In this paper, we discuss the conditions for Euler midpoint rule to be volume-preserving and present explicit volume preserving schemes. Some numerical experiments are done to test these schemes.
In this paper, we discuss the conditions for Euler midpoint rule to be volume-preserving and present explicit volume preserving schemes. Some numerical experiments are done to test these schemes.
In this paper, we discuss the conditions for the Euler midpoint rule to be volume-preserving and present Euler type explicit volume-preserving schemes. Some numerical applications to the system defining rigid body mot...
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In this paper, we discuss the conditions for the Euler midpoint rule to be volume-preserving and present Euler type explicit volume-preserving schemes. Some numerical applications to the system defining rigid body motion and the ABC flow are also given.
作者：
KANGTong(康彤)YUDe-hao(余德浩)State Key Laboratory of Scientific and Engineering Computing
Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Science Chinese Academy of Sciences Beijing 100080 P R China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Science Chinese Academy of Sciences Beijing 100080 P R China
A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illus...
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A posteriori error estimate of the discontinuous-streamline diffusion method for first-order hyperbolic equations was presented, which can be used to adjust space mesh reasonably. A numerical example is given to illustrate the accuracy and feasibility of this method.
Based on the PMHSS preconditioning matrix, we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks, and analyze the eigen-properties of the corresponding pr...
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Based on the PMHSS preconditioning matrix, we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks, and analyze the eigen-properties of the corresponding preconditioned matrices. Numerical experiments show that these rotated block triangular pre- conditioners can be competitive to and even more efficient than the PMHSS preconditioner when they are used to accelerate Krylov subspeme iteration methods for solving block two-by-two linear systems with coefficient matrices possibly of nonsymmetric sub-blocks.
Conjugate gradient methods are very important ones for solving nonlinear optimization problems,especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods wereusually analyzed...
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Conjugate gradient methods are very important ones for solving nonlinear optimization problems,especially for large scale problems. However, unlike quasi-Newton methods, conjugate gradient methods wereusually analyzed individually. In this paper, we propose a class of conjugate gradient methods, which can beregarded as some kind of convex combination of the Fletcher-Reeves method and the method proposed byDai et al. To analyze this class of methods, we introduce some unified tools that concern a general methodwith the scalarβk having the form of φk/φk-1. Consequently, the class of conjugate gradient methods canuniformly be analyzed.
The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relax...
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The convergence of the parallel matrix multisplitting relaxation methods presented by Wang (Linear Algebra and Its Applications 154/156 (1991) 473 486) is further investigated. The investigations show that these relaxation methods really have considerably larger convergence domains.
Deep neural network approaches show promise in solving partial differential equations. However, unlike traditional numerical methods, they face challenges in enforcing essential boundary conditions. The widely adopted...
Deep neural network approaches show promise in solving partial differential equations. However, unlike traditional numerical methods, they face challenges in enforcing essential boundary conditions. The widely adopted penalty-type methods, for example, offer a straightforward implementation but introduces additional complexity due to the need for hyper-parameter tuning; moreover, the use of a large penalty parameter can lead to artificial extra stiffness, complicating the optimization process. In this paper, we propose a novel, intrinsic approach to impose essential boundary conditions through a framework inspired by intrinsic structures. We demonstrate the effectiveness of this approach using the deep Ritz method applied to Poisson problems, with the potential for extension to more general equations and other deep learning techniques. Numerical results are provided to substantiate the efficiency and robustness of the proposed method.
This paper investigates the global convergence properties of the Fletcher-Reeves (FR) method for unconstrained optimization. In a simple way, we prove that a kind of inexact line search condition can ensure the conver...
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This paper investigates the global convergence properties of the Fletcher-Reeves (FR) method for unconstrained optimization. In a simple way, we prove that a kind of inexact line search condition can ensure the convergence of the FR method. Several examples are constructed to show that, if the search conditions are relaxed, the FR method may produce an ascent search direction, which implies that our result cannot be improved.
A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite...
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A framework for parallel algebraic multilevel preconditioning methods presented for solving large sparse systems of linear equstions with symmetric positive definite coefficient matrices,which arise in suitable finite element discretizations of many second-order self-adjoint elliptic boundary value problems. This framework not only covers all known parallel algebraic multilevel preconditioning methods, but also yields new ones. It is shown that all preconditioners within this framework have optimal orders of complexities for problems in two-dimensional(2-D) and three-dimensional (3-D) problem domains, and their relative condition numbers are bounded uniformly with respect to the numbers of both levels and nodes.
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