Method of difference potentials and its applications:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch Russisch |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2002
|
| Schriftenreihe: | Springer series in computational mathematics
30 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009586474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Erscheint: Dezember 2001 |
| Umfang: | XVIII, 538 S. graph. Darst. |
| ISBN: | 3540426337 |
Internformat
MARC
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| 100 | 1 | |a Rjabenʹkij, Viktor Solomonovič |d 1923- |e Verfasser |0 (DE-588)1028057067 |4 aut | |
| 240 | 1 | 0 | |a Metod raznostnykh potentsialov i ego primeneniya |
| 245 | 1 | 0 | |a Method of difference potentials and its applications |c Viktor S. Ryaben'kii |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2002 | |
| 300 | |a XVIII, 538 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Springer series in computational mathematics |v 30 | |
| 500 | |a Erscheint: Dezember 2001 | ||
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Datensatz im Suchindex
| _version_ | 1819380786231508992 |
|---|---|
| adam_text | Contents
Preface to the English Edition VII
From the Preface to the Russian Edition XI
Introduction 1
0.1 Statement of Model Problems 3
0.2 Difference Potentials 7
0.3 Solution of Model Problems 25
Part I. Justification of Algorithms of the Method
of Difference Potentials for Calculating
Numerical Solutions of Interior
Boundary Value Problems
for the Laplace Equation
1. Preliminaries 37
1.1 Local Splines 37
1.2 Finite Fourier Series 40
1.3 Calculation of the Solution of a Difference Analog
of the Dirichlet Problem for the Poisson Equation
in a Square Region 41
1.4 Holder Spaces 44
1.5 Schauder and Thomee Estimates 48
1.6 On the Proximity of Solutions
of the Differential and Difference Dirichlet Problems
for the Poisson Equation in a Square Domain 49
2. Differential and Difference Potentials 53
2.1 Fundamental Solution and Green Functions and Operators .. 53
2.2 Potentials and Their Integral and Operator Representations . 56
2.3 Definition and Calculation of a Difference Potential 66
2.4 Approximation of a Differential Potential
by a Difference Potential 72
XIV Contents
3. Reduction of Boundary Value Problems
for the Laplace Equation to Boundary
Equations of Calderon—Seeley Type 81
3.1 Boundary Projection and a Boundary Condition
of Calderon Seeley Type 81
3.2 Passage from Boundary Value Problems
in a Domain to Equations on Its Boundary 84
4. Numerical Solution of Boundary Value Problems 87
4.1 Intermediate Discretization 87
4.2 Final Discretization 97
4.3 Conjugate Gradient Method 117
4.4 Reduction of the Discrete Problem to a Form
Convenient for the Solution by the Conjugate
Gradient Method 123
4.5 An Algorithm for the Numerical Solution
of the Discrete Problem by the Conjugate Gradient
Method 129
4.6 A Computational Example 135
Part II. General Constructions of Surface Potentials
and Boundary Equations on the Basis
of the Concept of a Clear Trace
1. Generalized Potentials and Boundary
Equations with Projections for Differential
Operators 141
1.1 Clear Trace and General Constructions
of Differential Potentials and Boundary Equations
with Projections 141
1.2 Conditionality of Boundary Equations
with Projections 151
1.3 Comments on the Literature 154
2. General Constructions of Potentials and
Boundary Equations for Difference Operators 159
2.1 General Constructions 159
2.2 Examples 167
2.3 Cauchy Type Potentials for General Linear Systems
of Difference Equations on Abstract Grids 172
2.4 Cauchy Type Potentials and Uniquely Solvable
Difference Boundary Value Problems 179
2.5 Reznik s Algorithm for Calculating the Difference Potential .. 198
2.6 Comments on the Literature 201
Contents XV
3. Lazarev s Results on the Algebraic
Structure of the Set of Surface Potentials
of a Linear Operator 207
3.1 Preliminaries 207
3.2 Potentials with Density from the Space of Clear
