Bibliography

General Electromagnetics

l. M.A. Plonus, "Applied Electromagnetics", McGraw-Hill Book Company, New York, 1978.

2. I.D. Kraus, and K.R. Carver, "Electromagnetics," 2d ed., McGraw- Hill Book Company, New York, 1973.

3. I.A. Stratton, "Electromagnetic Theory," McGraw-Hill Book Company, New York, 1952.

4. W. K. H. Panofsky and M. Phillips, "Classical Electricity and Magnetism," Addison-Wesley Publishing Company, Inc., Reading, Mass., 1956.

5. R. Plosney and R.E. Collin, "Principles and Applications of Electromagnetic Fields," McGraw-Hill Book Company, New York, 1961.

6. P. Lorain and D.R. Corson, "Electromagnetism", W. H. Freeman, San Francisco, 1978.

7. I.A. Kong, "Theory of Electromagnetic Waves," Iohn Wiley & Sons, Inc., New York, 1975.

8. R.E. Collin, "Electromagnetic Theory of Guided Waves", NMcGraw-Hill, NY, 1991, pp. 564-568.

Books on Computational Electromagnetics

l. C.W. Steele, "Numerical Computation of Electric and Magnetic Fields", Van Nostrand Reinhold Co., New York, 1987.

2. P.P. Sylvester and R.P. Ferrari, "Finite Elements for Electrical Engineers", Cambridge University Press, Cambridge, 1990.

3. I.C. Sabonnadierre and I.L. Coulomb, "Finite Element Methods in CAD", Springer Verlag, NY., 1989.

4. S.R.H. Hoole, "Computer-Aided Analysis and Design of Electromagnetic Devices", Elsevier, NY, 1989.

5. D.A. Lowther and P.P. Sylvester, "Computer Aider Design in Magnetics", Springer Verlag, NY, 1986.

Bibliography 447

Nonlinear Methods

1. P.P. Silvester and M.V.K. Chari, "Finite element solution of saturable magnetic field problems", IEEE Transactions on Power Apparatus and Systems, Vol. 89, 1970, pp. 1642-1651.

2. J.P.A. Bastos, G. Quichaud, "3D modeling of a nonlinear anisotropic lamination", IEEE Transactions on Magnetics, Vol. 21, No.6, Nov. 1985, pp.2366-2369.

3. J. Penman and A. M.A. Kamar, "Linearization of saturable magnetic field problems, including eddy currents", IEEE Transactions on Magnetics, Vol. MAG-18, No.2, March 1982, pp. 563-566.

4. C.S. Holzinger, "Computation of magnetic fields within three-dimensional highly nonlinear media", IEEE Transactions on Magnetics, Vol. MAG-6, No. 1, March 1970, pp. 60-65.

5. J.R. Brauer, R.Y. Bodine and L.A. Larkin, "Nonlinear anisotropic three dimensional magnetic energy functional," presented at the COMPUMAG Conference, Santa Marguerita, Italy, May 1983.

6. J.R. Brauer, "Saturated magnetic energy function for finite element analysis of electrical machines", IEEE PES winter Meeting, New York, 1976, paper C75, pp. 151-156.

Solution Methods

1. J.A. Meijerink, and H.A. van der Vorst, "An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix", Mathematics of Computation, Vol. 31, No. 137, January 1977, pp. 148-162.

2. D.M. Young, "Iterative Solution of Large Linear Systems", Computer Science and Applied Mathematics, Academic Press, New York, 1971.

3. R. V. Southwell, "Relaxation Methods in Theoretical Physics", Oxford, London, 1946.

4. R.L. Stoll, "Solution of linear steady state eddy current problems by complex successive over-relaxation", lEE Proceedings, Pt. A, Vol. 117, 1970, pp. 1317-1323.

5. lK. Reid, "On the method of conjugate gradients for the solution of large sparse systems of linear equations", in Large Sparse Sets of Linear Equations, Reid, J. K., Ed., Academic Press, 1971, pp. 231-252.

6. J.K. Reid, "Solution of linear systems of equations: direct methods (general)", in Lecture Notes in Mathematics, Barker, V. A., Ed., Springer-Verlag, Berlin, 1976, No. 572, pp. 102-130.

