A review of finite element open boundary techniques for static and quasi-static electromagnetic field problems

This paper presents a review of finite element open boundary techniques for the computation of static and quasistatic electromagnetic fields. The underlying assumptions and ideas behind these techniques are outlined and explained. The advantages and shortcomings of each technique are discussed. The goal of this review is to aid those working on numerical solutions of open boundary problems using the finite element method to gain perspectives on the variety of techniques presently available or being developed. This review is also intended to facilitate the communication of numerical techniques between the low-frequency field computation community and those in the high-frequency community.

[1]  C. Wilcox.  An expansion theorem for electromagnetic fields , 1956 .

[2]  A. M. Winslow,et al.  MAGNETIC FIELD CALCULATIONS IN AN IRREGULAR TRIANGLE MESH , 1965 .

[3]  D. Greenspan,et al.  The calculation of electrostatic capacity by means of a high-speed digital computer , 1965 .

[4]  P. Silvester,et al.  Solution of 2-dimensional field problems by boundary relaxation , 1968 .

[5]  P. Silvester,et al.  Finite-element solution of 2-dimensional exterior-field problems , 1971 .

[6]  B. McDonald,et al.  Finite-Element Solution of Unbounded Field Problems , 1972 .

[7]  K. Mei.  Uni-moment method of solving antenna and scattering problems , 1973 .

[8]  Warwick D. Smith.  A nonreflecting plane boundary for wave propagation problems , 1974 .

[9]  A. Taflove,et al.  Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations , 1975 .

[10]  E. Lindman.  “Free-space” boundary conditions for the time dependent wave equation , 1975 .

[11]  Z. Csendes.  A Note on the Finite-Element Solution of Exterior-Field Problems (Short Papers) , 1976 .

[12]  Shu-Kong Chang,et al.  Application of the unimoment method to electromagnetic scattering of dielectric cylinders , 1976 .

[13]  P. Silvester,et al.  Exterior finite elements for 2-dimensional field problems with open boundaries , 1977 .

[14]  D. Lowther,et al.  A finite element technique for solving 2-D open boundary problems , 1978 .

[15]  S. B. Dong,et al.  Single-mode optical waveguides. , 1979, Applied optics.

[16]  B. Nath,et al.  The w‐plane finite element method for the solution of scalar field problems in two dimensions , 1980 .

[17]  G. Mur.  Absorbing Boundary Conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations , 1981, IEEE Transactions on Electromagnetic Compatibility.

[18]  S. J. Salon,et al.  A hybrid finite element-boundary integral formulation of Poisson's equation , 1981 .

[19]  A. Konrad.  The numerical solution of steady-state skin effect problems--An integrodifferential approach , 1981 .

[20]  H. Niki,et al.  Analysis of Open-Type Dielectric Waveguides by the Finite-Element Iterative Method , 1981 .

[21]  J. L. Meek,et al.  `Infinite domain' elements , 1981 .

[22]  P. Silvester,et al.  A static ballooning technique for 2‐D open boundary problems , 1982 .

[23]  S. Pissanetzky.  Solution of three-dimensional, anisotropic, nonlinear problems of magnetostatics using two scalar potentials, finite and infinite multipolar elements and automatic mesh generation , 1982 .

[24]  J.-C. Verite,et al.  A mixed fem-biem method to solve 3-D eddy-current problems , 1982 .

[25]  S. J. Salon,et al.  A hybrid finite element–boundary element formulation of Poisson’s equation for axisymmetric vector potential problems , 1982 .

[26]  John R. Brauer,et al.  Open boundary finite elements for axisymmetric magnetic and skin effect problems , 1982 .

[27]  S. Salon,et al.  A hybrid finite element-boundary integral formulation of the eddy current problem , 1982 .

[28]  M. Gunzburger,et al.  Boundary conditions for the numerical solution of elliptic equations in exterior regions , 1982 .

[29]  O. C. Zienkiewicz,et al.  A novel boundary infinite element , 1983 .

[30]  Isaak D. Mayergoyz,et al.  Boundary Galerkin's method for three-dimensional finite element electromagnetic field computation , 1983 .

[31]  Approximate ballooning techniques , 1983 .

[32]  S. Salon,et al.  Hybrid finite element boundary element solutions using half‐space Green’s functions , 1984 .

[33]  Jr. H. Hurwitz,et al.  Infinitesimal scaling--A new procedure for modeling exterior field problems , 1984 .

[34]  B. Rahman,et al.  Finite-Element Analysis of Optical and Microwave Waveguide Problems , 1984 .

[35]  G. Dasgupta.  Computation of exterior potential fields by infinite substructuring , 1984 .

