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

-coercivity      26
A posteriori error estimate      355
A posteriori error estimate, duality estimate      359
A posteriori error estimate, numerical results      363
A posteriori error estimate, residual estimate      361
ABC      see “Absorbing boundary condition”
Absorbing boundary condition      11 365
Absorbing boundary condition, error estimate      366
Annihilator      19
Arithmetic geometric mean inequality      16
Assumptions on data, coefficients      83
Assumptions on data, domain      83
Assumptions on data, impedance      84
Assumptions on data, source fields      84
Asymptotic expansion of $\Phi$       233
Babuska — Brezzi condition, continuous      22
Babuska — Brezzi condition, discrete      27
Backscattered RCS      392
Barycentric coordinate      109
Bessel differential equation      236
Bessel differential equation, spherical      239
Boundary component map      see “Caldcron operator”
Boundary condition, impedance      9
Boundary condition, perfectly conducting      9
Boundary inverse estimate      152
Boundary projection $P_{\Sigma}$       211
Boundary spaces      150
Boundary to far field map      23 419
Buried object      see “Scattering problem layered
Calderon Extension      40
Calderon operator, electric-to-magnetic      249
Calderon operator, exterior coercive $\tilde{G}_c$       251
Calderon operator, exterior elcctric-to-magnetic       249
Calderon operator, exterior magnetic-to-electric $\mathfrak{G}_e$       253
Calderon operator, interior magnetic-to-clectric $\mathfrak{G}_i$       253
Calderon operator, interior magnetic-to-clectric $\tilde{\mathfrak{G}}_1$       254
Calderon operator, magnetic-to-clectric      252
Carding inequality      171
Cartesian coordinates      425
Cauchy — Schwarz inequality      16
Cavity problem      12
Cavity problem, collective compactness      180
Cavity problem, discrete      168
Cavity problem, eigenvalues, continuous      13 96
Cavity problem, eigenvalues, discrete      195
Cavity problem, ellipticized      189
Cavity problem, ellipticized, discrete      191
Cavity problem, error analysis via collective compactness      176
Cavity problem, error analysis via duality      168
Cavity problem, error estimate      169 187
Cavity problem, existence      95
Cavity problem, numerical results      188
Cavity problem, scalar potential      89
Cavity problem, uniqueness      92
Cavity problem, variational      83
Cavity resonances      see “Cavity problem eigenvalues”
Cea’s lemma      25
Clement interpolant      147
Clement macro-element      147
Closed Hilbert space      17
Closure      17
Collectively compact      32
Compact imbedding, into $(L^2(\Omega))^3$       87
Compact imbedding, $\bar{X}_0$ into $(L^2(\Omega))^3$       286
Compact imbedding, $\tilde{X}_0$ into $(L^2(\Omega))^3$       268
Conditioning for small $\kappa$       193
Conductivity      6
Conforming finite element      105
Constitutive equations      5
Continuity required of elements      107
Continuous elements, danger      191
Curl      50
Curved domains      209 213
Curved domains, large elements      214
Curved domains, method of Dubois      210
de Rham diagram, continuous      65
de Rham diagram, discrete      149
Debye potential      235
Degrees of freedom, $H^1(\Omega)$ conforming, hexahedra      162
Degrees of freedom, $H^1(\Omega)$ conforming, hp      219
Degrees of freedom, $H^1(\Omega)$ conforming, tetrahedra      143 209
Degrees of freedom, curl conforming, hexahedra      158
Degrees of freedom, curl conforming, hp      220
Degrees of freedom, curl conforming, tetrahedra      129 205
Degrees of freedom, definition      102
Degrees of freedom, divergence conforming, hexahedra      156
Degrees of freedom, divergence conforming, hp      222
Degrees of freedom, divergence conforming, tetrahcdra      119 202
Degrees of freedom, shorthand      102
Dense subspace      17
Density, in X      178
Deny — Lions Theorem      109
Dielectric      6
Dipole source, explicit formula      411
Dipole source, free space      305
Dipole source, half space      316
Dipole source, horizontal polarization      325
