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Castillo J. — Mathematical Aspects of Numerical Grid Generation
Castillo J. — Mathematical Aspects of Numerical Grid Generation



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Название: Mathematical Aspects of Numerical Grid Generation

Автор: Castillo J.

Аннотация:

Numerical grid generation plays a critical role in any scientific computing problem when the geometry of the underlying region is complex or when the solution has a complex structure. The mathematical aspects of grid generation are discussed to provide a deeper understanding of the algorithms and their limitations. Variational methods are emphasized because they are more robust, but elliptic and transcendental algebraic methods are also considered.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1991

Количество страниц: 172

Добавлена в каталог: 14.03.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adaptation, geometric(al)      111 113
Adaptation, physical      111 113
Algorithm(s), grid-generation      3—4 59
Algorithm(s), grid-generation, anomalous behavior of      59
Algorithm(s), grid-generation, surface      4
Algorithm(s), intrinsic      4
Algorithm(s), solution-adaptive      73
Algorithm(s), transfinite interpolation      3—4
Alternative methods      94
Analysis, near-identity      32
Angle control      39
Area, control      3 48
Area, control, critical points of      47
Area, equal solutions      48
Area, functional      36 48
Bifurcation, diagram      59—60
Bifurcation, pitchfork      60—61 73
Bifurcation, points      71 72
Bifurcation, problems      61
Bifurcation, properties      3
Bilinear form      80
Boundary, angles      39
Boundary, conditions (Dirichlet)      11 114
Boundary, functions      87
Boundary, layers      105
Boundary, points      61
Boundary, points, fixed      69
Boundary-matching conditions      79 82
Boundary-value problems      31
Boundary-value problems, elliptic      19
Boundary-value problems, variational form      25
Centered differences      69
Central differences      111
Christoffel symbols      100 107—108
Coefficient matrix      30
Compatibility conditions      100
Constraints, one-sided      20
Continuum, theories      3
Continuum, variational problem      3
Convergence      20
Convergence, properties      66
Coordinate transformations      114
Coordinate transformations, optimal      111
Coordinate(s), cartesian      100
Coordinate(s), computational      114
Coordinate(s), curvilinear      99—100 102 105 114
Coordinate(s), local      107
Corner identities      79
Curvature      107 131
Curvature, covariant      101
Curvature, Gaussian      101
Curvature, negative      129
Curvature, nonpositive      108
Curvilinear coordinate(s)      99 100 105
Curvilinear coordinate(s), directions      17
Decoupling      see "Problems"
Derivatives, directional      22
Diffeomorphism      109 123 129
Differentiable manifolds      7
Differential geometry      101 121
Dimensions, correct      15
Dimensions, three      15
Direct approach/method      36
Direct approach/method, variational      37 39
Dirichlet principle      137
Discrete geometry      3
Discretization methods, finite-difference      105
Discretization methods, finite-element      105
Domain(s), computational      111 114
Domain(s), logical      111
Domain(s), physical      111—112
Domain(s), simply connected      130
Domain(s), simply connected bounded      123
Elliptic methods      4 14
Elliptic systems      15
Elliptic systems, uncoupled      32
Equation(s), analytic      14
Equation(s), Cauchy — Riemann      10
Equation(s), Codazzi      101
Equation(s), convection-diffusion      106 114
Equation(s), discrete grid-generation      73
Equation(s), elliptic      12
Equation(s), elliptic partial differential      99
Equation(s), Euler — Lagrange      3 33 63 65—66
Equation(s), Euler — Lagrange, discretized      70
Equation(s), Gaussian      99 101
Equation(s), grid      118
Equation(s), harmonic map      129
Equation(s), Laplacian      10 42 99
Equation(s), model      99
Equation(s), ordinary differential (ODEs)      30 63
Equation(s), partial differential (PDEs)      1 4 15 32
Equation(s), Weingarten      99
Errors, average      115
Errors, maximum      115
Extrinsic Method      78
Finite-difference approximation central      26
Function(s), blending      4 78 88
Function(s), boundary      87
Function(s), characteristic      114 115 121
Function(s), harmonic      125
Function(s), nonconstant harmonic      124
Function(s), subharmonic      140
Functional(s), area      36 48
Functional(s), continuous      36
Functional(s), energy      123 127
Functional(s), length control      95
Functional(s), minimum      20
Functional(s), orthogonality      39 48
Functional(s), smoothness      33
Functional(s), volume      19 29 33
Geometric shape      14
Godunov — Thompson method      106
Gradients      11
Grid at infinity      90 95
Grid(s), adapted      114 116
Grid(s), adaptive      61 106 114 116 122
Grid(s), angles      39
Grid(s), area of      26
Grid(s), boundary-adapted      1
Grid(s), boundary-conforming      1
Grid(s), cells      3 15 26 29 35—37
Grid(s), continuum      61 63 73
Grid(s), control      106
Grid(s), coordinates      38
Grid(s), density      109
Grid(s), desired      12
Grid(s), discrete      40
Grid(s), folding      11—12 91 109
Grid(s), generator      59
Grid(s), geometry-adapted      1
Grid(s), ideal      95
Grid(s), initial      12 15 71
Grid(s), lines      26 35
Grid(s), methods (adaptive)      105
