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