Monk P. — Finite Element Methods for Maxwell's Equations :: Электронная библиотека попечительского совета мехмата МГУ

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Monk P. — Finite Element Methods for Maxwell's Equations

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Название: Finite Element Methods for Maxwell's Equations

Автор: Monk P.

Аннотация:

In light of increasing uses for direct numerical approximations of Maxwell's equations in science and engineering, this text provides mathematics graduate students and researchers with a theoretical foundation for finite element methods in computational electromagnetism. Monk (mathematical sciences, U. of Delaware) emphasizes finite element methods for scattering problems involving the solutions of Maxwell's equations on infinite domains. The book's main focus is on an error analysis of edge finite element methods that are well suited to Maxwell's equations. The book concludes with a short introduction to inverse problems in electromagnetism.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2003

Количество страниц: 464

Добавлена в каталог: 21.05.2008

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Предметный указатель

Operator, pointwise convergent      33
Operator, range      18
Operator, self-adjoint      24
Orthogonal complement      17
Perfectly matched layer      375
Perfectly matched layer, numerical results      382
Perfectly matched layer, rectilinear      377
Perfectly matched layer, spherical      378
Perfectly matched layer, truncated domain      380
Permeability      5
Permeability, relative $\mu_r$       6
Permittivity      5
Permittivity, relative $\epsilon_r$       6
Phase error      344
Phase error, $\kappa$ dependence      347
Phase error, three dimensional edge elements      351 354
Plane wave      9
Plane wave, polarization      9
PML      see “Perfectly matched layer”
Poincare inequality      46
Pointwise convergence      178
Poisson problem, Dirichlet boundary condition      45
Poisson problem, Neumann boundary condition      46
Poynting vector      233
Preasymptotic convergence      348
Preconditioned iteration      335
Prismatic elements      200
Projection       171 275
Projection theorem      17
Properties of $H(curl;\Omega)$       55
Properties of $H(div, \Omega)$       52
Pyramidal elements      201
Quasi-uniform mesh on S      152
Radar cross section      392
Radiating solution      230
Radiation condition, integral for layered medium      12
Radiation condition, Silver Muller      10
Radiation condition, Sommerfeld      226 240
RCS      see “Radar cross section”
Reciprocity      418
Regular mesh      116
Regularity, divergence-free projection      182
Regularity, elliptic problems      45
Regularity, Maxwell’s equations      69 71 283
Regularization      399
Rellich’s lemma      255
Rellich’s uniqueness theorem      255
Residual based error estimator      356
Resonance region      1 10
Richardson iteration      334
Riesz theorem      19
Rodrigues’ formula      237
Scalar potential      61
Scalar product      15
Scattered field      9
Scattering problem, Babuska— Brezzi condition      273
Scattering problem, bounded scatterer      13
Scattering problem, convergence      277
Scattering problem, discrete      275
Scattering problem, discrete Babuska — Brezzi condition      275
Scattering problem, domain decomposition      281
Scattering problem, existence      272 289

Scattering problem, half space      315
Scattering problem, layered medium      14 318
Scattering problem, non-homogeneous      272
Scattering problem, overlapping scheme      307
Scattering problem, overlapping, discrete      308
Scattering problem, uniqueness      256 264 288
Scattering problem, variational      263
Schwarz iteration      337
Second family of elements, tetrahedra      202
Series expansion for       246 248
Sesquilinear form,       89
Sesquilinear form, ,       265
Sesquilinear form, ,       270
Sesquilinear form, $\tilde{a}$       87
Sesquilinear form, $\tilde{b}$       89
Sesquilinear form, A      265
Sesquilinear form, bounded      20
Sesquilinear form, coercive      20
Sesquilinear form, definition      20
Singular system      400
Sobolev imbedding theorem      41
Solution of the linear system      333
speed of light      5
Spherical Bessel function, asymptotics      239 240
Spherical Bessel functions      239
Spherical coordinates      425
Spherical harmonic      236 238
Starlike      56
Stoke’s Theorem      52
Stratton — Chu formula      228 230 304
Strong convergence      16
Super-convergence      188 201
Surface divergence $\nabla_{\partial\Omega}$       48
Surface gradient $\nabla_{\partial\Omega}$       48
Surface scalar curl $\nabla_{\partial\Omega^{\times}}$       49
Surface vector curl $\vec{\nabla}_{\partial\Omega^{\times}}$       49
Tikhonov regularization      400
Time harmonic field      3
Total field      10
Trace, $\gamma_0$ for $H^1(\Omega)$       43
Trace, $\gamma_1$ , $\gamma_T$ for $H(curl;\Omega)$       57
Trace, $\gamma_n$ for $H(div;\Omega)$       53
Transformation for scalar functions      77
Transformation, affine      113
Transformation, curl preserving      77
Transformation, divergence preserving      79
Unique continuation      92
Unisolvent element      102
Vector addition theorem      245
Vector potential      63
Vector spherical harmonics      241
Vector wave functions, exterior      245
Vector wave functions, interior      245
Wavelength      10 344
Wavenumbcr dependence of error      345
Wavenumber      7
Weak convergence      16
Wesson’s trick for orienting edges      143
Whitney element      139
Wilcox expansion      366
Wronskian identity      240
Z-cocrcivity      21

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