Результаты поиска по 'adjoint problem':
Найдено статей: 4
  1. Mokin A.Y.
    Correctness of task family with nonclassical boundary conditions
    Computer Research and Modeling, 2009, v. 1, no. 2, pp. 139-146

    A boundary value problem for partial differential equation with nonlocal boundary relations of special type is resolved by means of a slight modification of the separation of variables method. Ordinal differential operator of the second order subject to boundary conditions of the main problem is not self-adjoint. The system of eigenfunctions generated by the operator has no basis property in L2[0,1] space. A special system of functions is proposed to expand the solution of the boundary value problem.

    Keywords: nonclassical boundary conditions, parabolic type problem, separation of variables method.
    Views (last year): 2.
  2. Chernov I.A., Manicheva S.V.
    Adjoint grid parabolic quazilinear boundary-value problems
    Computer Research and Modeling, 2012, v. 4, no. 2, pp. 275-291

    In the paper we construct the adjoint problem for the explicit and implicit parabolic quazi-linear grid boundary-value problems with one spatial variable; the coefficients of the problems depend on the solution at the same time and earlier times. Dependence on the history of the solution is via the state vector; its evolution is described by the differential equation. Many models of diffusion mass transport are reduced to such boundary-value problems. Having solutions to the direct and adjoint problems, one can obtain the exact value of the gradient of a functional in the space of parameters the problem also depends on. We present solving algorithms, including the parallel one.

    Keywords: adjoint problem, evaluation of parameters, mathematical modelling, gradient methods.
    Views (last year): 1.
  3. Pletnev N.V., Matyukhin V.V.
    On the modification of the method of component descent for solving some inverse problems of mathematical physics
    Computer Research and Modeling, 2023, v. 15, no. 2, pp. 301-316

    The article is devoted to solving ill-posed problems of mathematical physics for elliptic and parabolic equations, such as the Cauchy problem for the Helmholtz equation and the retrospective Cauchy problem for the heat equation with constant coefficients. These problems are reduced to problems of convex optimization in Hilbert space. The gradients of the corresponding functionals are calculated approximately by solving two well-posed problems. A new method is proposed for solving the optimization problems under study, it is component-by-component descent in the basis of eigenfunctions of a self-adjoint operator associated with the problem. If it was possible to calculate the gradient exactly, this method would give an arbitrarily exact solution of the problem, depending on the number of considered elements of the basis. In real cases, the inaccuracy of calculations leads to a violation of monotonicity, which requires the use of restarts and limits the achievable quality. The paper presents the results of experiments confirming the effectiveness of the constructed method. It is determined that the new approach is superior to approaches based on the use of gradient optimization methods: it allows to achieve better quality of solution with significantly less computational resources. It is assumed that the constructed method can be generalized to other problems.

    Keywords: inverse problems, convex optimization, optimization in a Hilbert space, first order methods, component descent, imprecise oracle.
  4. Rusyak I.G., Ermolaev M.A.
    On the solution of the adjoint problem of gas dynamics, ignition and combustion of gunpowder in terms of artillery shot
    Computer Research and Modeling, 2014, v. 6, no. 1, pp. 99-106

    This article is dedicated to numerical algorithms for solving problems of ignition and unsteady combustion of gunpowder on a uniform computational grid, and a grid with concentration near the surface of the combustion at a constant and adapts the depth under the heated layer of computational domain. The analysis of efficiency of a numerical grid.

    Keywords: ignition, unsteadiness, combustion, adaptive difference grid, numerical methods.
    Views (last year): 4. Citations: 3 (RSCI).

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