Traces and Boundary Equations with Projections
of an Abstract Operator 209
Part III. A General Scheme of the Method of Difference
Potentials for the Numerical Solution
of Differential and Difference Boundary Value
Problems of Mathematical Physics
1. A General Scheme of the Method
of Difference Potentials for Differential Problems 217
1.1 Nonclassical Auxiliary Problems 217
1.2 Admissible Arbitrariness in the Choice
of the Construction of a Clear Trace 221
1.3 Scheme for Approximating Differential Potentials
by Difference Potentials 225
1.4 The Reznik Theorems on the Approximation
of the Surface Potentials of Elliptic Operators
by Difference Potentials 231
1.5 Intermediate Discretization of Boundary Equations
with Projections 234
1.6 Constructive Discretization Scheme for Boundary
Equations with Projections 240
1.7 Fragments of Other Methods of Constructive
Discretization 249
1.8 Methods of Deriving an Algebraic System
of Simple Structure 252
1.9 On the Operator adjoint to the Green Operator
of the Difference Auxiliary Problem 257
2. Illustrations of Constructions of the Method
of Difference Potentials 273
2.1 Examples of Interior Problems 273
2.2 Examples of Exterior Problems 279
2.3 An Example of Constructing the Difference
Potential for Solving Numerically Boundary Value
Problems in a Domain with a Cut 282
2.4 An Example of Boundary Equations with Projections
for the Stokes System 287
XVI Contents
3. General Scheme of the Method of Difference Potentials
for Solving Numerically the Difference Analogs
of Differential Boundary Value Problems 291
3.1 Statement of Difference Problems 291
3.2 Abstract Equations with Projections 293
3.3 Reduction of Difference Problems to Equations
for the Density of the Difference Potential and
the Scheme for Calculating Solutions to These Equations .... 302
3.4 Methods for Obtaining Boundary Conditions
with Projections that are Convenient for Iterations 305
3.5 Difference Single Layer Potential as an Example
of Potentials of Special Form. Resonance
in the Complementary Domain. Relation
to the Capacity Matrix Method 315
3.6 Remark on the Combined Use of the Finite
Element Method, the Fedorenko Multigrid Method,
and the Method of Difference Potentials 321
Part IV. Examples of MDP Algorithms for Solving
Numerically Boundary Value Problems
of Mathematical Physics
1. The Tricomi Problem 329
1.1 Difference Analogs of the Tricomi Problem 330
1.2 Algorithms of the Method of Difference Potentials 334
1.3 Computational Results 339
2. Constructions of the Method of Difference
Potentials for the Computation of Stressed
States of Elastic Compressible Materials 341
2.1 Difference Potential 341
2.2 Remarks on Algorithms of the Method of Difference
Potentials 343
3. Problems of Internal Flows of Viscous
Incompressible Fluids 345
3.1 An Algorithm for Solving the Two Dimensional
Stokes Problem Numerically in the Natural Variables
(Torgashov Algorithm) 346
4. An Example of the MDP Algorithm
for Computing the Stationary Acoustic
Wave Field outside a Solid of Revolution 371
4.1 Difference Spherical Harmonics 371
Contents XVII
4.2 Constructions of the Difference Potential
for Exterior Problems 376
4.3 An Algorithm for Solving Exterior Problems
for Solids of Revolution 380
4.4 Numerical Examples 389
Part V. Artificial Boundary Conditions
for Stationary Problems
1. An Efficient Algorithm for Constructing
Artificial Boundary Conditions for a Model
Problem 395
2. On the Results of the Application
of the Method of Difference Potentials
to the Construction of Artificial Boundary
Conditions for External Flow Computations 403
2.1 Introduction 403
2.2 Formulation of the Problem 404
2.3 Two Dimensional Flows Around Airfoils 411
2.4 Three Dimensional Flows Past a Wing 419
2.5 Three Dimensional Flow with Jet Exhaust 429
Part VI. General Constructions of Difference
Nonreflecting Artificial Boundary Conditions
for Time Dependent Problems
1. Nonreflecting Difference Conditions
on the Moving and Shape Varying Boundary
of the Computational Domain 445
