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Hansen G.A., Zardecki A., Douglass R.A. — Mesh Enhancement: Selected Elliptic Methods, Foundations and Applications
Hansen G.A., Zardecki A., Douglass R.A. — Mesh Enhancement: Selected Elliptic Methods, Foundations and Applications

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Название: Mesh Enhancement: Selected Elliptic Methods, Foundations and Applications

Авторы: Hansen G.A., Zardecki A., Douglass R.A.

Аннотация:

This book focuses on mesh (grid) enhancement techniques — specifically, the use of selected elliptic methods for both structured and unstructured meshes associated with computational physics applications. Mesh enhancement is the process in which an existing mesh is modified to better meet the requirements of the physics application. To provide the reader with sufficient background information, seven of the nine chapters contain a summary of the numerical simulation process, basic background on mesh terminology and generation approaches, computational geometry, discretization of differential equations, methods of solving linear and nonlinear algebraic systems, geometry of surfaces in Euclidean space, and general elliptic methods for mesh enhancement. Furthermore, these chapters use the concept of harmonic coordinates to develop a unifying framework, the Laplace-Beltrami system, which is the governing principle of the book. The final two chapters apply this scheme, along with other selected elliptic methods, to various structured and unstructured example problems.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 515

Добавлена в каталог: 10.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
ad hoc Laplace Beltrami enhancement      406
Algebraic equation system, data structure, compressed sparse row (CSR)      219
Algebraic equation system, finite element systems      226
Algebraic equation system, finite element systems, Newton linearization      228
Algebraic equation system, finite element systems, Picard linearization      227
Algebraic equation system, library      218
Algebraic equation system, library, BPKIT      218
Algebraic equation system, library, SPARSEKIT      218
Algebraic equation system, nonlinear      221
Algebraic equation system, nonlinear, finite element systems      226
Algebraic equation system, nonlinear, Newton linearization      223
Algebraic equation system, nonlinear, Picard linearization      222
Algebraic equation system, preconditioner, PCG      216
Algebraic equation system, preconditioner, PGMRES      217
Algebraic equation system, preconditioner, PTFQMR      217
Algebraic equation system, solution      209
Algebraic equation system, solution, direct solution      211
Algebraic equation system, solution, Gauss — Seidel method      216
Algebraic equation system, solution, Jacobi iteration method      213
Algebraic equation systems, finite element systems, TSM assembly      230
Algorithm, assembly of Hermite FEM      176
Algorithm, boundary node redistribution      85
Algorithm, ELEM      440
Algorithm, equal angle distribution for a PC curve      83
Algorithm, finite difference marching      103
Algorithm, Laplacian smoothing      330
Algorithm, trans-finite interpolation      326
Algorithm, tridiagonal matrix solver      110
Atlas      480
Basis function      139
Basis, coordinate      485
Basis, dual      486
Beltrami equation      265
Boundary discretization      78
Boundary discretization, equal angle-increment      81
Boundary discretization, equal Euclidean length      79
Boundary discretization, equal parameter-increment      78
Boundary redistribution      84
Boundary value problem, classical solution      124
Boundary value problem, Dirichlet      130
Boundary value problem, generalized solution      124
Boundary value problem, grid      422
Boundary value problem, Neumann      131
Bundle, associated      488
Bundle, homomorphism      494
Bundle, principal      486
Bundle, reduced      494
Bundle, tangent      484
Chart      480
Christoffel symbols      245 250 293 499
Christoffel symbols of the first kind      245
Christoffel symbols of the second kind      245
Coarse graining      434
Codazzi equations      249
Commutator      490
Complex dilation      271
Compressed sparse row      219
Conformal metric      253
Connection coefficients      491
Connection, Levi — Civita      498
Connection, linear      490
Consistency      104
Constructive solid geometry      74
Coordinates, harmonic      420
Covariant derivative      250
Crank — Nicolson      109
CSG      74
