In[Dai et al.,***.18(4)(2020)],a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory,based on which a linearized method was developed in[Hu et...
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In[Dai et al.,***.18(4)(2020)],a structure-preserving gradient flow method was proposed for the ground state calculation in Kohn-Sham density functional theory,based on which a linearized method was developed in[Hu et al.,EAJAM.13(2)(2023)]for further improving the numerical *** this paper,a complete convergence analysis is delivered for such a linearized method for the all-electron Kohn-Sham ***,the convergence,the asymptotic stability,as well as the structure-preserving property of the linearized numerical scheme in the method is discussed following previous works,while spatially,the convergence of the h-adaptive mesh method is demonstrated following[Chen et al.,***.12(2014)],with a key study on the boundedness of the Kohn-Sham potential for the all-electron Kohn-Sham *** examples confirm the theoretical results very well.
In this paper, we propose a discrete perfectly matched layer (PML) for the peridynamic scalar wave-type problems in viscous media. Constructing PMLs for nonlocal models is often challenging, mainly due to the fact tha...
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Ref. [BCOW17] introduced a pioneering quantum approach (coined BCOW algorithm) for solving linear differential equations with optimal error tolerance. Originally designed for a specific class of diagonalizable linear ...
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In this paper, we introduce the Nonconforming Virtual Element Method (NVEM) to solve nonlinear coupled prey–predator equations on general polygonal meshes, employing a linearized variable two-step backward differenti...
In this paper, we introduce the Nonconforming Virtual Element Method (NVEM) to solve nonlinear coupled prey–predator equations on general polygonal meshes, employing a linearized variable two-step backward differentiation formula (BDF2) for time discretization. The analysis of boundedness and error estimates for the time discrete system is conducted using discrete orthogonal convolution kernels and discrete complementary convolution kernels. Then, the time–space error splitting technique and the projection operator are integrated to establish the L ∞ -norm boundedness of the fully discrete solution, independent of any grid ratio conditions, thereby naturally deriving the unconditionally optimal error estimate. The analytical method presented herein is not restricted to the NVEM and can be readily extended to other numerical techniques. Finally, the theoretical results are validated through numerical examples, demonstrating the scheme’s effectiveness across various grid configurations.
This study presents a novel mixed-precision iterative refinement algorithm, GADI-IR, within the general alternating-direction implicit (GADI) framework, designed for efficiently solving large-scale sparse linear syste...
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We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unstea...
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We concentrate on the parallel,fully coupled and fully implicit solution of the sequence of 3-by-3 block-structured linear systems arising from the symmetrypreserving finite volume element discretization of the unsteady three-temperature radiation diffusion equations in high *** this article,motivated by[***,***,***,SIAM *** ***.33(2012)653–680]and[***,***,***,***.442(2021)110513],we aim to develop the additive and multiplicative Schwarz preconditioners subdividing the physical quantities rather than the underlying domain,and consider their sequential and parallel implementations using a simplified explicit decoupling factor approximation and algebraic multigrid subsolves to address such linear ***,computational efficiencies and parallel scalabilities of the proposed approaches are numerically tested in a number of representative real-world capsule implosion benchmarks.
The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential *** electric potential equation is approximated by a mixed finite element method,and the concentration equa...
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The mathematical model of a semiconductor device is governed by a system of quasi-linear partial differential *** electric potential equation is approximated by a mixed finite element method,and the concentration equations are approximated by a standard Galerkin *** estimate the error of the numerical solutions in the sense of the *** linearize the full discrete scheme of the problem,we present an efficient two-grid method based on the idea of Newton *** main procedures are to solve the small scaled nonlinear equations on the coarse grid and then deal with the linear equations on the fine *** estimation for the two-grid solutions is analyzed in *** is shown that this method still achieves asymptotically optimal approximations as long as a mesh size satisfies H=O(h^1/2).Numerical experiments are given to illustrate the efficiency of the two-grid method.
We propose a new stable variational formulation for the quad-div problem in three dimensions and prove its well-posedness. Using this weak form, we develop and analyze the H(grad-div)-conforming virtual element method...
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In this paper,a robust modified weak Galerkin(MWG)finite element method for reaction-diffusion equations is proposed and *** advantage of this method is that it can deal with the singularly perturbed reaction-diffusio...
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In this paper,a robust modified weak Galerkin(MWG)finite element method for reaction-diffusion equations is proposed and *** advantage of this method is that it can deal with the singularly perturbed reaction-diffusion *** advantage of this method is that it produces fewer degrees of freedom than the traditional WG method by eliminating the element boundaries *** is worth pointing out that,in our method,the test functions space is the same as the finite element space,which is helpful for the error *** error estimates are established for the corresponding numerical approximation in various *** numerical results are reported to confirm the theory.
The truncated Euler–Maruyama (EM) method, developed by Mao (2015), is used to solve multi-dimensional nonlinear stochastic differential equations (SDEs). However, its convergence rate is suboptimal due to an unnecess...
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