A computational differential geometry approach to grid generation:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2003
|
| Schriftenreihe: | Scientific computation
Physics and astronomy online library |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 264 S. graph. Darst. : 24 cm |
| ISBN: | 3540140085 |
Internformat
MARC
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| 100 | 1 | |a Lisejkin, Vladimir Dmitrievič |d 1945- |e Verfasser |0 (DE-588)12085533X |4 aut | |
| 245 | 1 | 0 | |a A computational differential geometry approach to grid generation |c Vladimir D. Liseikin |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2003 | |
| 300 | |a XIV, 264 S. |b graph. Darst. : 24 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Scientific computation | |
| 490 | 0 | |a Physics and astronomy online library | |
| 650 | 4 | |a Differentialgeometrie | |
| 650 | 4 | |a Gittererzeugung | |
| 650 | 0 | 7 | |a Differentialgeometrie |0 (DE-588)4012248-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Gittererzeugung |0 (DE-588)4402542-7 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Gittererzeugung |0 (DE-588)4402542-7 |D s |
| 689 | 0 | 1 | |a Differentialgeometrie |0 (DE-588)4012248-7 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010402774&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-010402774 | |
Datensatz im Suchindex
| _version_ | 1808225783259332608 |
|---|---|
| adam_text |
CONTENTS
PART
I.
GEOMETRIC
BACKGROUND
TO
GRID
TECHNOLOGY
1.
INTRODUCTORY
NOTIONS
.
5
1.1
REPRESENTATION
OF
PHYSICAL
GEOMETRIES
.
5
1.2
GENERAL
CONCEPTS
RELATED
TO
GRIDS
.
8
1.2.1
GRID
CELLS
.
8
1.2.2
REQUIREMENTS
IMPOSED
ON
CELLS
AND
GRIDS
.
10
1.3
GRID
GENERATION
MODELS
.
15
1.3.1
MAPPING
APPROACH
.
16
1.3.2
REQUIREMENTS
IMPOSED
ON
MATHEMATICAL
MODELS
.
20
1.3.3
ALGEBRAIC
METHODS
.
22
1.3.4
DIFFERENTIAL
METHODS
.
23
1.3.5
VARIATIONAL
METHODS
.
27
1.4
COMPREHENSIVE
CODES
.
30
2.
GENERAL
COORDINATE
SYSTEMS
IN
DOMAINS
.
33
2.1
JACOBI
MATRIX
.
33
2.2
COORDINATE
LINES,
TANGENTIAL
VECTORS,
AND
GRID
CELLS
.
34
2.3
COORDINATE
SURFACES
AND
NORMAL
VECTORS
.
36
2.4
REPRESENTATION
OF
VECTORS
THROUGH
THE
BASE
VECTORS
.
38
2.5
METRIC
TENSORS
.
40
2.5.1
COVARIANT
METRIC
TENSOR
.
40
2.5.2
LINE
ELEMENT
.
41
2.5.3
CONTRAVARIANT
METRIC
TENSOR
.
42
2.5.4
RELATIONS
BETWEEN
COVARIANT
AND
CONTRAVARIANT
ELEMENTS
.
43
2.6
CROSS
PRODUCT
.
44
2.6.1
GEOMETRIC
MEANING
.
44
2.6.2
RELATION
TO
VOLUMES
.
45
2.6.3
RELATION
TO
BASE
VECTORS
.
46
2.7
RELATIONS
CONCERNING
SECOND
DERIVATIVES
.
47
2.7.1
CHRISTOFFEL
SYMBOLS
OF
DOMAINS
.
47
2.7.2
DIFFERENTIATION
OF
THE
JACOBIAN
.
49
2.7.3
BASIC
IDENTITY
.
50
XII
CONTENTS
3.
GEOMETRY
OF
CURVES
.
53
3.1
CURVES
IN
MULTIDIMENSIONAL
SPACE
.
53
3.1.1
DEFINITION
.
53
3.1.2
BASIC
CURVE
VECTORS
.
54
3.2
CURVES
IN
THREE-DIMENSIONAL
SPACE
.
55
3.2.1
BASIC
VECTORS
.