[36]  K. Chiang.  Finite element method for cutoff frequencies of weakly guiding fibres of arbitrary cross-section , 1984 .

[37]  S. Pissanetzky.  A SIMPLE INFINITE ELEMENT , 1984 .

[38]  Peter Bettess,et al.  Infinite elements for static problems , 1984 .

[39]  R. Wu,et al.  A Variational Analysis of Dielectric Waveguides by the Conformal Mapping Technique , 1985 .

[40]  Kin Seng Chiang,et al.  Finite-element analysis of optical fibres with iterative treatment of the infinite 2-D space , 1985 .

[41]  M. de Pourcq,et al.  Field and power-density calculations in closed microwave systems by three-dimensional finite differences , 1985 .

[42]  S. Salon.  The hybrid finite element-boundary element method in electromagnetics , 1985 .

[43]  I. Ciric,et al.  METHOD OF CONFORMAL TRANSFORMATION FOR THE FINITE‐ELEMENT SOLUTION OF AXISYMMETRIC EXTERIOR‐FIELD PROBLEMS , 1985 .

[44]  Hybrid boundary‐volume Galerkin’s method for nonlinear magnetostatic problems , 1985 .

[45]  J. D'Angelo,et al.  Power line insulator analysis and design using finite elements and infinitesimal scaling , 1985 .

[46]  C.D. Taylor,et al.  On the parasitic capacitances of multilevel parallel metallization lines , 1985, IEEE Transactions on Electron Devices.

[47]  J. Lavers,et al.  A skin depth-independent finite element method for Eddy current problems , 1986 .

[48]  S. J. Salon,et al.  Hybrid finite element boundary element solutions for three dimensional scalar potential problems , 1986 .

[49]  I. Ciric,et al.  INVERSION TRANSFORMATION FOR THE FINITE‐ELEMENT SOLUTION OF THREE‐DIMENSIONAL EXTERIOR‐FIELD PROBLEMS , 1986 .

[50]  J. D'Angelo,et al.  Solution of open boundary problems by differential and integral methods , 1986 .

[51]  R. Higdon.  Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation , 1986 .

[52]  S. Hayano,et al.  Finite element solution of open boundary magnetic field problems , 1987 .

[53]  Aleksander Gasiorski,et al.  Application of Finite-Element Method to Calculation of the Impedance of Nonsymmetrically Shaped Bars Conducting Current , 1987, IEEE Transactions on Electromagnetic Compatibility.

[54]  M. V. K. Chari,et al.  Hybrid harmonic/finite element method for two-dimensional open boundary problems , 1987 .

[55]  Robert L. Higdon,et al.  Numerical absorbing boundary conditions for the wave equation , 1987 .

[56]  Jin-Fa Lee,et al.  Transfinite elements: A highly efficient procedure for modeling open field problems , 1987 .

[57]  A. Taflove,et al.  A new formulation of electromagnetic wave scattering using an on-surface radiation boundary condition approach , 1987 .

[58]  M. V. K. Chari.  Electromagnetic field computation of open boundary problems by a semi-analytic approach , 1987 .

[59]  E. M. Freeman,et al.  A novel mapping technique for open boundary finite element solutions to Poisson's equation , 1988 .

[60]  Skin and proximity effect calculation using the method of fundamental solutions (MFS) , 1988 .

[61]  Allen Taflove,et al.  Theory and application of radiation boundary operators , 1988 .

[62]  Yoshifuru Saito,et al.  Finite element solution of unbounded magnetic field problem containing ferromagnetic materials , 1988 .

[63]  J. D'Angelo,et al.  Applications of the hybrid finite element-boundary element method in electromagnetics , 1988 .

[64]  P. Bettess.  Finite element modelling of exterior electromagnetic problems , 1988 .

[65]  Hybrid finite element/boundary element analysis for axisymmetric magnetostatic fields , 1988 .

[66]  A hybrid method for eddy current open‐boundary field computation , 1988 .

[67]  L. Udpa,et al.  Application of the substructure-frontal method for repeated solution of large sparse matrix equations to field problems , 1988 .

[68]  A. Kameari,et al.  Calculation of three dimensional eddy current by FEM-BEM coupling method , 1988 .

[69]  C. Emson.  Methods for the solution of open-boundary electromagnetic-field problems , 1988 .

[70]  Andrew F. Peterson,et al.  Absorbing boundary conditions for the vector wave equation , 1988 .

[71]  A. Razek,et al.  Hybrid numerical methods for movement consideration in electromagnetic systems , 1988 .

[72]  Comparison of different boundary integral formulations when coupled with finite elements in three dimensions , 1988 .

[73]  A. Gąsiorski.  Finite-element method for power losses calculation in long rectangular conductors located in transverse harmonic magnetic field , 1988 .

