesh Generation
195
Chapter 13 The hp Finite Element Method on hRefined Meshes
211
Chapter 14 Automatic hp Adaptivity in 2D
227
Chapter 22 A Quick Summary and Outlook
369
Appendix A Construction of makefile
371
Bibliography
375
Index
389
Back cover
399
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