7. A. Jennings, "A compact storage scheme for the soluticn of symmetric simultaneous equations", Computer Journal, No.9, September 1969, pp. 281-285.

448 Bibliography

8. J.A. George, "Nested disection of a regular finite element mesh", SIAM Journal of Numerical Analysis, Vol. 10, No.2, April 1973, pp. 345-363.

9. J.A. George, "On block elimination of finite element systems of equations", Sparse Matrices and Their Applications, Rose, D. J. and Willowghby, R. A., Ed., Plenum Press, New York, 1972, pp. 101-114.

10. lA. George, "Solution of linear systems of equations: direct methods for finite element problems", in Lecture Notes in Mathematics, Barker, V. A., Ed., Springer-Verlag, Berlin, 1976, No. 572, pp. 52-101.

11. J.A. George, "Sparse matrix aspects of the finite element method", Proceedings of the Second International Symposium on Computing Methods in Applied Science and Engineering, Springer-Verlag, 1976.

12. IF. Gloudeman, "The impact of supercomputers on finite element analysis", Proceedings of the IEEE, Vol. 72, No.1, January 1984, pp. 80-84.

13. F.G. Gustavson, "Some basic techniques for solving sparse systems of equations", Sparse Matrices and Their Applications, Rose, D. J. and Willoughby, R. A., Ed., Plenum Press, New York, 1972, pp. 41-53.

General Numerical Techniques

1. M.L. James, S.M. Smith and J.C. Wolford, "Applied numerical methods for digital computation with FORTRAN and CSMP", International Text Book Company, 1967.

2. J. Pachner, Handbook of Numerical Analysis Applications, McGraw Hill, NY., 1984.

3. R. Courant and D. Hilbert, "Methods of Computational Physics",Vol. 2, Interscience, 1961.

Magnetostatic and Electroststic Formulations

1. P. Hammond, and T.D. Tsiboukis, "Dual finite-element calculations for static electric and magnetic fields", lEE Proceedings, Vol. 130, Pt. A, No.3, May 1983, pp. 105-111.

2. M.V.K. Chari, M.A. Palmo and Z.J. Czendes, "Axisymmetric and three dimensional electrostatic field solution by the finite element method", Electric Machines and Electromechanics, Vol. 3, 1979, pp. 235-244.

3. M.V.K. Chari, P.P. Silvester and A. Konrad, "Three-dimensional magnetostatic field analysis of electrical machinery by the finite element method," IEEE Transactions on Power Apparatus and Systems, Vol. PAS-100, No.8, pp. 4007-4019, August 1981.

4. Z.J. Cendes, J. Weiss and S.R.H. Hoole, "Alternative vector potential formulations of 3-D magneto static problems," IEEE Transactions on Magnetics, Vol. MAG-18, No.2, pp. 367-372, March 1982.

Bibliography 449

5. O.W. Andersen, "Two stage solution of three dimensional electrostatic fields by finite differences and finite elements", IEEE trans on Power apparatus and systems,Vol PAS 100, No.8, Aug 81.

Eddy Current Formulations

1. C.J. Carpenter and M. Djurovic, "Three-dimensional numerical solution of eddy currents in thin plates", Proceedings of the lEE, Vol 122, No.6, 1975, pp. 681-688.

2. M.L. Brown, "Calculation of 3-dimensional eddy currents at power frequencies", lEE Proceedings, Vol. 129, Part A, No.1, January 1982, pp. 46-53.

3. c.s. Biddlecombe, E.A. Heighway, J. Simkin and C.W. Trowbridge, "Methods for eddy current computation in three dimensions," IEEE Transactions on Magnetics, Vol. MAG-18, No.2, pp. 492-497, March 1982.

4. P. Hammond, "Use of potentials in the calculation of electromagnetic fields", lEE Proceedings, Vol. 129, Part A, No.2, March 1982, pp. 106-112.

5. T.W. Preston and A. B.J. Reece, "Solution of 3-dimensional eddy current problems: the T - method," IEEE Transactions on Magnetics, Vol. MAG-18, No.2, pp. 486-491, March 1982.

6. C.R.I. Emson, J. Simkin and C.W. Trowbridge, "Further developments in three-dimensional eddy current analysis", IEEE Transactions on Magnetics, Vol. MAG-21, No.6, Nov. 1985, pp. 2231-2234.

