查看更多>>摘要：This paper deals with the study a finite-difference approximation of the one dimensional initial-boundary value problem for a pseudo-parabolic equation containing time delay in second derivative. We propose three layer difference scheme and obtain the error estimates for its solution. Based on the method of energy estimates the fully discrete scheme is shown to be convergent of order four in space and order two in time. Numerical results are presented to illustrate the theoretical findings. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we introduce a weak Galerkin (WG) least squares finite element method for the Cauchy problem. This finite element method generates a symmetric, positive definite system and can work on general mesh. Optimal order of convergence for the WG approximation in an energy norm is established. The numerical examples confirm the theory. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Computationally quantifying uncertainties in the mathematical modeling of physical processes is crucial for understanding the errors induced by both numerical approximations of the model and lack of precise input data assumed in the continuous model. Uncertain input parameters in the continuous model are typically treated as random variables, leading to the need to consider solutions of both the continuous and discrete models as stochastic processes. Computing statistical moments of the stochastic processes is an extremely important part of the uncertainty quantification problem. In this work, we consider a class of physical processes that are modeled by the Allen-Cahn (A-C) partial differential equation (PDE) evolutionary system, with uncertainties in the initial state of the evolution and the A-C PDE. We develop a hybrid computational model for the stochastic A-C system to efficiently compute statistical moments of the numerical counterparts of the A-C stochastic processes. The hybrid framework comprises finite element method in-space approximations, high-order digital nets based sampling in high dimensional probability space, and an interplay of discretization parameters in the spatial and stochastic approximations. We demonstrate marked efficiency of the hybrid framework, compared to the standard methods, using two- and three-dimensional in space and high stochastic dimensional A-C example systems. (C) 2021 Elsevier B.V. All rights reserved.
Patel, J. K.Moraes, L. R. C.Vasques, R.Barros, R. C....
9页
查看更多>>摘要：The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle's free-path. Recently, a spectral approach was developed to generate nonclassical spectral S-N equations, which can be numerically solved in a deterministic fashion using classical numerical techniques. This paper introduces a transport synthetic acceleration procedure to speed up the iteration scheme for the solution of the monoenergetic slab-geometry nonclassical spectral S-N equations. We present numerical results that confirm the benefit of the acceleration procedure for this class of problems. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Most algorithms for determining a Jordan basis for an endomorphism of a finite dimensional vector space suffer from the major drawback that they are computationally inefficient. In this paper, a universal and efficient algorithm for an endomorphism of a finite dimensional vector space over an arbitrary field is presented. Three computational examples are considered which show how our new algorithm works. A computational comparison to the Jordan basis algorithm in Kudo et al. (2010) completes the paper (algorithmic aspects). (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：The aim of this paper is to establish the Levitin-Polyak well-posedness (LP well-posedness, for short) for two new classes of controlled systems of the bounded quasi-equilibrium problems, and two new classes of associated optimal control problems. First, we introduce two classes of the bounded quasi-equilibrium problems, and show, under suitable conditions, the equivalence between the LP well-posedness and existence of solution to these problems. Results on metric characterization of the LP well-posedness and LP well-posedness in the generalized sense for such problems in terms of the behavior of the approximate solution sets are provided. Second, we establish two classes of optimal control problems for systems described by the generalized bounded quasi-equilibrium problems. We also studied the LP well-posedness and LP well-posedness in the generalized sense for these problems. Finally, as a real-world application, we study the special case of controlled systems of the bounded traffic network problems. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A method for solving zero-finding problems is developed by tracking homotopy paths, which define connecting channels between an auxiliary problem and the objective problem. Current algorithms' success highly relies on empirical knowledge, due to manually, inherently selected homotopy paths. This work introduces a homotopy method based on the Theory of Functional Connections (TFC). The TFC-based method implicitly defines infinite homotopy paths, from which the most promising ones are selected. A two-layer continuation algorithm is devised, where the first layer tracks the homotopy path by monotonously varying the continuation parameter, while the second layer recovers possible failures resorting to a TFC representation of the homotopy function. Compared to pseudo-arclength methods, the proposed TFC-based method retains the simplicity of direct continuation while allowing a flexible path switching. Numerical simulations illustrate the effectiveness of the presented method. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this article, a modified weak Galerkin finite element method is developed for a second order elliptic problem with mixed boundary conditions. The basic idea of modified weak Galerkin method is to reduce the degrees of freedom in comparison to the standard weak Galerkin method. The optimal convergence orders in a discrete L-2 norm and H-1 norm are established. Numerical examples are presented to verify the theoretical estimates. Published by Elsevier B.V.
Chavarria-Molina, JeffryFallas-Monge, Juan JoseSoto-Quiros, Pablo
17页
查看更多>>摘要：This paper proposes a new method to compute generalized low-rank matrix approximation (GLRMA). The GLRMA is a general case of the well-known low-rank approximation problem proposed by Eckart-Young in 1936. This new method, so-called the fast-GLRMA method, is based on tensor product and Tikhonov's regularization to approximate the pseudoinverse and bilateral random projections to estimate, in turn, the low-rank approximation. The fast-GLRMA method significantly reduces the execution time to compute the optimal solution, while preserving the accuracy of the classical method of solving the GLRMA. Computational experiments to measure execution time and speedup confirmed the efficiency of the proposed method. (C) 2021 Published by Elsevier B.V.
查看更多>>摘要：This paper presents a family of numerical solvers for anisotropic subdiffusion problems in annuli and also cylindrical and spherical shells. The fractional order Caputo temporal derivative is discretized based on linear interpolation. The spatial Laplacian is discretized by utilizing Chebyshev and Fourier spectral collocation. Detailed discussion and useful formulas are presented for polar, cylindrical, and spherical coordinate systems. Numerical experiments along with a brief analysis are presented to demonstrate the accuracy and efficiency of these solvers. These solvers represent a continuation of our work in Tan and Liu (2020) and shall be useful for numerical simulations of subdiffusion problems in cellular cytoplasm and other similar settings. (C) 2021 Elsevier B.V. All rights reserved.
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Elsevier