Summary and Overview

The goal of any analysis or optimization is to achieve sufficient accuracy with minimum effort, where effort usually is interpreted as computational cost in terms of computational time and memory requirements. However, there may also be a considerable effort associated with other issues such as the programming of the numerical algorithm or the construction of geometrical descriptions suitable for the the computations at hand.

[1]  J. Nédélec.  Mixed finite elements in ℝ3 , 1980 .

[2]  J. P. Webb.  Hierarchal vector basis functions of arbitrary order for triangular and tetrahedral finite elements , 1999 .

[3]  W. L. Golik.  Wavelet packets for fast solution of electromagnetic integral equations , 1998 .

[4]  Jiming Song,et al.  Multilevel fast multipole algorithm for electromagnetic scattering by large complex objects , 1997 .

[5]  Xin-Qing Sheng,et al.  Essentials of Computational Electromagnetics: Sheng/Essentials of Computational Electromagnetics , 2012 .

[6]  Bryan P. Rynne,et al.  INSTABILITIES IN TIME MARCHING METHODS FOR SCATTERING PROBLEMS , 1986 .

[7]  Roberto D. Graglia,et al.  On the numerical integration of the linear shape functions times the 3-D Green's function or its gradient on a plane triangle , 1993 .

[8]  R. Coifman,et al.  The fast multipole method for the wave equation: a pedestrian prescription , 1993, IEEE Antennas and Propagation Magazine.

[9]  William Gropp,et al.  Extensible Toolkit for Scientific Computing , 1996 .

[10]  R. Mittra,et al.  Time-domain (FE/FDTD) technique for solving complex electromagnetic problems , 1998 .

[11]  Andrew J. Poggio,et al.  CHAPTER 4 – Integral Equation Solutions of Three-dimensional Scattering Problems , 1973 .

[12]  Ralf Hiptmair,et al.  Multilevel solution of the time‐harmonic Maxwell's equations based on edge elements , 1999 .

[13]  Nathan M. Newmark,et al.  A Method of Computation for Structural Dynamics , 1959 .

[14]  D. J. Riley,et al.  VOLMAX: a solid-model-based, transient volumetric Maxwell solver using hybrid grids , 1997 .

[15]  O. Axelsson.  Iterative solution methods , 1995 .

[16]  P. Smith,et al.  Instabilities in Time Marching Methods for Scattering: Cause and Rectification , 1990 .

[17]  D. Cheng.  Fundamentals of Engineering Electromagnetics , 2014 .

[18]  Ruey-Beei Wu,et al.  Hybrid finite-difference time-domain modeling of curved surfaces using tetrahedral edge elements , 1997 .

[19]  Roberto Sorrentino,et al.  A revised formulation of modal absorbing and matched modal source boundary conditions for the efficient FDTD analysis of waveguide structures , 2000 .

[20]  Jian-Ming Jin,et al.  Fast and Efficient Algorithms in Computational Electromagnetics , 2001 .

[21]  Wolfgang J. R. Hoefer,et al.  The Transmission-Line Matrix Method--Theory and Applications , 1985 .

[22]  V. Rokhlin.  Rapid solution of integral equations of classical potential theory , 1985 .

[23]  P. Johns.  A Symmetrical Condensed Node for the TLM Method , 1987 .

[24]  F. X. Canning,et al.  Fast direct solution of standard moment-method matrices , 1998 .

[25]  Richard Barrett,et al.  Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods , 1994, Other Titles in Applied Mathematics.

[26]  Allen Taflove,et al.  Computational Electrodynamics the Finite-Difference Time-Domain Method , 1995 .

[27]  A. Cangellaris,et al.  Analysis of the numerical error caused by the stair-stepped approximation of a conducting boundary in FDTD simulations of electromagnetic phenomena , 1991 .

[28]  Jian-Ming Jin,et al.  On the variational formulation of hybrid finite element-boundary integral techniques for electromagnetic analysis , 2004, IEEE Transactions on Antennas and Propagation.

[29]  Jiming Song,et al.  Fast Illinois solver code (FISC) , 1998 .

[30]  D. Wilton,et al.  Electromagnetic scattering by surfaces of arbitrary shape , 1980 .

[31]  Jian-Ming Jin,et al.  Perfectly matched layer for the time domain finite element method , 2004 .

[32]  O. Biro,et al.  A joint vector and scalar potential formulation for driven high frequency problems using hybrid edge and nodal finite elements , 1996 .

[33]  D. Wilton,et al.  Transient scattering by conducting surfaces of arbitrary shape , 1991 .

[34]  Thomas Weiland,et al.  Numerical stability of finite difference time domain methods , 1998 .

[35]  R. Mittra,et al.  Computational Methods for Electromagnetics , 1997 .

[36]  Ortwin Farle,et al.  A stabilized multilevel vector finite-element solver for time-harmonic electromagnetic waves , 2003 .

[37]  Wolfgang Hackbusch,et al.  Multi-grid methods and applications , 1985, Springer series in computational mathematics.