Dipole source, vertical polarization      322
Discrete compactness      181 292
Discrete compactness of $X_{0,h}$       183 184
Discrete divergence      192
Discrete divergence-free      170
Discrete divergence-free, approximation by divergence-free      173
Discrete Helmholtz decomposition      170 177
Dispersion error      see “Phase error”
Distributional derivative      37
Divergence      50
Divergence theorem      50
Domain      37
Dot product      2
DtN map      see “Calderon operator”
Dual pairing      19
Dual space      19
Duality estimate      174
Dyadic Green’s function      see “Green’s dyadic”
Edge element      127 158 219
Edge element, linear      139
Edge element, quadratic      140
Eigenfunction      24
Eigenvalue      24
Element size parameters: and $\rho_K$       112
Enhanced elements      199
Euclidean norm      2
Far field equation      397
Far field operator F      397
Far field pattern      233
Far field recovery      386
Finite covering      336
Finite element spaces on curved domains      216
Finite element spaces, $S_{h,l}$       336
Finite element spaces,       145 163
Finite element spaces, $U_h^{(2)}$       209
Finite element spaces, $U_{h,p}$       219
Finite element spaces,       134 159
Finite element spaces, $V_h^{(2)}$       207
Finite element spaces, $V_{h,p-1}$       220
Finite element spaces,       124 157
Finite element spaces, $W_h^{(2)}$       204
Finite element spaces, $W_{h,p-2}$       221
Finite element spaces,       168
Finite element spaces, $X_{h,l}$       336
Finite element spaces,       149 164
Finite element spaces, $Z_{h,p-3}$       222
Finite element, general definition      101
Finite elements, $H^1(\Omega)$ conforming, hexahedra      162
Finite elements, $H^1(\Omega)$ conforming, hp      218
Finite elements, $H^1(\Omega)$ conforming, tetrahedra      143 209
Finite elements, $L^2(\Omega)$ conforming, hexahedra      164
Finite elements, $L^2(\Omega)$ conforming, tetrahedra      149
Finite elements, curl conforming, hexahedra      158

Finite elements, curl conforming, hp      219
Finite elements, curl conforming, tetrahcdra      126 205
Finite elements, divergence conforming, hexahedra      155
Finite elements, divergence conforming, hp      221
Finite elements, divergence conforming, tetrahedra      118 202
Finite elements, one dimensional      101
Finite elements, one dimensional, estimates      106
First family of elements, hexahedra      155
First family of elements, tetrahedra      99
Fourier space, error estimate      289
Fourier space, inverse estimate      290
Fourier space, on $\Sigma$       289
Fredholm alternative      24
Friedrichs inequality      72 88 185
Function spaces, classical, $L^p(\Omega)$       36
Function spaces, classical, $\mathcal{C}^(\bar{\Omega})$       36
Function spaces, classical, $\mathcal{C}^(\Omega)$       36
Function spaces, classical, $\mathcal{C}_0^(\Omega)$       36
Function spaces, polynomial, ,       212
Function spaces, polynomial,       119
Function spaces, polynomial, , $\tilde{P}_k$       108
Function spaces, polynomial, ,       108
Function spaces, polynomial, $Q_{l, m, n}$       109
Function spaces, polynomial,       128
Function spaces, polynomial, $\mathcal{S}_k$       128
Function spaces, polynomial, $\tilde{P}_k$       108
Function spaces, Sobolev, $H^{-1}(\Omega)$       42
Function spaces, Sobolev, $H^{s}(\Omega)$       38
Function spaces, Sobolev, $H^{s}_0(\Omega)$       38
Function spaces, Sobolev, $H^{\pm1/2}(\partial\Omega)$       44
Function spaces, Sobolev, $L^{2}_{loc}(\Omega)$       45
Function spaces, Sobolev, $W^{s,p}(\Omega)$       37
Function spaces, Sobolev, $W^{s,p}(\partial\Omega)$       43
Function spaces, Sobolev, $W^{s,p}_0(\Omega)$       38
Function spaces, Sobolev, $\hat{S}$       286
Function spaces, Sobolev, $\tilde{S}$       265
Function spaces, Sobolev, S      85
Function spaces, vector, $H(curl;\Omega)$       55
Function spaces, vector, $H(div;\Omega)$       52
Function spaces, vector, $H^s(curl;\Omega)$       55
Function spaces, vector, $H^{-1/2}(Curl;\Gamma)$       59
Function spaces, vector, $H^{-1/2}(Div;\Gamma)$       59
Function spaces, vector, $H^{\pm1/2}(Div;\Gamma)$       244