CSR      219
Curvature      492
Curvature, Gaussian      242
Curvature, mean      242 275
Curve, parametric construction      35
Curve, parametric cubic      50
Curve, rotation      54
Curve, scaling      58
Curve, spline Wilson — Fowler      39
Curve, translation      54
Derivative, approximation      97
Derivative, definition      96
Different iable manifold      480—486
Differential map      497
Dirichlet principle      113
Einstein convention      236 474
ELEM      440
Embedding      498
Enneper’s surface      275
Field, scalar      473
Field, spinor      479
Field, vector      473
Finite difference method      96
Finite difference method, backward difference      98
Finite difference method, central difference      98
Finite difference method, consistency      104
Finite difference method, explicit difference      103
Finite difference method, forward difference      98
Finite difference method, fully implicit method      109
Finite difference method, implicit differences      109
Finite difference method, non-uniform differences      100
Finite difference method, operator, backward difference      99
Finite difference method, operator, central difference      99
Finite difference method, operator, forward difference      99
Finite difference method, operator, generalized      99
Finite difference method, second derivative, central difference      98
Finite difference method, semi-implicit method      110
Finite difference method, stability      105
Finite element method      152
Finite element method, 1D      157
Finite element method, 3D elements      199
Finite element method, assembly      169
Finite element method, errors      204
Finite element method, Gaussian quadrature      202
Finite element method, interpolation error      181
Finite element method, interpolation, 1D cubic      171
Finite element method, interpolation, 1D quadratic      163
Finite element method, interpolation, 1D simplex      161
Finite element method, interpolation, 2D bi-linear      181
Finite element method, interpolation, 2D linear      195
Finite element method, interpolation, 2D triangles      195
Finite element method, interpolation, cubic Hermitian      171
Finite element method, interpolation, hexahedral element      201
Finite element method, interpolation, tetrahedral element      199
Finite element method, Jacobian      188
Finite element method, map, isoparametric      186
Finite element method, map, sub-parametric      186
Finite element method, map, super-parametric      186
Finite element method, master element      184
Finite element method, smoothing      422
Finite element method, two-dimensional      178
Finite element, enhancement 2D      424
Finite element, enhancement 3D      428
Finite volume method      141
Fundamental form, first      237 263
Fundamental form, second      240
Galerkin method      136 150
Gauss equations      245
Gauss — Seidel relaxation      216
Geodesic      254 295
Geometric data structures      89—94
Geometric data structures, IGES      89
Geometric data structures, stereo lithography      90
Geometric modeling, solid      74
Geometry, differential, second fundamental form      238
Geometry, first fundamental form      236
Geometry, operations on      77
Geometry, operations on, discretization      78
Graph connectivity      229
Grid generation, trans-finite interpolation      326
Grid generator, Khamayseh — Mastin      284
Grid generator, Thompson — Thames — Mastin      287
Grid generator, Winslow      290
Harmonic coordinate      276
Harmonic coordinates      420
Harmonic function      114 295
Harmonic map      293
Heat equation, one-dimensional      101
Hexahedral element      201
Hilbert space      114
Hilbert space, basis      117
Hilbert space, functional      118
Hilbert space, operator      120
Hilbert space, operator, domain      120
Hilbert space, operator, positive      123
Hilbert space, operator, positive definite      123
Hilbert space, operator, self-adjoint      123
Hilbert space, operator, symmetric      123
Hilbert space, operator, weak derivative      122
Hilbert space, separable      118
Homotopic      270
IGES      89
Immersion      276 497
Inequality, Minkowski      117
Inequality, Poincare — Priedrichs      126
Inequality, Schwartz      116
Influence graph      230
Interpolation, transfinite      17
Isometry      498
Isothermal coordinates      263
Jacobi relaxation      213
Jacobian      188
Jacobian matrix      224
Killing equations      253 477
Laplace — Beltrami, enhancement equation      419
Laplace — Beltrami, optimization      363