[74]  R. Mittra,et al.  A review of absorbing boundary conditions for two and three-dimensional electromagnetic scattering problems , 1989 .

[75]  J. D'Angelo,et al.  On the use of local absorbing boundary conditions for RF scattering problems , 1989 .

[76]  Christian Hafner,et al.  Electromagnetic field calculations on PC's and workstations using the MMP method , 1989 .

[77]  Constrained indirect BEM for eddy current calculations in multiple conductor TM induction problem , 1989, International Magnetics Conference.

[78]  L. Pearson,et al.  An exact radiation boundary condition for the finite-element solution of electromagnetic scattering on an open domain , 1989 .

[79]  J. D. Lavers,et al.  An evaluation of the direct boundary element method and the method of fundamental solutions , 1989 .

[80]  E. M. Freeman,et al.  A sparse matrix open boundary method for finite element analysis , 1989 .

[81]  E. Freeman,et al.  An open boundary technique for axisymmetric and three dimensional magnetic and electric field problems , 1989, International Magnetics Conference.

[82]  Jon P. Webb,et al.  Infinite elements for the analysis of open dielectric waveguides , 1989 .

[83]  Jon P. Webb,et al.  Absorbing boundary conditions for the finite element solution of the vector wave equation , 1989 .

[84]  J. C. Sabonnadiere,et al.  Finite element modeling of open boundary problems , 1990 .

[85]  David L. Atherton,et al.  Open-boundary finite-element calculations for remote-field eddy-current systems , 1990 .

[86]  Adel Razek,et al.  A new hybrid model using electric field formulation for 3-D eddy current problems , 1990 .

[87]  G. Mur.  A mixed finite element method for computing three-dimensional time-domain electromagnetic fields in strongly inhomogeneous media , 1990 .

[88]  T. Sarkar,et al.  Finite difference frequency-domain treatment of open transmission structures , 1990 .

[89]  A data base method for 3D open boundary field computation , 1990 .

[90]  Z. Ren,et al.  Calculation of 3D eddy current problems by an hybrid T- Omega method , 1990 .

[91]  Takashi Onuki,et al.  Hybrid finite element and boundary element method applied to electromagnetic problems , 1990 .

[92]  J. P. Webb.  Absorbing boundary conditions for the finite-element analysis of planar devices , 1990 .

[93]  R. Mittra,et al.  Asymptotic boundary conditions for finite element analysis of three-dimensional transmission line discontinuities , 1990 .

[94]  R. Mittra,et al.  Higher order asymptotic boundary condition for the finite element modeling of two-dimensional transmission line structures , 1990 .

[95]  J. D. Lavers,et al.  A new hybrid method using hinged finite element formulations for the skin effect eddy current problems , 1990 .

[96]  Koji Fujiwara,et al.  3-D open boundary magnetic field analysis using infinite element based on hybrid finite element method , 1990 .

[97]  J. Sroka,et al.  On the coupling of the generalized multipole technique with the finite element method , 1990 .

[98]  R. Mittra,et al.  Asymptotic boundary condition for three dimensional magnetostatic finite elements , 1991 .

[99]  R. Mittra,et al.  Numerically derived absorbing boundary condition for the solution of open region scattering problems , 1991 .

[100]  J. P. Webb,et al.  A numerical study of vector absorbing boundary conditions for the finite-element solution of Maxwell's equations , 1991, IEEE Microwave and Guided Wave Letters.

[101]  Chang-Hoi,et al.  Efficient hybrid finite element-boundary element method for 3-dimensional open-boundary field problems , 1991 .

[102]  G. I. Costache,et al.  An Overview of the Absorbing Boundary Conditions , 1991 .

[103]  R. Mittra,et al.  Finite element solution for a class of unbounded geometrics (EM scattering) , 1991 .

[104]  A. Konrad,et al.  Engineering software-computing EM fields , 1992 .

[105]  Shinji Wakao,et al.  Novel boundary element formulation in hybrid FE-BE method for electromagnetic field computations , 1992 .

[106]  L. Nicolas,et al.  2D elctromagnetic scattering by simple shapes: a quantification of the error due to open boundary , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[107]  Gérard Meunier,et al.  Ship magnetizations modelling by the finite element method , 1992 .

[108]  Gérard Meunier,et al.  Finite element modeling of unbounded problems using transformations: a rigorous, powerful and easy solution , 1992 .

[109]  J. D. Lavers,et al.  The method of fundamental solutions with a minimum order formulation applied to 3D eddy current problems , 1992 .

[110]  J. R. Brauer,et al.  Surface integrals on 3D and 2D finite element models for skin effect excitations and open boundaries , 1992 .

