PIER

Progress in Electromagnetic Research

J. A. Kong, Chief Editor

PIER 32 – Geometric Methods for Computational Electromagnetics

F. L. Teixeira, Guest Editor

http://ceta.mit.edu/pier/pier.php?volume=32

Contributors:

A. Bossavit, Eletricite de France, France

M. W. Buskas, Los Alamos National Laboratory, USA

M. Clemens, Technische Universitat Darmstadt, Germany

P. W. Gross, Mathematical Sciences Research Institute, USA

R. Hiptmair, Universitat Tubingen, Germany

J. M. Hyman, Los Alamos National Laboratory, USA

L. Kettunen, Tampere University of Technology, Finland

P. R. Kotiuga, Boston University, USA

M. Marrone, Universita di Trieste, Italy

C. Mattiussi, Swiss Federal Institute of Technology, Switzerland

P. Puska, Helsinki University of Technology, Finland

U. van Rienen, Universitat Rostock, Germany

R. Schuhmann, Technische Universitat Darmstadt, Germany

M. Shashkov, Los Alamos National Laboratory, USA

T. Tarhasaari, Tampere University of Technology, Finland

F. L. Teixeira, The Ohio State University, USA

E. Tonti, Universita di Trieste, Italy

T. Weiland, Technische Universitat Darmstadt, Germany

CONTENTS:

Section I. Geometric Methods and Discrete Electromagnetics

Chapter 1. Finite Formulation of the Electromagnetic Field

E. Tonti

Chapter 2. ‘Generalized Finite Differences' in Computational Electromagnetics

A. Bossavit

Chapter 3. Discrete Electromagnetism with the Finite Integration Technique

M. Clemens and T. Weiland

Chapter 4. Mimetic Finite Difference Methods for Maxwell's Equations and the Equations of Magnetic Diffusion

M. Shashkov and J. M. Hyman

Chapter 5. The Geometry of Time-Stepping

C. Mattiussi

Section II. Homological and Algebraic Techniques

Chapter 6. Data Structures for Geometric and Topological Aspects of Finite Element Algorithms

P. W. Gross and P. R. Kotiuga

Chapter 7. Geometric Aspects of the Simplicial Discretization of Maxwell's Equations

F. L. Teixeira

Chapter 8. Topological Approach to Computational Electromagnetism

T. Tarhasaari and L. Kettunen

Chapter 9. Finite Element-based Algorithms to Make Cuts for Magnetic Scalar Potentials: Topological Constraints and Computational Complexity

P. W. Gross and P. R. Kotiuga

Chapter 10. Discrete Hodge-Operators: An Algebraic Perspective

R. Hiptmair

Chapter 11. Higher Order Whitney Forms

R. Hiptmair

Section III. Implementation Aspects

Chapter 12. Conservation of Discrete Energy and Related Laws in the Finite Integration Technique

R. Schuhmann and T. Weiland

Chapter 13. Computational Aspects of the Cell Method in Electrodynamics

M. Marrone

Chapter 14. Frequency Domain Analysis of Waveguides and Resonators with FIT on Non-orthogonal Triangular Grids

U. van Rienen

Chapter 15. Implementing the Perfectly Matched Layer Absorbing Boundary Condition with Mimetic Differencing Schemes

M. W. Buksas

Section IV. Geometric Algebra for Electromagnetics

Chapter 16. Covariant Isotropic Constitutive Relations in Clifford's Geometric Algebra

P. Puska