[38]  Tapan K. Sarkar,et al.  Iterative and Self-Adaptive Finite-Elements in Electromagnetic Modeling , 1998 .

[39]  M. Bluck,et al.  Time-domain BIE analysis of large three-dimensional electromagnetic scattering problems , 1997 .

[40]  J. S. Chen,et al.  The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving Maxwell's equations , 1997 .

[41]  J. Bey,et al.  Tetrahedral grid refinement , 1995, Computing.

[42]  K. S. Yee,et al.  Numerical experiments on PEC boundary condition and late time growth involving the FDTD/FDTD and FDTD/FVTD hybrid , 1995, IEEE Antennas and Propagation Society International Symposium. 1995 Digest.

[43]  Thomas Rylander,et al.  Stability of Explicit-Implicit Hybrid Time-Stepping Schemes for Maxwell's Equations , 2002 .

[44]  Ramesh Garg,et al.  Analytical and Computational Methods in Electromagnetics , 2008 .

[45]  Manfred Kaltenbacher,et al.  Nested multigrid methods for the fast numerical computation of 3D magnetic fields , 2000 .

[46]  Wolfgang J. R. Hoefer,et al.  A new finite-difference time-domain formulation and its equivalence with the TLM symmetrical condensed node , 1991 .

[47]  Weng Cho Chew,et al.  A study of wavelets for the solution of electromagnetic integral equations , 1995 .

[48]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[49]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[50]  Andreas C. Cangellaris,et al.  A Reflectionless Sponge Layer Absorbing Boundary Condition for the Solution of Maxwell's Equations with High-Order Staggered Finite Difference Schemes , 1998 .

[51]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[52]  Karl F. Warnick.  Numerical Methods for Engineering: An introduction using MATLAB® and computational electromagnetics examples , 2020 .

[53]  V. Rokhlin.  Rapid Solution of Integral Equations of Scattering Theory , 1990 .

[54]  Rolf Schuhmann,et al.  Stability of the FDTD algorithm on nonorthogonal grids related to the spatial interpolation scheme , 1998 .

[55]  Claes Johnson,et al.  Eddy-current computations using adaptive grids and edge elements , 2002 .

[56]  Jean-Pierre Berenger,et al.  A perfectly matched layer for the absorption of electromagnetic waves , 1994 .

[57]  Mats Viberg,et al.  Estimation of resonant frequencies and quality factors from time domain computations , 2003 .

[58]  Jin-Fa Lee,et al.  A fast vector-potential method using tangentially continuous vector finite elements , 1998 .

[59]  P.-S. Kildal,et al.  Analysis of Nearly Cylindrical Antennas and Scattering Problems Using a Spectrum of Two-Dimentional Solutions , 1996 .

[60]  T. Weiland.  Time Domain Electromagnetic Field Computation with Finite Difference Methods , 1996 .

[61]  Jianming Jin.  Theory and Computation of Electromagnetic Fields , 2010 .

[62]  P. Wesseling.  An Introduction to Multigrid Methods , 1992 .

[63]  Jian-Ming Jin,et al.  The Finite Element Method in Electromagnetics , 1993 .

[64]  F. X. Canning,et al.  Improved impedance matrix localization method (EM problems) , 1993 .

[65]  Claes Johnson,et al.  Computational Differential Equations , 1996 .

[66]  Sadasiva M. Rao,et al.  A stable procedure to calculate the transient scattering by conducting surfaces of arbitrary shape , 1992 .

[67]  Jonathan Richard Shewchuk,et al.  Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator , 1996, WACG.

[68]  Thomas Rylander,et al.  Computational Electromagnetics , 2005, Electronics, Power Electronics, Optoelectronics, Microwaves, Electromagnetics, and Radar.

[69]  Peter P. Silvester,et al.  Finite Elements for Electrical Engineers , 1983 .

[70]  Manfred Kaltenbacher,et al.  Algebraic multigrid methods for magnetostatic field problems , 2002 .

[71]  C. Balanis.  Advanced Engineering Electromagnetics , 1989 .

[72]  R. Hiptmair.  Multigrid Method for Maxwell's Equations , 1998 .

[73]  Richard W. Ziolkowski,et al.  A Three-Dimensional Modified Finite Volume Technique for Maxwell's Equations , 1990 .

[74]  Peter Monk.  A Comparison of Three Mixed Methods for the Time-Dependent Maxwell's Equations , 1992, SIAM J. Sci. Comput..

[75]  M. J. Bluck,et al.  Costs and cost scaling in time-domain integral-equation analysis of electromagnetic scattering , 1998 .

[76]  Weng Cho Chew,et al.  The Fast Illinois Solver Code: requirements and scaling properties , 1998 .

[77]  Pär Ingelström.  Higher Order Finite Elements and Adaptivity in Computational Electromagnetics , 2004 .

[78]  M. Celuch-Marcysiak,et al.  Generalized TLM algorithms with controlled stability margin and their equivalence with finite-difference formulations for modified grids , 1995 .