[111]  K. K. Mei,et al.  Superabsorption-a method to improve absorbing boundary conditions (electromagnetic waves) , 1992 .

[112]  M. Feliziani.  Numerical solutions of low-frequency scattering problems , 1992 .

[113]  Hybrid FEM-BIM formulation using electric and magnetic variables , 1992 .

[114]  S. Subramaniam,et al.  Open Boundary Eddy-current Problems Using Edge Elements , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[115]  A. Stohchniol,et al.  A general transformation for open boundary finite element method for electromagnetic problems , 1992 .

[116]  T Omega formulation by hybrid FEM-BIM and its gauges for 3D electromagnetic calculations , 1992 .

[117]  M. Feliziani.  Characteristic Impedance Boundary Conditions (cibc) for the Solution of Open Boundary Problems , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[118]  A. Cangellaris,et al.  Application of the Measured Equation of Invariance Approach to Electromagnetic Scattering by Penetrable Bodies , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[119]  Qiushi Chen,et al.  An Integrodifferential Finite Element - Green's Functon Method for the Solution of Unbouded Eddy Current Problems , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[120]  A. Konrad,et al.  Time domain simulation of lossy planar networks , 1992 .

[121]  Salvatore Coco,et al.  Charge iteration for N-dimensional unbounded electrical field computations , 1992 .

[122]  E. M. Freeman,et al.  Further aspects of the Kelvin transformation method for dealing with open boundaries , 1992 .

[123]  S. Wakao,et al.  Electromagnetic Field Computations by the Hybrid Fe-Be Method Using Edge Elements , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[124]  Y. S. Sun,et al.  The application of the database method for 3-D open boundary field computation , 1992 .

[125]  S. Gratkowski,et al.  A three-dimensional infinite element for modeling open-boundary field problems , 1992 .

[126]  S. Coco,et al.  Axisymmetric Unbounded Electrical field computation by Charge Iteration , 1992, Digest of the Fifth Biennial IEEE Conference on Electromagnetic Field Computation.

[127]  Rafael Pous,et al.  The measured equation of invariance-a new concept in field computation , 1992, IEEE Antennas and Propagation Society International Symposium 1992 Digest.

[128]  J. D'Angelo,et al.  A new finite element formulation for RF scattering by complex bodies of revolution , 1993 .

[129]  K. Chamberlin,et al.  Finite difference time-domain calculation of transients in antennas with nonlinear loads , 1993 .

[130]  J. D. Lavers.  Electromagnetic field computation in power engineering , 1993 .

[131]  G. Mur,et al.  The finite-element modeling of three-dimensional electromagnetic fields using edge and nodal elements , 1993 .

[132]  Qiushi Chen,et al.  A hybrid approach to the solution of open boundary eddy current problems under TM field excitation , 1993 .

[133]  A. Konrad,et al.  Time domain solution of planar circuits , 1993 .

[134]  R. Pous,et al.  A new approach to quasi-static analysis with application to microstrip , 1993, IEEE Microwave and Guided Wave Letters.

[135]  M. Towers,et al.  Electromagnetic scattering from an arbitrary, inhomogeneous 2-D object-a finite and infinite element solution , 1993 .

[136]  P.S. Simon,et al.  Closed-form expressions for coefficients used in FD-TD high-order boundary conditions , 1993, IEEE Microwave and Guided Wave Letters.

[137]  Qiushi Chen,et al.  Asymptotic boundary conditions for axisymmetric finite element electrostatic analysis , 1994 .

[138]  R. Mittra,et al.  Finite element analysis of MMIC structures and electronic packages using absorbing boundary conditions , 1994 .

[139]  Rafael Pous,et al.  Measured equation of invariance: a new concept in field computations , 1994 .

[140]  J. Simkin,et al.  Solving open boundary problems using finite elements , 1994 .

[141]  Qiushi Chen,et al.  A finite element-Green's function method for the solution of unbounded three-dimensional eddy current problems , 1994 .

[142]  Cj Railton,et al.  A comparison of the properties of radiating boundary conditions in the FDTD method for finite discretisation and non-planar waves , 1994 .

[143]  Robert J. Lee,et al.  A theoretical and numerical analysis of the measured equation of invariance , 1994 .

[144]  R. Mittra,et al.  A theoretical study of numerical absorbing boundary conditions , 1995 .

[145]  Jiangjun Ruan,et al.  3D transient eddy current calculation by the hybrid FE-BE method using magnetic field intensity H , 1995 .

[146]  Qiushi Chen,et al.  Computation of three-dimensional unbounded eddy current problems using asymptotic boundary conditions , 1995 .

[147]  L. Nicolas,et al.  H(curl) elements on hexahedral and vector A.B.C.'s for unbounded microwave problems , 1995 .