Laplace — Beltrami, target metric (LBTM)      390
Laplacian      121 252 280 285
Laplacian smoothing, advantages      335
Lax equivalence theorem      103
Lie group      486
Linear connection      489—493
Lipschitz condition      131
Manifold, differentiate      480
Manifold, Riemannian      493
Master element      184
Mesh generation, advancing front      19
Mesh generation, algebraic transfinite interpolation      17
Mesh generation, Delaunay triangulation      20
Mesh generation, multi-block      19
Mesh generation, octree method      21
Mesh generation, quadtree method      21
Mesh generation, quality      23
Mesh generation, solution-based methods      18
Mesh generation, solution-based methods, Laplacian      18
Mesh generation, solution-based methods, TTM      19
Mesh, boundary conditions      309
Mesh, enhancement, 2D structured      323
Mesh, enhancement, 3D structured, Laplace — Beltrami      410
Mesh, enhancement, control function      310
Mesh, enhancement, definition      1
Mesh, enhancement, Dirichlet boundary condition      310
Mesh, enhancement, ghost boundary node      312
Mesh, enhancement, Laplace      328
Mesh, enhancement, Laplace — Beltrami elliptic equation      419
Mesh, enhancement, Laplace — Beltrami optimization      363
Mesh, enhancement, methods      308
Mesh, enhancement, Neumann boundary condition      311
Mesh, enhancement, node point averaging      327
Mesh, enhancement, orthogonality boundary condition      311
Mesh, enhancement, prescriptive      345
Mesh, enhancement, Spekreijse      354
Mesh, enhancement, target metric tensor      386
Mesh, enhancement, trans-finite interpolation      326
Mesh, enhancement, unstructured ad hoc Laplace — Beltrami      406
Mesh, enhancement, unstructured Winslow-based method      408
Mesh, enhancement, Winslow — Crowley      335
Mesh, impedance      308
Mesh, quality      316
Mesh, quality, metric      316
Mesh, semi-structured      306
Mesh, structured      12 305
Mesh, structured, data structure      13
Mesh, topology      12
Mesh, unstructured      15
Mesh, unstructured Laplace smoothing      404
Mesh, unstructured, properties      15
Metric tensor, geometric interpretation      372
Minimal surface      275
Moduli space      272
Monitor function      299
Monitor functions      299
Nodes, boundary distribution      78
Nodes, boundary distribution, equal angle-increment      81
Nodes, boundary distribution, equal Euclidean length      79
Nodes, boundary distribution, equal parameter-increment      78
Nodes, boundary redistribution      84
Nodes, renumbering      16
Norm, $l_2$      141
Operator, adjoint      121
Operator, bounded      120
Operator, unbounded      120
Parallelogram identity      117
Parametric bi-cubic patch      65 66
Parametric surface      60
Parametric surface, bi-cubic patch, 16-point surface      65
Parametric surface, bi-cubic patch, 4-curve surface      66
Parametric surface, blending, common border      72
Parametric surface, blending, non-adjacent patches      74
Parametric surface, patch      60
Parametric surface, properties      69
Parametric surface, properties, normal      70
Parametric surface, properties, planar test      70
Parametric surface, properties, surface area      71
Parametric surface, properties, tangent      69
Parametric surface, properties, twist      70
Parametric surface, ruled surface      60
Parametric surface, tensor product surface      63
Parametric surface, translational surface      61
Prescriptive methods      345
Prescriptive methods, modified interpolated control function (MICF)      346
Prescriptive methods, Thompson — Thames — Mastin (TTM)      345
Quadrature, Gaussian      202
Quasi-conformal      271
Rayleigh — Ritz method      135
Ricci curvature      277
Smoothness functional      421 453 465
Sobolev space      124—126
Solid modeling      74
Solid modeling, constructive solid geometry      75
Spinor objects      478
Stability, numerical      105
Stereo lithography      90
STL      90
Submanifold      276 498
surface      60 236
Surface, CSG      74
Tangent bundle      484
Tangent space      484
Tangent stiffness matrix (TSM)      228
Target metric tensor      386
Target metric tensor, estimation      430
Target metric tensor, estimation, coarse graining      433
Teichmuller space      271
Tensor      475
Tensor, curvature      247 259 492
Tensor, density      478
Tensor, metric      236
Tensor, mixed      475
Tensor, Ricci      277
Tensor, torsion      492
Tetrahedral element      199
TFI      17
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