1.1 Introduction 445
1.2 Formulation of the Problem 446
1.3 Construction of NRABCs 450
1.4 Possibility of Speeding up Computations by Taking
Account of the Properties of Specific Problems 457
1.5 Bibliographical Comments 460
2. Spectral Approach to the Construction
of Nonreflecting Boundary Conditions 461
2.1 Finite Difference Nonreflecting Boundary Conditions 462
2.2 Algorithm for NRABC Approximation 469
2.3 Choice of a Particular Basis 476
2.4 Numerical Experiments 477
XVIII Contents
2.5 Potential Generalizations 481
Part VII. Nonreflecting Artificial Boundary Conditions
for Replacing the Rejected Equations
with Lacunas
1. Problem of Constructing NRABCs
and the Corresponding Auxiliary Cauchy
Problem 489
1.1 Definition of Nonreflecting Artificial Boundary
Conditions (NRABCs) 489
1.2 Auxiliary Difference Cauchy Problem
for Constructing NRABCs 492
2. Algorithm for Solving the Cauchy Problem
with the Help of Lacunas 495
2.1 Lacunas 495
2.2 Economical Algorithm for Computing the Solution
of the Difference Cauchy Problem 499
2.3 Taking Account of the Special Properties
of the Auxiliary Difference Cauchy Problem Used
to Compute the Nonreflecting Artificial Boundary
Conditions 505
2.4 Turchaninov s Phenomenon 506
2.5 Numerical Experiments 507
2.6 On Problems in a Moving Computational Domain 510
Part VIII. Problems of Active Shielding and Imitation
1. Active Shielding Control 515
1.1 Difference Stationary Problem of Active Shielding 515
1.2 Brief Bibliographic Review 518
2. Difference Imitation Problems 519
2.1 Difference Schemes 519
2.2 Statement and General Solution of the Imitation Problem ... 520
Appendix 523
References 525
Index 537
|
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| author | Rjabenʹkij, Viktor Solomonovič 1923- |
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| author_sort | Rjabenʹkij, Viktor Solomonovič 1923- |
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| bvnumber | BV014002970 |
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| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV014002970 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T10:57:24Z |
| institution | BVB |
| isbn | 3540426337 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009586474 |
| oclc_num | 635178947 |
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| owner | DE-703 DE-634 DE-83 DE-11 |
| owner_facet | DE-703 DE-634 DE-83 DE-11 |
| physical | XVIII, 538 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | Springer |
| record_format | marc |
| series | Springer series in computational mathematics |
| series2 | Springer series in computational mathematics |
| spellingShingle | Rjabenʹkij, Viktor Solomonovič 1923- Method of difference potentials and its applications Springer series in computational mathematics Differenzenpotenzial-Methode (DE-588)4667670-3 gnd Integralgleichung (DE-588)4027229-1 gnd |
| subject_GND | (DE-588)4667670-3 (DE-588)4027229-1 |
| title | Method of difference potentials and its applications |
| title_alt | Metod raznostnykh potentsialov i ego primeneniya |
| title_auth | Method of difference potentials and its applications |
| title_exact_search | Method of difference potentials and its applications |
| title_full | Method of difference potentials and its applications Viktor S. Ryaben'kii |
| title_fullStr | Method of difference potentials and its applications Viktor S. Ryaben'kii |
| title_full_unstemmed | Method of difference potentials and its applications Viktor S. Ryaben'kii |
| title_short | Method of difference potentials and its applications |
| title_sort | method of difference potentials and its applications |
| topic | Differenzenpotenzial-Methode (DE-588)4667670-3 gnd Integralgleichung (DE-588)4027229-1 gnd |
| topic_facet | Differenzenpotenzial-Methode Integralgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009586474&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012004 |
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