Method of difference potentials and its applications. (Metod raznostnykh potentsialov i ego prilodzheniya). 2nd augmented and revised ed. (Metod raznostnykh potentsialov i ego prilodzheniya.) (Russian) Zbl 1014.65112
Moskva: FIZMATLIT. 494 p. (2002).
The book describes the current state of the art in the method of difference potentials (MDP) and is a revised and essentially supplemented version of the author’s first book devoted to this method [The method of difference potentials for some problems of continuum mechanics (1987; Zbl 0631.73069)]. This monograph deals with the MDP apparatus and several of its applications, particularly to the following problems:
The numerical solution of interior and exterior boundary-value problems for systems of partial differential equations;
the construction of conditions at the artificial boundary of the computational domain, which equivalently replace the equations and conditions at infinity in stationary problems of gas flow past immersed bodies as well as in some other steady-state problems;
the spectral approach to the construction of artificial boundary conditions replacing the equations of propagation of physical fields outside the computational domain containing perturbation sources;
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;
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.
The new possibilities provided by the method of difference potentials originate from the fact that this method combines several advantages of the classical Cauchy-type integral from the theory of analytic functions and the universality of difference schemes.
The book can be useful to readers interested in different fields and pursuing different goals.
The studies described in the book were chiefly carried out at the M. V. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, as well as at the Institute for Mathematical Modeling of the Russian Academy of Sciences, at Tel Aviv University, and at ICASE, NASA Langley Research Center.
The numerical solution of interior and exterior boundary-value problems for systems of partial differential equations;
the construction of conditions at the artificial boundary of the computational domain, which equivalently replace the equations and conditions at infinity in stationary problems of gas flow past immersed bodies as well as in some other steady-state problems;
the spectral approach to the construction of artificial boundary conditions replacing the equations of propagation of physical fields outside the computational domain containing perturbation sources;
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;
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.
The new possibilities provided by the method of difference potentials originate from the fact that this method combines several advantages of the classical Cauchy-type integral from the theory of analytic functions and the universality of difference schemes.
The book can be useful to readers interested in different fields and pursuing different goals.
The studies described in the book were chiefly carried out at the M. V. Keldysh Institute of Applied Mathematics of the Russian Academy of Sciences, as well as at the Institute for Mathematical Modeling of the Russian Academy of Sciences, at Tel Aviv University, and at ICASE, NASA Langley Research Center.
Reviewer: Leonid B.Chubarov (Novosibirsk)
MSC:
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 74S20 | Finite difference methods applied to problems in solid mechanics |
| 65E05 | General theory of numerical methods in complex analysis (potential theory, etc.) |
| 76N15 | Gas dynamics (general theory) |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 78A45 | Diffraction, scattering |
| 65-02 | Research exposition (monographs, survey articles) pertaining to numerical analysis |
| 78M20 | Finite difference methods applied to problems in optics and electromagnetic theory |
| 35J55 | Systems of elliptic equations, boundary value problems (MSC2000) |
| 65N35 | Spectral, collocation and related methods for boundary value problems involving PDEs |
| 76M22 | Spectral methods applied to problems in fluid mechanics |