7. P.I. Koltermann, J.P.A. Bastos and S.S. Arruda, "A model for dynamic analysis of AC contactor", IEEE Transactions on Magnetics, Vol. 28, No.2, March 1992, pp. 1,348-1350.

8. R.C. Mesquita, J.P.A. Bastos, "3D finite element solution of induction heating problems with efficient time-stepping", IEEE Transactions on Magnetics, Vol. 27, No.5, Sept.. 1991, pp. 4065-4068.

9. N. Ida, "Three Dimensional Eddy Current Modeling," Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti, Eds., Plenum Press, New York, Nov. 1987, Vol. 6A, pp. 201-209.

10. H. Song and N. Ida, "An eddy current constraint formulation for 3D electromagnetic field calculation", in IEEE Transactions on Magnetics, Vol. 27, No.5, Sept. 1991, pp. 4012-4015.

11. R.D. Pillsbury, "A three dimensional eddy-current formulation using two potentials: the magnetic vector potential and total magnetic scalar potential", IEEE Transactions on Magnetics, Vol. MAG-19, No.6, 1983, pp. 2284-2287.

12. R.L. Ferrari, "Complementary variational formulation for eddy-current problems using the field variables E and H directly", lEE Proceedings, Vol. 132, Pt. A, No.4, July 1985, pp. 157-164.

450 Bibliography

13. P. Hammond, "Calculation of eddy currents by dual energy methods," Proceedings of lEE, Vol. 125, No.7, 1978, pp.701-708.

14. C.R.I. Emson and J. Simkin, "An optimal method for 3-D eddy-currents", IEEE Transactions on Magnetics, Vol. MAG-19, No.6, 1983, pp. 2450-2452.

Formulations with Velocity Terms

1. N. Ida, "Modeling of velocity effects in eddy current applications," Journal of Applied Physics, Vol. 63, No.8, April 15, 1988, pp.3007-3009.

2. N. Ida, "Velocity effects and low level fields in axisymmetric geometries", in COMPEL - International Journal for Computation and Mathematics in Electrical Engineering, Vol. 9, No.3, September 1990, pp. 169-180.

High Frequency Formulations

1. A. Konrad, "A direct three-dimensional finite elemenmt method for the solution of magnetic fields in cavities", IEEE Transactions on Magnetics, Vol. MAG-21, No.6, November 1985, pp. 2276-2279.

2. N. Ida, "Microwave NDT", in Electrosoft, special issue on NDT Vol. 2, No. 2/3, June/Sept. 1991, pp. 215-237.

3. 1.S. Wang and N. Ida, "Eigenvalue analysis in Electromagnetic cavities using divergence free finite elements", in IEEE Transactions on Magnetics, Vol. 27, No.5, Sept. 1991, pp. 3978-3981.

4. J.S. Wang and N. Ida, "A numerical model for characterization of specimens in a microwave cavity", in Review of Progress in Quantitative Nondestructive Evaluation, D. O. Thompson and D. E. Chimenti, Eds., Vol. lOA, Plenum Press, New York 1991, pp. 567-574.

Computation Systems and CAD

5. A. Bossavit and J.C. Verite, "The TRIFOU code: Solving the 3-D eddy currents problem by using H as a sate variable", IEEE Transactions on Magnetics, Vol. MAG- 19, 1983, pp. 2465-2470.

6. N. Ida, "PCNDT - An electromagnetic finite element package for personal computers", IEEE Transactions on Magnetics, Vol. 24, No.1, January 1988, pp. 366-369.

7. P. Masse, J.L. Coulomb and B. Ancelle, "System design methodology in C.A.D. programs based on finite element method", IEEE Transactions on Magnetics, Vol. MAG-18, No.2, March 1982, pp. 609-616.

Bibliography 451

8. M.L. Barton, V.K. Garg, I. Ince, E. Sternheim and J. Weiss, "WEMAP: a general purpose system for electromagnetic analysis and design", IEEE Transactions on Magnetics, Vol. MAG-19, No.6, November 1983, pp. 2674-2677.

9. B. Ancelle, E. Gallagher and P. Masse, "ENTREE: a fully parametric preprocessor for computer aided design of magnetic devices", IEEE Transactions on Magnetics, Vol. MAG-18, No.2, March 1982, pp. 630-632.