55
3.2.2
CURVATURE
.
56
3.2.3
TORSION
.
57
4.
MULTIDIMENSIONAL
GEOMETRY
.
59
4.1
TANGENT
AND
NORMAL
VECTORS
AND
TANGENT
PLANE
.
59
4.2
FIRST
GROUNDFORM
.
61
4.2.1
COVARIANT
METRIC
TENSOR
.
61
4.2.2
CONTRAVARIANT
METRIC
TENSOR
.
62
4.3
GENERALIZATION
TO
RIEMANNIAN
MANIFOLDS
.
65
4.3.1
DEFINITION
OF
THE
MANIFOLDS
.
65
4.3.2
EXAMPLE
OF
A
RIEMANNIAN
MANIFOLD
.
67
4.3.3
CHRISTOFFEL
SYMBOLS
OF
MANIFOLDS
.
68
4.4
TENSORS
.
72
4.4.1
DEFINITION
.
72
4.4.2
EXAMPLES
OF
TENSORS
.
73
4.4.3
TENSOR
OPERATIONS
.
76
4.5
BASIC
INVARIANTS
.
77
4.5.1
BELTRAMI
'
S
DIFFERENTIAL
PARAMETERS
.
77
4.5.2
MEASURE
OF
RELATIVE
SPACING
.
78
4.5.3
MEASURE
OF
RELATIVE
CLUSTERING
.
80
4.5.4
MEAN
CURVATURE
.
80
4.6
GEOMETRY
OF
HYPERSURFACES
.
81
4.6.1
NORMAL
VECTOR
TO
A
HYPERSURFACE
.
81
4.6.2
SECOND
FUNDAMENTAL
FORM
.
85
4.6.3
SURFACE
CURVATURES
.
85
4.6.4
FORMULAS
OF
THE
MEAN
CURVATURE
.
86
4.7
RELATIONS
TO
THE
PRINCIPAL
CURVATURES
OF
TWO-DIMENSIONAL
SURFACES
.
101
4.7.1
SECOND
FUNDAMENTAL
FORM
.
101
4.7.2
PRINCIPAL
CURVATURES
.
101
PART
II.
APPLICATION
TO
ADVANCED
GRID
TECHNOLOGY
5.
COMPREHENSIVE
GRID
MODELS
.
ILL
5.1
FORMULATION
OF
A
DIFFERENTIAL
GRID
GENERATOR
.
112
5.1.1
BELTRAMIAN
OPERATOR
.
112
5.1.2
BOUNDARY
VALUE
PROBLEM
FOR
GRID
EQUATIONS
.
113
CONTENTS
XIII
5.1.3
INTERPRETATION
AS
A
MULTIDIMENSIONAL
EQUIDISTRIBUTION
PRINCIPLE
.
116
5.1.4
EXAMPLES
OF
FAMILIAR
GRID
EQUATIONS
.
116
5.1.5
REALIZATION
OF
SPECIFIED
GRIDS
.
118
5.1.6
FORMULATION
OF
MONITOR
METRICS
.
122
5.2
VARIATIONAL
FORMULATION
.
125
5.2.1
FUNCTIONAL
OF
GRID
SMOOTHNESS
.
125
5.2.2
GEOMETRIC
INTERPRETATION
.
127
5.2.3
RELATION
TO
HARMONIC
FUNCTIONS
.
130
5.2.4
APPLICATION
TO
ADAPTIVE
GRID
GENERATION
.
132
5.3
CONCLUSION
.
134
6.
RELATIONS
TO
MONITOR
MANIFOLDS
.
137
6.1
COMPUTATION
OF
GEOMETRIC
CHARACTERISTICS
.
138
6.1.1
RECURSIVE
REPRESENTATION
OF
THE
MONITOR
METRIC
.
138
6.1.2
JACOBIAN
OF
THE
COVARIANT
METRIC
TENSOR
.
139
6.1.3
CONTRAVARIANT
METRIC
TENSOR
.
140
6.1.4
BELTRAMI
'
S
MIXED
AND
FIRST
DIFFERENTIAL
PARAMETERS
.
142
6.1.5
CHRISTOFFEL
SYMBOLS
.