Function spaces, vector, $H_0(curl;\Omega)$       55
Function spaces, vector, $H_0(div;\Omega)$       54
Function spaces, vector, $H_{imp}(curl;\Omega)$       69
Function spaces, vector, $H_{loc}(curl;\mathbb{R}^3\\bar{D})$       230
Function spaces, vector, $K_N(\Omega)$       67
Function spaces, vector, $K_T(\Omega)$       67
Function spaces, vector, $L^2_t\partial\Omega)$       48
Function spaces, vector, , , , $X_{N,0}$ , , $X_{T,0}$       71
Function spaces, vector,       86
Function spaces, vector, $Y(\Gamma)$       58 410
Function spaces, vector, $\hat{X}_0$       286
Function spaces, vector, $\tilde{X}$       263
Function spaces, vector, $\tilde{X}_0$       267
Function spaces, vector, X      82
Fundamental solution $\Phi$       225
Funk Hecke formula      241
Generalized Lax — Milgram lemma      21
Generous overlap      336
Geometric constraints on elements      112
Gradient      43
Green’s dyadic      303
Green’s dyadic, discrete, admissible      307
Green’s dyadic, layered medium      321
Green’s dyadic, layered medium, first column      325
Green’s dyadic, layered medium, third column      322
Green’s dyadic, perfectly conducting half space      316
H-independent uniformity      336
Health warning      399
Helmholtz decomposition      65 69 86 267 286
Herglotz wave function      398 414
Herglotz wave function, approximation property      415
Herglotz wave function, characterization      414
Herglotz wave function, uniqueness      414
Hertz vector      321
Hilbert space      16
Hilbert space, compact      23
Hilbert space, relatively compact      23
Hilbert — Schmidt theorem      24
Hodge operator      172
hp-finite elements      217
Ill-posed/well-posed      399
Imbedding      40
Incident field      9
Infinite element method      370
Infinite element method, discrete problem      374
Inner product, boundary, $\langle\dot,\dot\rangle$       82
Inner product, boundary, $\langle\dot,\dot\rangle_S$       44
Inner product, volume, $(\dot,\dot)$       49
Integral identities      50
Interface condition      8
Interior cut      65
Interpolant, definition,       134 160 207
Interpolant, definition, $r_{h,p-1}$       220
Interpolant, definition,       124 157 204
Interpolant, definition, $w_{h,p-2}$       222
Interpolant, definition, $\pi_h$       145 163
Interpolant, definition, $\pi_{h,p}$       219
Interpolant, definition, $\Prod_{Clem}$       148
Interpolant, error estimate,       136 160 208
Interpolant, error estimate,       124 157 204
Interpolant, error estimate, $\pi_h$       163
Interpolant, error estimate, $\pi_{h,p}$       145 164
Interpolant, error estimate, $\Prod_{Clem}$       149
Inverse problem      394
Inverse problem, linear sampling method      397
Inverse problem, uniqueness      411
Jacobi — Anger expansion      241
Jump across a face $[\dot]_N$       359
Jump across a face $[\dot]_T$       358
Laplace — Beltrami operator $\Delta_{\partial\Omega}$       49
Lax — Milgram lemma      20
Legendrc polynomials      237
Legendre differential equation      237
Legendre differential equation, associated      237
Legendre function, associated      238
Linear sampling method      397
Linear sampling method, implementation      402
Linear sampling method, mathematics      422
Linear sampling method, numerical results      405
Lipschitz domain      38
Lois’ variational method      371
LSM      see “Linear sampling method”
Matrix problem      334
Maxwell’s equations, time dependent      2
Maxwell’s equations, time harmonic      7
Mei series      256 259
Mesh parameter h      112
Minimum rule      218
Mixed problem      22
Mixed reciprocity      411
Morozov discrepancy principle      402
NEA      see “Normalized echo area”
Neumann series      23
Non-conforming elements      200
Normal vector      39
Normalized echo area      392
NtD map      see “Calderon operator”
Ohm’s Law      6
Operator, adjoint      18
Operator, bounded      18
Operator, collectively compact      32
Operator, compact      23
Operator, continuous      18
Operator, dual      19
Operator, linear      18
Operator, norm      18
Operator, nullspace      18

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