Special Aspects

1. A.A. Abdel-Razek, J.L. Coulomb, M. Feliachi and J.C. Sabonnadiere, "Conception of an air-gap element for the analysis of the electromagnetic field in electric machines", IEEE Transactions on Magnetics, Vol. MAG-18, No.2, March 1982, pp. 655-659.

2. N. Sadowski, Y. Lefevre, M. Lajoie-Mazenc and J.P.A. Bastos, "Calculation of transient electromagnetic forces in axisymmetrical electromagnetic devices with conductive solid parts", ISEF - International Symposium on Electromagnetic Field Calculation, Southampton, England, Sept. 1991.

3. J.P. Bastos, N. Sadowski, R. Carlson, "A modeling approach of a coupled problem between electrical current and its thermal effects", IEEE Transactions on Magnetics, Vol.26, No.2, March 1990, pp. 536-539.

4. J.S. van Welij, "Calculation of eddy currents in terms of hexahedra", IEEE Transactions on Magnetics, Vol. MAG-21, No.6, November 1985, pp. 2239-2241.

8. B. Davat, Z. Ren and M. Lajoie-Meznec, "The movement in field bmodeling", IEEE Transactions on Magnetics, Vol. MAG-21, No. 6,November 1985, pp. 2296-2298.

9. N. Ida, "Efficient treatment of infinite boundaries in electromagnetic field problems," COMPEL - International Journal for Computation and Mathematics in Electrical Engineering, Vol. 6, No.3, November 1987, pp. 137-149.

Analytic Methods of Solution

1. K.J. Binns and PJ. Lawrenson, Analysis and Computation of Electric and Magnetic Field Problems, Pergamon Press, 1973.

2. W.R. Smythe, "Static and Dynamic Electricity," McGraw-Hill, Inc., New York, 1968, pp. 284-287.

452 Bibliography

General Finite Element Method

1. J.T. Oden, "A general theory of finite elements I: Topological considerations," INternal Journal for Numerical Methods in Engineering, Vol. 1, No.2, 1969, pp. 205-221.

2. J.T. Oden, "A general theory of finite elements II: Applications," International Journal for Numerical Methods in Engineering, Vol. 1, No.3, 1969, pp. 247-259.

3. G. Dhatt and G. Touzot, "The Finite Element Method Displayed", Wiley Interscience, Chichester, 1984.

4. K.H. Huebner, The Finite Element Method for Engineers, Wiley-Interscience, John Wiley & Sons, Inc., New York, 1975.

5. C.S. Desai and J.F. Abel, "Introduction to the Finite Element Method", Van Nostrand Reinhold, 1972.

6. O.C. Zienkiewicz, The Finite Element Method in Engineering, third edition, McGraw-Hill Book Co., London, 1977.

Variational Techniques

1. S.G. Mikhlin, "Variational Methods in Mathematical Physics", The Macmillan Co., New York, 1964.

2. M.E. Gurtin, "Variational principles for linear initial-value problems", Q. Appl. Math., Vol. 22, 1964, pp. 252-256.

Mesh Generation

1. J.R. Adamek, "An automatic mesh generator using two and three-dimensional isoparametric finite elements", M. Sc. Thesis, Naval Postgraduate School, Monterey, Ca. 1973.

2. N.N. Shenton and Z.J. Cendes, "Three-dimensional finite element mesh generation using Delaunay tesselation", IEEE Transactions on Magnetics, Vol. MAG-21, No.6, November 1985, pp. 25235-2538.

3. K. Sagawa, "Automatic mesh generation for three-dimensional structures based on their three views," in Theory and Practice in Finite Element Structural Analysis, Y.Yoshioki and R.H. Gallagher, Eds., 1973, pp. 687-703.

4. M.S. Shephard, "Automatic and adaptive mesh generation", IEEE Transactions on Magnetics, Vol. MAG-21, No.6, November 1985, pp. 2484-2489.

5. J.P.A. Bastos and R.Carison, "An efficient automatic 2D mesh generation method", Compumag 1991, Sorrento, Italy, July 7-11,1991.

Bibliography 453

6. A.R. Pinchuk and P.P. Silvester, "Error estimation for automatic adaptive fmite element mesh generation", IEEE Transactions on Magnetics, Vol. MAG-21, No.6, November 1985, pp. 2551-2554.

