In[Dai et al.,***.1.(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...
详细信息
In[Dai et al.,***.1.(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.1.(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.,***.1.(201.)],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 investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded *** the boundary,the velocity fiel...
详细信息
In this paper,we investigate the solvability,regularity and the vanishing dissipation limit of solutions to the three-dimensional viscous magnetohydrodynamic(MHD)equations in bounded *** the boundary,the velocity field fulfills a Navier-slip condition,while the magnetic field satisfies the insulating *** is shown that the initial boundary value problem has a global weak solution for a general smooth *** importantly,for a flat domain,we establish the uniform local well-posedness of the strong solution with higher-order uniform regularity and the asymptotic convergence with a rate to the solution of the ideal MHD equation as the dissipations tend to zero.
A novel arbitrary high-order energy-stable fully discrete schemes are proposed for the nonlinear Benjamin-Bona-Mahony-Burgers equation based on linearized Crank-Nicolson scheme in time and the virtual element discreti...
详细信息
Abstract: In this paper, we consider a coupled flow and transport process described by partial differential equations for pressure and concentration. We derive the multicontinuum coupled flow and transport model using...
详细信息
Self-consistent field theory (SCFT) is one of the most widely-used frameworks in studying the equilibrium phase behavior of inhomogeneous polymers. For liquid-crystalline polymeric systems, the primary numerical chall...
Self-consistent field theory (SCFT) is one of the most widely-used frameworks in studying the equilibrium phase behavior of inhomogeneous polymers. For liquid-crystalline polymeric systems, the primary numerical challenges in solving SCFT involve efficiently solving a large number of 6-dimensional (6D, 3D space + 2D orientation + 1. contour) partial differential equations (PDEs), accurately determining subtle energy differences between self-assembled structures, and developing effective iterative methods for nonlinear SCFT iterations. To address these challenges, this work introduces a suite of high-order and efficient numerical methods tailored to SCFT of liquid-crystalline polymers. These methods include various advanced PDE solvers, an improved Anderson iteration algorithm to accelerate SCFT calculations, and an optimization technique for adjusting the computational domain during SCFT iterations. Extensive numerical tests demonstrate the efficiency of the proposed methods. Based on these algorithms, we further explore the self-assembly behavior of liquid-crystalline polymers through 4D, 5D, and 6D {1.s, uncovering intricate 3D spatial structures.
Solving high-wavenumber and heterogeneous Helmholtz equations presents a longstanding challenge in scientific computing. In this paper, we introduce a deep learning-enhanced multigrid solver to address this issue. By ...
详细信息
In this paper, we apply the practical GADI-HS iteration as a smoother in algebraic multigrid (AMG) method for solving second-order non-selfadjoint elliptic problem. Additionally, we prove the convergence of the derive...
详细信息
Recently, designing neural solvers for large-scale linear systems of equations has emerged as a promising approach in scientific and engineering computing. This paper first introduce the Richardson(m) neural solver by...
详细信息
In this work, we propose an efficient nullspace-preserving saddle search (NPSS) method for a class of phase transitions involving translational invariance, where the critical states are often degenerate. The NPSS meth...
详细信息
In this paper, we propose a conservative nonconforming virtual element method for the full stationary incompressible magnetohydrodynamics model. We leverage the virtual element satisfactory divergence-free property to...
详细信息
暂无评论