142
6.1.6
MIXED
DERIVATIVES
.
143
6.1.7
BELTRAMI
'
S
SECOND
DIFFERENTIAL
PARAMETER
.
144
6.1.8
GEOMETRIC
CHARACTERISTICS
FOR
A
SPHERICAL
MONITOR
METRIC
.
144
6.1.9
COMPUTATION
OF
GEOMETRIC
CHARACTERISTICS
OF
A
MONITOR
MANIFOLD
.
145
6.2
GEOMETRIC
CHARACTERISTICS
OF
MONITOR
SURFACES
.
147
6.2.1
COMPUTATION
OF
THE
ELEMENTS
OF
THE
CONTRAVARIANT
METRIC
TENSOR
.
148
6.2.2
BELTRAMI
'
S
MIXED
AND
FIRST
DIFFERENTIAL
PARAMETERS
.
153
6.2.3
CHRISTOFFEL
SYMBOLS
.
154
6.2.4
MIXED
DERIVATIVES
.
155
6.2.5
BELTRAMI
'
S
SECOND
DIFFERENTIAL
PARAMETER
.
156
6.3
PARTICULAR
TWO-DIMENSIONAL
CASE
.
158
6.3.1
PRELIMINARY
RESULTS
.
159
6.3.2
CONTRAVARIANT
METRIC
TENSOR
.
162
6.3.3
BELTRAMI
'
S
MIXED
AND
FIRST
DIFFERENTIAL
PARAMETERS
.
164
7.
GRID
EQUATIONS
WITH
RESPECT
TO
INTERMEDIATE
TRANSFORMATIONS
.
169
7.1
RELATIONS
TO
COMPREHENSIVE
EQUATIONS
.
169
7.2
RESOLVED
GRID
EQUATIONS
.
171
7.2.1
BASIC
ELLIPTIC
OPERATOR
.
171
7.2.2
GENERAL
GRID
EQUATIONS
.
171
7.2.3
EQUATIONS
FOR
A
SPHERICAL
MONITOR
METRIC
.
172
XIV
CONTENTS
7.2.4
EQUATIONS
FOR
A
SPHERICAL
MONITOR
METRIC
OVER
A
SURFACE
.
173
7.2.5
DOMAIN
GRID
EQUATIONS
WITH
RESPECT
TO
A
MONITOR
SURFACE
.
174
7.2.6
DOMAIN
GRID
EQUATIONS
WITH
RESPECT
TO
A
MONITOR
METRIC
.
176
7.2.7
SURFACE
GRID
EQUATIONS
WITH
RESPECT
TO
A
MONITOR
SURFACE
.
179
7.2.8
SURFACE
GRID
EQUATIONS
WITH
RESPECT
TO
A
MONITOR
METRIC
.
182
7.3
ROLE
OF
THE
MEAN
CURVATURE
IN
THE
GRID
EQUATIONS
.
183
7.4
PRACTICAL
GRID
EQUATIONS
.
185
7.4.1
EQUATIONS
FOR
GENERATING
GRIDS
ON
CURVES
.
186
7.4.2
EQUATIONS
FOR
GENERATING
GRIDS
ON
TWO-DIMENSIONAL
SURFACES
.
188
7.4.3
EQUATIONS
FOR
GENERATING
GRIDS
IN
DOMAINS
.
191
8.
CONTROL
OF
GRID
CLUSTERING
.
195
8.1
FUNDAMENTAL
FORMULA
FOR
GRID
CLUSTERING
.
196
8.1.1
RELATIVE
SPACING
BETWEEN
COORDINATE
SURFACES
.
197
8.1.2
RATE
OF
CHANGE
OF
THE
RELATIVE
SPACING
.
197
8.1.3
RELATIONS
TO
GEOMETRY
CHARACTERISTICS
.
199
8.1.4
BASIC
RELATION
TO
GRID
COORDINATES
.
205
8.1.5
REMARKS
.
205
8.1.6
GRID
BEHAVIOR
NEAR
BOUNDARY
SEGMENTS
OF
A
MONITOR
SURFACE
.
208
8.2
APPLICATION
OF
THEOREM
TO
POPULAR
ELLIPTIC
MODELS
.
