作者：
ZHANG XinZHOU AihuiSWIEE
Southwest China Research Institute of Electronic Equipment LSEC
Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems Science Chinese Academy of Sciences
We show that the eigenfunctions of Kohn-Sham equations can be decomposed as ■ = F ψ, where F depends on the Coulomb potential only and is locally Lipschitz, while ψ has better regularity than ■.
We show that the eigenfunctions of Kohn-Sham equations can be decomposed as ■ = F ψ, where F depends on the Coulomb potential only and is locally Lipschitz, while ψ has better regularity than ■.
A class of hybrid algebraic multilevel preconditioning methods is presented for solving systems of linear equations with symmetric positive-definite matrices resulting from the discretization of many second-order elli...
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A class of hybrid algebraic multilevel preconditioning methods is presented for solving systems of linear equations with symmetric positive-definite matrices resulting from the discretization of many second-order elliptic boundary value problems by the finite element method. The new preconditioners are shown to be of optimal orders of complexities for 2-D and 3-D problem domains, and their relative condition numbers are estimated to be bounded uniformly with respect to the numbers of both levels and nodes.
This paper presents a new algebraic multigrid (AMG) solution strategy for large linear systems with a sparse matrix arising from a finite element discretization of some self-adjoint, second order, scalar, elliptic par...
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This paper presents a new algebraic multigrid (AMG) solution strategy for large linear systems with a sparse matrix arising from a finite element discretization of some self-adjoint, second order, scalar, elliptic partial differential equation. The AMG solver is based on Ruge/Stuben's method. Ruge/Stuben's algorithm is robust for M-matrices, but unfortunately the "region of robustness" between symmetric positive definite M-matrices and general symmetric positive definite matrices is very fuzzy. For this reason the so-called element preconditioning technique is introduced in this paper. This technique aims at the construction of an M-matrix that is spectrally equivalent to the original stiffness matrix. This is done by solving small restricted optimization problems. AMG applied to the spectrally equivalent M-matrix instead of the original stiffness matrix is then used as a preconditioner in the conjugate gradient method for solving the original problem. The numerical experiments show the efficiency and the robustness of the new preconditioning method for a wide class of problems including problems with anisotropic elements.
By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod func...
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By the aid of an idea of the weighted ENO schemes, some weight-type high-resolution difference schemes with different orders of accuracy are presented in this paper by using suitable weights instead of the minmod functions appearing in various TVD schemes. Numerical comparisons between the weighted schemes and the non-weighted schemes have been done for scalar equation, one-dimensional Euler equations, two-dimensional Navier-Stokes equations and parabolized Navier-Stokes equations.
We set up a class of parallel nonlinear multisplitting AOR methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems. The different choices of the relaxation parameter...
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We set up a class of parallel nonlinear multisplitting AOR methods by directly multisplitting the nonlinear mapping involved in the nonlinear complementarity problems. The different choices of the relaxation parameters can yield all the known and a lot of new relaxation methods, as well as a lot of new relaxed parallel nonlinear multisplitting methods for solving the nonlinear complementarity problems. The two-sided approximation properties and the influences on the convergence rates from the relaxation parameters about our new methods are shown, and sufficient conditions guaranteeing the methods to converge globally are discussed. Finally, a lot of numerical results show that our new methods are feasible and efficient.
The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,whic...
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The speeding-up and slowing-down(SUSD)direction is a novel direction,which is proved to converge to the gradient descent direction under some *** authors propose the derivative-free optimization algorithm SUSD-TR,which combines the SUSD direction based on the covariance matrix of interpolation points and the solution of the trust-region subproblem of the interpolation model function at the current iteration *** analyze the optimization dynamics and convergence of the algorithm *** of the trial step and structure step are *** results show their algorithm’s efficiency,and the comparison indicates that SUSD-TR greatly improves the method’s performance based on the method that only goes along the SUSD *** algorithm is competitive with state-of-the-art mathematical derivative-free optimization algorithms.
A new comparison theorem on the monotone convergence rates of the parallel nonlinear multisplitting accelerated overrelaxation (AOR) method for solving the large scale nonlinear complementarity problem is established....
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A new comparison theorem on the monotone convergence rates of the parallel nonlinear multisplitting accelerated overrelaxation (AOR) method for solving the large scale nonlinear complementarity problem is established. Thus, the monotone convergence theory of this class of method is completed.
In this paper, we propose an adaptive proximal inexact gradient (APIG) framework for solving a class of nonsmooth composite optimization problems involving function and gradient errors. Unlike existing inexact proxima...
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The convergence rate of the gradient descent method is considered for unconstrained multi-objective optimization problems (MOP). Under standard assumptions, we prove that the gradient descent method with constant step...
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The convergence rate of the gradient descent method is considered for unconstrained multi-objective optimization problems (MOP). Under standard assumptions, we prove that the gradient descent method with constant stepsizes converges sublinearly when the objective functions are convex and the convergence rate can be strengthened to be linear if the objective functions are strongly convex. The results are also extended to the gradient descent method with the Armijo line search. Hence, we see that the gradient descent method for MOP enjoys the same convergence properties as those for scalar optimization.
In this work, we generalize the mass-conserving mixed stress (MCS) finite element method for Stokes equations [12], involving normal velocity and tangential-normal stress continuous fields, to incompressible finite el...
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