Method of Difference Potentials and Its Applications

By: N.K. Kulman (Translator), Viktor S. Ryaben'kii

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Hardcover | 6 November 2001

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The method of difference potentials (MDP) was proposed in 1]- 8] and sig- nificantly developed in 9]- 101] and some other works. The present book describes the current state of the art in the method of difference potentials and is a revised and essentially supplemented version of the author's first book devoted to this method, which was published by "Nauka" in 1987 100]. This monograph deals with the MDP apparatus and several of its appli- cations, particularly to the following problems: 1. the numerical solution ofinterior and exterior boundary-value problems for systems of partial differential equations; 2. the construction of conditions at the artificial boundary ofthe compu- tational domain, which equivalently replace the equations and conditions at infinity in stationary problems of gas flowpast immersed bodies as well as in some other steady-state problems; 3. the spectral approach to the construction of artificial boundary con- ditions replacing the equations of propagation of physical fields outside the computational domain containing perturbation sources; 4. the construction of artificial boundary conditions on the boundary of the computational domain for numerically solving the scattering problems in large time in a neighborhood of a fixed or a moving scatterer; 5. the statement and solution of stationary mathematical problems of the active shielding of a given subdomain from the influence of perturbation sources located outside the screened subdomain.

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Preface to the English Edition
From the Preface to the Russian Edition
Introduction	p. 1
Justification of Algorithms of the Method of Difference Potentials for Calculating Numerical Solutions of Interior Boundary-Value Problems for the Laplace Equation
Preliminaries	p. 37
Differential and Difference Potentials	p. 53
Reduction of Boundary-Value Problems for the Laplace Equation to Boundary Equations of Calderon-Seeley Type	p. 81
Numerical Solution of Boundary-Value Problems	p. 87
General Constructions of Surface Potentials and Boundary Equations on the Basis of the Concept of a Clear Trace
Generalized Potentials and Boundary Equations with Projections for Differential Operators	p. 141
General Constructions of Potentials and Boundary Equations for Difference Operators	p. 159
Lazarev's Results on the Algebraic Structure of the Set of Surface Potentials of a Linear Operator	p. 207
A General Scheme of the Method of Difference Potentials for the Numerical Solution of Differential and Difference Boundary-Value Problems of Mathematical Physics
A General Scheme of the Method of Difference Potentials for Differential Problems	p. 217
Illustrations of Constructions of the Method of Difference Potentials	p. 273
General Scheme of the Method of Difference Potentials for Solving Numerically the Difference Analogs of Differential Boundary-Value Problems	p. 291
Examples of MDP Algorithms for Solving Numerically Boundary-Value Problems of Mathematical Physics
The Tricomi Problem	p. 329
Constructions of the Method of Difference Potentials for the Computation of Stressed States of Elastic Compressible Materials	p. 341
Problems of Internal Flows of Viscous Incompressible Fluids	p. 345
An Example of the MDP Algorithm for Computing the Stationary Acoustic Wave Field outside a Solid of Revolution	p. 371
Artificial Boundary Conditions for Stationary Problems
An Efficient Algorithm for Constructing Artificial Boundary Conditions for a Model Problem	p. 395
On the Results of the Application of the Method of Difference Potentials to the Construction of Artificial Boundary Conditions for External Flow Computations	p. 403
General Constructions of Difference Nonreflecting Artificial Boundary Conditions for Time-Dependent Problems
Nonreflecting Difference Conditions on the Moving and Shape Varying Boundary of the Computational Domain	p. 445
Spectral Approach to the Construction of Nonreflecting Boundary Conditions	p. 461
Nonreflecting Artificial Boundary Conditions for Replacing the Rejected Equations with Lacunas
Problem of Constructing NRABCs and the Corresponding Auxiliary Cauchy Problem	p. 489
Algorithm for Solving the Cauchy Problem with the Help of Lacunas	p. 495
Problems of Active Shielding and Imitation
Active Shielding Control	p. 515
Difference Imitation Problems	p. 519
Appendix	p. 523
References	p. 525
Index	p. 537
Table of Contents provided by Blackwell. All Rights Reserved.

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At a Glance

Hardcover

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