查看更多>>摘要：Beside an account on Gaussian quadrature formulas and several interesting generalizations and modifications, this paper is mainly devoted to weighted nonstandard quadrature formulas of Gaussian type based on values of certain linear differential operators at some nodes. In addition to their theoretical significance, such kinds of quadrature formulas can be interesting in applications when the operator values are available, instead of the values of the original integrand function. Several numerical examples, including the construction of such non-standard quadratures, are also presented.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the companion paper (Bellet et al., 2021), a spherical harmonic subspace associated to the Cubed Sphere has been introduced. This subspace is further analyzed here. In particular, it permits to define a new Cubed Sphere based quadrature. This quadrature inherits the rotational invariance properties of the spherical harmonic subspace. Contrary to Gaussian quadrature, where the set of nodes and weights is solution of a nonlinear system, only the weights are unknown here. Despite this conceptual simplicity, the new quadrature displays an accuracy comparable to optimal quadratures, such as the Lebedev rules. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The Wigner equation is a remarkable tool to model complex problems of quantum physics in phase space. The main objective of this paper is to propose a new hybrid algorithm for the time-dependent Wigner equation. This scheme is based on sinc-Galerkin and finite difference approximations and is moderately simple but highly efficient. Error estimation, stability, and convergence are also investigated concretely. Numerical experiments validate the theoretical results and present the reliability and efficiency of the proposed algorithm to simulate quantum effects. (C) 2022 Elsevier B.V. All rights reserved.
Gatica, Gabriel N.Gomez-Vargas, BryanRuiz-Baier, Ricardo
23页
查看更多>>摘要：We develop the a posteriori error analysis for mixed-primal and fully-mixed finite element methods approximating the stress-assisted diffusion of solutes in elastic materials. The systems are formulated in terms of stress, rotation and displacements for the elasticity equations, whereas the nonlinear diffusion is cast using either solute concentration (leading to a four-field mixed-primal formulation), or the triplet concentration - concentration gradient - and nonlinear diffusive flux (yielding the six-field fully-mixed variational formulation). We have addressed the well-posedness of these formulations in two recent works, also introducing discretisations based on PEERS or Arnold-Falk-Winther elements for the linear elasticity and either Lagrange, or Lagrange - Raviart-Thomas - Lagrange triplets for the approximation of the diffusion equation. Here we advocate the derivation of two efficient and reliable residual-based a posteriori error estimators focusing on the two-dimensional case. The proofs of reliability depend on adequately formulated inf-sup conditions in combination with a Helmholtz decomposition, and they also rely on the local approximation features of Clement and Raviart-Thomas interpolations. The efficiency of the estimators results from classical inverse and discrete trace inequalities together with localisation techniques based on edge-and triangle-bubble functions. The theoretical properties of these error indicators are confirmed through numerical tests, also serving to illustrate the performance of the adaptive mesh refinement. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper is concerned with generalized Hyers-Ulam stability of the diffusion equation, partial differential & part;u(x, t)/& part;t = delta u(x, t) with u(x, 0) = f(x) for t > 0 and x is an element of R(n .)Most of the Hyers Ulam stability problems of differential equations are involved with L-infinity-norm or the supremum norm of functions with consideration of either initial conditions or forcing terms. However, an integral method of Fourier transform can be used to obtain the L-2-estimates for generalized Hyers-Ulam stability of an IVP (initial value problem) of the diffusion equation with a function f(x) as an initial condition and we will present the generalized Hyers-Ulam stability of the IVP in the sense of L-2-norm. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：When the 8T-LE partition is recursively applied to any initial trirectangular tetrahedron T, only a finite number of dissimilar tetrahedra are generated. It implies the stability of the meshes. At each step of refinement the number of right -type or path tetrahedra grows, so the quality of the obtained meshes improves. The minimum angle condition and the maximum angle condition are trivially satisfied, since the number of similarity classes is finite. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：For the linear complementarity problem, we introduce a relaxation general two-sweep matrix splitting iteration method. Convergence analysis shows that the method converges to the exact solution of the linear complementarity problem when the system matrix is an H+-matrix. Numerical experiments show that the proposed method is more efficient than existing methods. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we develop a multiscale method for solving the Signorini problem with a heterogeneous field. The Signorini problem is encountered in many applications, such as hydrostatics, thermics, and solid mechanics. It is well-known that numerically solving this problem requires a fine computational mesh, which can lead to a large number of degrees of freedom. The aim of this work is to develop a new hybrid multiscale method based on the framework of the generalized multiscale finite element method (GMsFEM). The construction of multiscale basis functions requires local spectral decomposition. Additional multiscale basis functions related to the contact boundary are required so that our method can handle the unilateral condition of the Signorini type naturally. A complete analysis of the proposed method is provided and a result of the spectral convergence is shown. Numerical results are provided to validate our theoretical findings. (C) 2022 Elsevier B.V. All rights reserved.
Shurina, E. P.Itkina, N. B.Shtabel, N., VShtanko, E., I...
21页
查看更多>>摘要：The paper considers the problem of calculating effective anisotropic thermal, electric and mechanical properties of composite media. We propose numerical algorithms for the homogenization of heterogeneous media based on the upscaling technique and effective medium theory. The algorithms rely on the direct mathematical modelling of thermal conductivity, elastic deformation, and electromagnetic field. We discretize mathematical models using multiscale non-conforming finite element methods. We investigate the effect of the physical properties and the arrangement of the microinclusions on the effective tensors for various types of field excitation. (C) 2021 Published by Elsevier B.V.
查看更多>>摘要：Exponential integrators are a well-known class of time integration methods that have been the subject of many studies and developments in the past two decades. Surprisingly, there have been limited efforts to analyze their stability and efficiency on non-diffusive equations to date. In this paper we apply linear stability analysis to showcase the poor stability properties of exponential integrators on non-diffusive problems. We then propose a simple repartitioning approach that stabilizes the integrators and enables the efficient solution of stiff, non-diffusive equations. To validate the effectiveness of our approach, we perform several numerical experiments that compare partitioned exponential integrators to unmodified ones. We also compare repartitioning to the well-known approach of adding hyperviscosity to the equation right-hand-side. Overall, we find that the repartitioning restores convergence at large timesteps and, unlike hyperviscosity, it does not require the use of high-order spatial derivatives.(C) 2022 Elsevier B.V. All rights reserved.
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