查看更多>>摘要：Consider the shape identification of an inclusion in heat conductive medium from the time average measurement, which is modeled by an initial boundary value problem for a parabolic system with extra nonlocal measurement data specified on the outer boundary. For this nonlocal and nonlinear inverse problem for the two-dimensioned parabolic equation in a doubly-connected domain, the radius function describing the shape of inner boundary to be identified is defined as the minimizer of a regularizing cost functional. The existence of this minimizer is firstly proven in a suitable admissible set. Then we establish the convergence rate of the regularizing solution under alpha-posteriori choice strategy for the regularizing parameter. Finally the differentiability of the cost functional is proven, which provides a fundamental basis for gradient type iteration scheme. Based on the adjoint and sensitivity problem of the original problem which give the gradient of the cost functional, we propose a steepest descent iteration algorithm for finding the minimizer approximately. Numerical examples are presented to show the validity of our algorithm. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A class of block boundary value methods is constructed for the solution of linear neutral Volterra integro-differential equations with weakly singular kernels. Under suitable conditions on the data, it is shown that these methods yield optimal convergence rates when implemented on special graded meshes. Furthermore, these methods are easily extended to solve linear Volterra integral equations of the 2nd kind with weakly singular kernels. Numerical experiments confirm the theoretical results and the accuracy of the methods, and a comparison with piecewise polynomial collocation methods is provided. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper proposes a first- and second-order unconditionally stable direct discretization method based on a surface mesh consisting of piecewise triangles and its dual-surface polygonal tessellation for solving the N-component Cahn-Hilliard system. We define the discretizations of the gradient, divergence, and Laplace-Beltrami operators on triangle surfaces. We prove that the proposed schemes, which combine a linearly stabilized splitting scheme, are unconditionally energy-stable. We also prove that our method satisfies the mass conservation. The proposed scheme is solved by the biconjugate gradient stabilized (BiCGSTAB) method, which can be straightforwardly applied to GPU-accelerated biconjugate gradient stabilized implementation by using the Matlab Parallel Computing Toolbox. Several numerical experiments are performed and confirm the accuracy, stability, and efficiency of our proposed algorithm. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The considered topic, the dynamic study of new root solvers using computer tools, is actually a "bridge" between computer science and applied mathematics. The goal of this paper is the construction and dynamic study of two new one-parameter families for solving nonlinear equations using advanced computer tools such as symbolic computation, computer graphics and multi-precision arithmetic. First family, based on Popovski's third order method (Popovski, 1980), is modified and adapted for finding multiple zeros of differentiable functions. Its dynamic study is performed using basins of attraction and associated quantitative data. In the second part this one-point family for a single zero serves for the derivation of a very efficient family of iterative methods with corrections for the simultaneous determination of all multiple zeros of algebraic polynomials. The convergence analysis, performed by the help of symbolic computation in computer algebra system Mathematica, has shown that the order of convergence of the proposed family is four, five and six, depending of the type of used corrective approximations. A very fast convergence rate is obtained without any additional evaluations of a given polynomial P and its derivatives P' and P'', which points to the high computational efficiency of new methods. Choosing different values of the involved parameter, the presented family generates a variety of simultaneous methods. Employing multi-precision arithmetic, it has been shown by numerical experiments that four particular methods from the family produce approximations of very high accuracy. Computer visualization, carried out by plotting trajectories of zero approximations, points to the stability and robustness of the proposed simultaneous methods and indicates a conjecture on their globally convergent properties, one of the most important features of simultaneous methods for solving polynomial equations. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Numerical approximation of radiating waves, with a priori truncation parameter and error estimates, is crucial for efficient simulation of forward and inverse scattering models. Convergence of a series ansatz for the wave field using the classical radiating wave functions is known only when the field is evaluated exterior to a ball circumscribing the configuration. If the configuration comprises non-convex and/or elongated scatterers, evaluation of the scattered field in the interior region of the ball is important for applications including for the far-field-data based inverse problem of identifying the scatterer boundary. In this article we develop a new error estimate for the series ansatz that facilitates identification of the truncation-parameter dependent interior convergence region. This in turn facilitates an estimate-based approach for solving the boundary identification inverse problem. We demonstrate, through numerical experiments, excellent agreement of the theoretical error estimate with respect to the truncation parameter, and the efficiency of the approach to identify scatterer shapes. Crown Copyright (c) 2021 Published by Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, a fully discrete numerical scheme is proposed and analyzed for the harmonic mapping flow, with the fourth order spatial accuracy and higher than third order temporal accuracy. The fourth order spatial accuracy is realized via a long stencil finite difference, and the boundary extrapolation is implemented by making use of higher order Taylor expansion. Meanwhile, the high order (third or fourth order) temporal accuracy is based on a semi-implicit algorithm, which uses a combination of explicit Adams-Bashforth extrapolation for the nonlinear terms and implicit Adams-Moulton interpolation for the viscous diffusion term, with the corresponding integration formula coefficients. Both the consistency, linearized stability analysis and optimal rate convergence estimate (in the l(infinity) (0, T; l(2)) boolean AND l(2) (0, T; H-h(l)) norm) are provided. A few numerical examples are also presented in this article. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we present a collocation method based on redefined cubic B-spline basis functions for solving Asian option pricing problem. The stability and convergence analysis of the present method are studied. The method is proved to be unconditionally stable and has second-order convergence with respect to space variable. Numerical experiment is performed to validate the theoretical results and demonstrate the applicability of the method. The option and delta values for various values of volatilities and interest rates are computed. Convergence of the delta values is analyzed. The obtained results are compared with the existing ones to show the advantage of our method. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A Barzilai and Borwein regularization feasible direction algorithm is proposed for convex nonlinear second-order cone programming with linear constraints. In the algorithm, a regularization penalty term based on the Barzilai and Borwein parameters is added to the Frank-Wolfe linearization objective function of the direction generating subproblem. The Barzilai and Borwein subproblem is transformed into a multi-block separable convex quadratic second-order cone programming (CQSOCP) subproblem. A parallel inexact alternating direction method is applied to solve the multi-block separable CQSOCP subproblem. The global convergence is given. Numerical results demonstrate that our method is efficient for some random convex nonlinear second-order cone programming problems with low accuracy. (C) 2021 Elsevier B.V. All rights reserved.
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