Grid(s), node distribution      105
Grid(s), nodes      112
Grid(s), one-point      69
Grid(s), optimal      40 42
Grid(s), optimal continuous      40 42
Grid(s), orthogonality      36
Grid(s), properties      121
Grid(s), properties, multiple      3
Grid(s), reference      19 32—33
Grid(s), solution-adapted      1
Grid(s), solution-adaptive      106
Grid(s), spacing      3 36
Grid(s), structured      1
Grid(s), three-dimensional      9
Grid(s), typical      12
Grid(s), unshifted      95
Grid(s), unstructured      1
Grid(s), useful      9
Grid-generation      9 12 14 127
Grid-generation, adaptive      121
Grid-generation, algebraic      2 75 78—79 83
Grid-generation, algebraic, intrinsic      75
Grid-generation, continuum      73
Grid-generation, curve      61 73
Grid-generation, discrete      60—61
Grid-generation, elementary      2
Grid-generation, elliptic      9
Grid-generation, hand      2
Grid-generation, harmonic      131
Grid-generation, iterative      91
Grid-generation, Laplacian      106
Grid-generation, method      2 89—90
Grid-generation, mirror flip invariant      90
Grid-generation, partial differential equation      2
Grid-generation, planar      5
Grid-generation, problems      31 60 73 134
Grid-generation, rotation ally invariant      89
Grid-generation, solution-adaptive      61 105
Grid-generation, stretch-invariant      89
Grid-generation, surface      61 73 101
Grid-generation, three-dimensional      124
Grid-generation, transform      140 145
Grid-generation, variational      2—3 19 35 48 59
Harmonic maps      see "Map(s)"
Homeomorphism      4 129—130 142
Homeomorphism, boundary      143—144
Incomplete rank      48
Integral, constraints      35
Integral, minimization of      27
Integral, smoothness      19 33
Integral, unique minimum of      29
Integral, volume      19 30—31
Interpolation      12
Iteration, fully lagged      60 66 70
Iteration, nominal      60 63 67 70—72
Iterative methods      12
Jacobian      6 11 27 31 130
Lower semi continuity      138
Map(s), discrete      2
Map(s), harmonic      2—4 106—107 109 121 123—124 127 145
Map(s), harmonic, existence      107
Map(s), harmonic, regularity      107
Map(s), harmonic, singularities of      4
Map(s), harmonic, uniqueness      107
Map(s), nearly identity      30
Map(s), one-to-one      111
Map(s), regular      131
Mapping(s), composite      10
Mapping(s), conformal      3 9 12 15
Mapping(s), conformal, practical      14
Mapping(s), harmonic      11 14—15 17 131
Mapping(s), proper      27
Mapping(s), properties of      9
Mapping(s), quasi-conformal      12
Mapping(s), reference      27 31
Mapping(s), scaled      17
Mapping(s), scaled, singularities of      4
Method(s), Gilding's      75 83 86
Method(s), Yanenko's      106
Metrics, Euclidean      109
Metrics, physical      113
Metrics, Riemannian      see "Riemannian metrics"
Minima      47
Minimum point (uniqueness of)      24
Minimum point, unique      27
Model, equation      99
Model, problem      42 48
Neumann      118
Nonintrinsic method      88
Notation      37
Numerical, coordinate generation      99
Numerical, models      105
Numerical, solution      121
Operators, Beltramian      100
Operators, Laplace — Beltrami      107
Operators, laplacian      100 132
Optimization      35
Optimization theory      19
Orthogonality      6
Parameterization      69
Parametric variables      14
Picard linearization      111
Principles, maximum      11 141
Principles, minimum      11
Principles, weak-maximum      142
Problems, area control      3 48
Problems, decoupling      35
Problems, discrete      60
Problems, minimization (nonlinear)      36
Problems, model      48
Problems, model, optimal solutions of      142
Problems, open      145
Problems, primal, optimal solutions of      142
Problems, quadratic      42
Problems, three-dimensional      48
Problems, two-dimensional      48
Problems, variational      61 63
Problems, variational, regularity property of      4
Quasilinearity      11
Region(s), arbitrary      15
Region(s), convex      12
Region(s), nonconvex      12
Region(s), parametric      14
Region(s), planar      75 99
Region(s), polygonal      37 40
Region(s), rectangular      12
Region(s), reference      33
Region(s), simply connected      9
Riemann — Christoffel tensor      101
Riemannian manifolds      107 123 129
Riemannian metrics      4 111 113 121
Riemannian metrics, adaptive      106
Riemannian metrics, solution adaptivity      4
Riemannian metrics, tensor      107
Sets, convex      20
Shearing transformation      86 89
Singularities      105
Smoothness, functional      33
Smoothness, integral      28
Smoothness, problem      27 31
Solution algorithms, appropriate      61
Solution algorithms, multiple      60—61 73
Solution algorithms, solution adaptive      1 111
Space(s), Euclidean      27 99 123
Space(s), Hilbert      20
Space(s), logical      5 26
Space(s), parametric      12
Space(s), physical      5 26
Space(s), Sobolev      4
Spherical harmonic      125
Subspaces      20
Surface(s)      59
Surface(s), arbitrary      14
Surface(s), coordinate generation      100
Surface(s), curved      99
Surface(s), curved, grid generator      59
Surface(s), Riemann      129
Theorem(s), inverse-function      6
Theorem(s), Rado's      4 125
Theorem(s), regularity      139
Three-dimensional methods      58
Transfinite, grid-generation formula      85
Transfinite, interpolation      3 75 85 88—89 94
Transformations, boundary-adapted      5
Transformations, boundary-conforming      5
1 2
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