7. S. Pisanetzky, "KUBIK: an automatic three-dimensional finite element mesh generator," International Journal for Numerical Methods in Engineering, Vol. 17, 1981, pp. 255-269.

8. 1. Penman and M.D. Grieve, "An approach to self adaptive mesh generator", IEEE Transactions on Magnetics, Vol. MAG-21, No.6, November 1985, pp. 2567-2570.

9. D.W. Kelly, J.P. De, S.R. Gago. D.C. Zienkiewicz and I. Babuska, "A posteriory error analysis and adaptive processes in the finite element method: I - error analysis," International Journal for Numerical Methods in Engineering, VOL 19, No. 11, 1983, pp. 1593-1619.

10. D.W. Kelly, J.P. De, S.R. Gago,O.C. Zienkiewicz and I. Babuska, "A posteriory error analysis and adaptive processes in the finite element method: II - adaptive mesh refinement," International Journal for Numerical Methods in Engineering, Vol. 19, No. 12, 1983, pp. 1621-1656.

Software Libraries

1. J.J. Dongarra, C.B. Moller and G.W. Stuart, "UNPAK Users' Guide," SIAM, Philadelphia, PA. 1979.

2. J.J. Dongara, "The UNPACK benchmark: An explanation - Part I,ll, SUPERCOMPUTING, Spring 1988, pp. 10-18.

Subject Index

Adaptive mesh 425 Ampere's Law 39,91 Anisotropy 35,327 Attenuation 229

attenuation constant 231 Axi-symmetry 301,349 Biot-Savart

examples 125,127 law 94

CAD 406 Capacitance 61

defmition 61 energy in 64 spherical 71,73 static electric charge 24, 43, 48

Cavity resonators 258 Characteristic modes 216 Charged line 67 Charged spherical half-shell 70 Choleski's method 392 Circulation, Electrostatic field 51 Computational aspects 444 Conductivity

electric 28 table of materials 89

Continuity electric equation 29,93,213 electric field intensity 56 electric flux density 57 magnetic field intensity 97 magnetic flux density 97

Coulomb gage 217

Coupling to cavities 261 Current

conduction 38,213 displacement 38, 213 penetration in conductors 148 stationary, equation 268,295,318

Cylindrical coordinates 20 Density

charge 27 current 27

Diamagnetism 99 Dielectric Strength

defmition 60 table of 88

Dirichlet condition 279,281 insertion of boundary conditions 85

Discretization 288, 408 delaunay method 412

Divergence 3, 6 example 11

Theorem 8 Eddy currents

brake 209 definition 146

Efect joule 15 penetration of fields 149

Eigenvalues 397 Eigenvectors 397 Electric field intensity 24,48

circulation 51

computation of 316 energy 64 equation of 147 fmite element example 84 nonconservative 266,291

Electric machines 434 Electromechanical 23 Electrostatics 23,47 Energy

in electric field 64 in magnetic field 122,180 of permanent magnet 108

Euler's equation 279 Evolving systems 425 Faraday's Law 42, 145 Ferromagnetic materials 100 Finite Elements

application of Variational method 290 division of domain 75 edge 443 example 84 first order 288, 332 hexahedral 388 introduction to 99,265 isoparametric, 2D 360 isoparametric, 3D 366, 368 local 332 method 287 program 81 quadrilateral 388 vector 445

Flow chart assembly of matrix 405 finite element program 403

Flux conservative 9, 11 definition 6 magnetic 40, 93

Flux density (Induction) electric 26 magnetic 25 penetration in conductors 152

Force

Subject Index 455

conductor 176,198 diamagnetic material 206 electromechanical 176 electromotive 53, 162 ferromagnetic material 205 Lorentz force 179 magnetomotive Maxwell's Tensor on moving charge variation of energy

Function

102,140 188 48,179

182

geometric transformation 333 interpolating potentials 334

Galerkin applic. anisotropic 327 applic. induced currents 332 method 326

Gauss elimination 390 theorem 43

Givens transformation 400 Gradient

definition example

Hall effect

2,3 5

200 Herz, Heinrich 215 ICCG method 395 Incidence plane 241 Induced currents 145,332

advantages,. limitations, 2D 357 complex Vector Potential 343 due to change in geometry 166 due to change in induction 164 in moving parts 347,372 time discretization 337, 370