210
8.2.1
CONTROL
OF
GRIDS
NEAR
BOUNDARIES
OF
DOMAINS
.
210
8.2.2
DIFFUSION
EQUATIONS
.
227
8.2.3
CONTROL
OF
GRID
SPACING
NEAR
BOUNDARIES
OF
PHYSICAL
SURFACES
.
229
9.
NUMERICAL
IMPLEMENTATION
OF
GRID
GENERATOR
.
241
9.1
ONE-DIMENSIONAL
EQUATION
.
241
9.1.1
NUMERICAL
ALGORITHM
.
241
9.2
TWO-DIMENSIONAL
EQUATIONS
.
243
9.2.1
ALGORITHMS
FOR
GENERATING
GRIDS
IN
TWO-DIMENSIONAL
DOMAINS
.
244
9.2.2
ALGORITHM
FOR
GENERATING
GRIDS
ON
TWO-DIMENSIONAL
SURFACES
.
250
9.3
THREE-DIMENSIONAL
EQUATIONS
.
253
REFERENCES
.
255
INDEX
.
263 |
| any_adam_object | 1 |
| author | Lisejkin, Vladimir Dmitrievič 1945- |
| author_GND | (DE-588)12085533X |
| author_facet | Lisejkin, Vladimir Dmitrievič 1945- |
| author_role | aut |
| author_sort | Lisejkin, Vladimir Dmitrievič 1945- |
| author_variant | v d l vd vdl |
| building | Verbundindex |
| bvnumber | BV017258760 |
| classification_rvk | SK 955 UH 5200 ZS 4500 |
| classification_tum | MAT 673f |
| ctrlnum | (OCoLC)488883424 (DE-599)BVBBV017258760 |
| discipline | Physik Handwerk und Gewerbe / Verschiedene Technologien Mathematik |
| format | Book |
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| id | DE-604.BV017258760 |
| illustrated | Illustrated |
| indexdate | 2024-08-24T00:14:46Z |
| institution | BVB |
| isbn | 3540140085 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010402774 |
| oclc_num | 488883424 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM |
| owner_facet | DE-91G DE-BY-TUM |
| physical | XIV, 264 S. graph. Darst. : 24 cm |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Springer |
| record_format | marc |
| series2 | Scientific computation Physics and astronomy online library |
| spelling | Lisejkin, Vladimir Dmitrievič 1945- Verfasser (DE-588)12085533X aut A computational differential geometry approach to grid generation Vladimir D. Liseikin Berlin [u.a.] Springer 2003 XIV, 264 S. graph. Darst. : 24 cm txt rdacontent n rdamedia nc rdacarrier Scientific computation Physics and astronomy online library Differentialgeometrie Gittererzeugung Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Gittererzeugung (DE-588)4402542-7 gnd rswk-swf Gittererzeugung (DE-588)4402542-7 s Differentialgeometrie (DE-588)4012248-7 s DE-604 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010402774&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lisejkin, Vladimir Dmitrievič 1945- A computational differential geometry approach to grid generation Differentialgeometrie Gittererzeugung Differentialgeometrie (DE-588)4012248-7 gnd Gittererzeugung (DE-588)4402542-7 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4402542-7 |
| title | A computational differential geometry approach to grid generation |
| title_auth | A computational differential geometry approach to grid generation |
| title_exact_search | A computational differential geometry approach to grid generation |
| title_full | A computational differential geometry approach to grid generation Vladimir D. Liseikin |
| title_fullStr | A computational differential geometry approach to grid generation Vladimir D. Liseikin |
| title_full_unstemmed | A computational differential geometry approach to grid generation Vladimir D. Liseikin |
| title_short | A computational differential geometry approach to grid generation |
| title_sort | a computational differential geometry approach to grid generation |
| topic | Differentialgeometrie Gittererzeugung Differentialgeometrie (DE-588)4012248-7 gnd Gittererzeugung (DE-588)4402542-7 gnd |
| topic_facet | Differentialgeometrie Gittererzeugung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010402774&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT lisejkinvladimirdmitrievic acomputationaldifferentialgeometryapproachtogridgeneration |