Inductance computation of 420 definition 119 energy in 120 of coaxial cable 129 of long solenoid 123 of torus 122

Inductive Heating 165

456 Subject Index

Intrinsic impedance Irrotational 218 Jacobi transformation Laplace

226

397

equation, electric equation, magnetic force 177

66,267,268,276 139,270

Laplacian 18 Lenz's law 145 Linear generator 203 Linear hexahedron 368 Linear motor 203 Loop

circular 125 rectangular 127

Lorentz force 178 Lorentz gage 219 Losses

conduction 228 dielectric 228 eddy currents 153 hysteresis 157

Magnetic circuit analog to electric circuit calculation of the field with permanent magnet

Magnetic Field 24 energy 122,181 fmite element example inside conductor 129 outside conductor 39

115 130,133 136

320,322,324

penetration in conductors 151 scalar Potential Equation 65, 270, 295 vector Potential Equation 272, 296

Magnetic levitation 207, 322 Magnetodynarnic fields 23, 143 Magnetostatic fields 23,91 Materials

diamagnetic 9 ferromagnetic 101 paramagnetic 100

Matrix system 381 assembly 299

banded 384 compact 384 direct solution 390 insertion of boundary conditions 387 iterative solution 394 storage 384 symmetric 384

Maxwell approximations to 44 equations 23,91, 143 equations in vacuum 29 force tensor 188 historical note 22 in general media 37 integral form 37 point form 29

MKS units 45 Modes 253,256,259,261

TE 249,251 TEM 249,251 TM 249,252

Nabla operator 2 Neper 229 Neumann condition 279,281 Newton-Raphson 309, 364 Nonlinear problems 308

Newton-Raphson 309 successive approximation 308

Numerical integration 361 Ohm's law 28,53 Operators

application to functions 19 nabla 2 second order 18

Organization of software system 406 Orthogonal transformation 398 Paramagnetism 100 Penetration

depth of 150,232,359 of fields 143 solution of equations 148 visual effect 172

Periodicity (anti) 383

Periodicity 381 Pennanent magnets 104

dynamic operation 114 energy 108 examples 136,169 ftnite element appl. 274,296,315 principal types 113

Permeability magnetic 25 relative 98 table of tensor 35,327

Pennittivity complex 228 electric 26 relative 47 table of 88

Phase constant 230 Phase velocity 229 Phasors 220 Plane waves 213

deftnition 222 in conductors 230, 232 in low loss dielectrics 229 propagation 222 in lossy dielectrics 227 reflection 235,236 refraction 235 solution for 223 transmission

Poisson's equation Polarization 233

circular 235 elliptical 235 linear 234 parallel 241 perpendicular

Potential

235,236 65,267

241

electric scalar 49, 266 electric, vector 275 magnetic, scalar 269 magnetic, vector 272 reduced 445

Subject Index 457

scalar, 3D 312 total 445 vector 184

Potential functions scalar potential 279 vector potential 283

Potential Poynting vector

example Processing 407, 413

calculation of ftelds 416 post-processing 414 pre-processing 407 visualization 414

Propagation constant 228 QR algorithm 397, 401 Quality factor 263 QZ algorithm 397,401 Refraction

electric fteld 55 magnetic fteld 97

Rotation (curl) deftnition 2, 12 example 17

Similarity transformation 398 Skin depth 232

deftnition 232 Solenoid, long 123 Solenoidal 218 Solution

coupled fteld/circuit 438 coupled thenna1Ielectric 430 system of equations 390

Stokes'theorem 14 Teta algorithm 343 Tetrahedron

frrst order second order

Thermal

313 366

coupling 430 equation 431

Time-harmonic ftelds 213 Torque on loop 199

458 Subject Index

Torus, inductance 122 Transfonner, voltage 171 Variational

application in 3D 314 method 77, 276, 277, 303

Vector character 1 circulation 12 derivation 2

Wave equation 215

homogeneous equation 219, 221 nonhomogeneous equation 219, 221 solution of equation 218,222 time dependent wave eq. 215 time harmonic wave eq. 220

Waveguides 249,253 Wavelength 225 Wavenumber 225,228 Weiss domains 106