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A Parallel Computational Model for Three-Dimensional,Thermo-Mechanical Stokes Flow Simulations of Glaciers and Ice Sheets

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Communications in Computational Physics 2014年第9期16卷 1056-1080页

作者： Wei Leng Lili Ju Max Gunzburger Stephen Price State Key Laboratory of Scientific and Engineering Computing Chinese Academy of SciencesBeijing 100190China. Department of Mathematics University of South CarolinaColumbiaSC 29208USA. Department of Scientific Computing Florida State UniversityTallahasseeFL 32306USA. Theoretical Division Los Alamos National LaboratoryLos AlamosNM 87545.USA.

This paper focuses on the development of an efficient,three-dimensional,thermo-mechanical,nonlinear-Stokes flow computational model for ice sheet *** model is based on the parallel finite element model developed in[14]which features high-order accurate finite element discretizations on variable resolution ***,we add an improved iterative solution method for treating the nonlinearity of the Stokes problem,a new high-order accurate finite element solver for the temperature equation,and a new conservative finite volume solver for handling mass *** result is an accurate and efficient numerical model for thermo-mechanical glacier and ice-sheet *** demonstrate the improved efficiency of the Stokes solver using the ISMIP-HOM Benchmark experiments and a realistic test case for the Greenland *** also apply our model to the EISMINT-II benchmark experiments and demonstrate stable thermo-mechanical ice sheet evolution on both structured and unstructured ***,we find no evidence for the“cold spoke”instabilities observed for these same experiments when using finite difference,shallow-ice approximation models on structured grids.

关键词： Stokes-flow modeling ice-sheet modeling finite element approximation finite volume approximation parallel implementation.

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THE QUADRATIC SPECHT TRIANGLE

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Journal of Computational Mathematics 2020年第1期38卷 103-124页

作者： Hongliang Li Pingbing Ming Zhongci Shi Department of Mathematics Sichuan Normal UniversityChengdu 610066China The State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesNo.55East Road ZhongGuanCunBeijing 100190China

We propose a class of 12 degrees of freedom triangular plate bending elements with quadratic rate of *** may be viewed as the second order Specht triangle,while the Specht triangle is one of the best first order plate bending *** convergence result is proved under minimal smoothness assumption on the *** results for both the smooth solution and nonsmmoth solution confirm the theoretical prediction.

关键词： Specht triangle Plate bending element Basis functions

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Construction of Symplectic Runge-Kutta Methods for Stochastic Hamiltonian Systems

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Communications in Computational Physics 2017年第1期21卷 237-270页

作者： Peng Wang Jialin Hong Dongsheng Xu Institute of Mathematics Jilin UniversityChangchun 130012P.R.China State Key Laboratory of Scientific and Engineering Computing Institute of ComputationalMathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences100080 BeijingP.R.China University of Chinese Academy of Sciences P.R.China

We study the construction of symplectic Runge-Kutta methods for stochastic Hamiltonian systems(SHS).Three types of systems,SHS with multiplicative noise,special separable Hamiltonians and multiple additive noise,respectively,are considered in this *** Runge-Kutta(SRK)methods for these systems are investigated,and the corresponding conditions for SRK methods to preserve the symplectic property are *** on the weak/strong order and symplectic conditions,some effective schemes are *** particular,using the algebraic computation,we obtained two classes of high weak order symplectic Runge-Kutta methods for SHS with a single multiplicative noise,and two classes of high strong order symplectic Runge-Kutta methods for SHS with multiple multiplicative and additive noise,*** numerical case studies confirm that the symplectic methods are efficient computational tools for long-term simulations.

关键词： Stochastic differential equation Stochastic Hamiltonian system symplectic integration Runge-Kutta method order condition

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Analysis of Sparse Quasi-Newton Updates with Positive Definite Matrix Completion

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Journal of the Operations Research Society of China 2014年第1期2卷 39-56页

作者： Yu-Hong Dai Nobuo Yamashita State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100080People’s Republic of China Department of Applied Mathematics and Physics Graduate School of InformaticsKyoto UniversityKyoto 606-8501Japan

Based on the idea of maximum determinant positive definite matrix completion,Yamashita(Math Prog 115(1):1–30,2008)proposed a new sparse quasi-Newton update,called MCQN,for unconstrained optimization problems with sparse Hessian *** exchange of the relaxation of the secant equation,the MCQN update avoids solving difficult subproblems and overcomes the ill-conditioning of approximate Hessian ***,local and superlinear convergence results were only established for the MCQN update with the DFP *** this paper,we extend the convergence result to the MCQN update with the whole Broyden’s convex *** results are also reported,which suggest some efficient ways of choosing the parameter in the MCQN update the Broyden’s family.

关键词： Quasi-Newton method Large-scale problems Sparsity Positive definite matrix completion Superlinear convergence

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Convergence analysis of the adaptive finite element method with the red-green refinement

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Science China Mathematics 2010年第2期53卷 499-512页

作者： ZHAO XuYing 1, 3 , HU Jun 2,? & SHI ZhongCi 1 1 state key laboratory of scientific and engineering computing, Institute of Computational Mathematics and scientific/engineering computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China 2 key laboratory of Mathematics and Applied Mathematics (Peking University), Ministry of Education and School of Mathematical Sciences, Peking University, Beijing 100871, China 3 Graduate University of Chinese Academy of Sciences, Beijing 100190, China 1. State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China3. Graduate University of Chinese Academy of Sciences Beijing 100190 China2. Key Laboratory of Mathematics and Applied Mathematics (Peking University) Ministry of Education and School of Mathematical Sciences Peking University Beijing 100871 China

In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Galerkin-orthogonality does not hold for this case. To overcome such a difficulty, we prove some quasi-orthogonality instead under some mild condition on the initial mesh (Condition A). Consequently, we show convergence of the adaptive method by establishing the reduction of some total error. To weaken the condition on the initial mesh, we propose a modified red-green refinement and prove the convergence of the associated adaptive method under a much weaker condition on the initial mesh (Condition B).

关键词： red-green refinement adaptive finite element method convergence non-nested local refinement

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Finite element method for a nonsmooth elliptic equation

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中国高等学校学术文摘·数学 2010年第2期5卷 191-209页

作者： Lili CHANG Wei GONG Ningning YAN State Key Laboratory of Scientific and Engineering Computing Institute of Systems Science Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing 100190 China

In this paper, we study the finite element method for a nonsmooth elliptic equation. Error analysis is presented, including a priori and a posteriori error estimates as well as superconvergence analysis. We also propose two algorithms for solving the underlying equation. Numerical experiments are employed to confirm our error estimations and the efficiency of our algorithms.

关键词： Finite element method nonsmooth elliptic equation a priori error estimate a posteriori error estimate superconvergence analysis active set method

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The exactness of the l_(1)penalty function for a class of mathematical programs with generalized complementarity constraints

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Fundamental Research 2024年第6期4卷 1459-1464页

作者： Yukuan Hu Xin Liu State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China University of Chinese Academy of Sciences Beijing 100049China

In a mathematical program with generalized complementarity constraints(MPGCC),complementarity relation is imposed between each pair of variable *** includes the traditional mathematical program with complementarity constraints(MPCC)as a special *** account of the disjunctive feasible region,MPCC and MPGCC are generally difficult to *** l_(1)penalty method,often adopted in computation,opens a way of circumventing the *** it remains unclear about the exactness of the l_(1)penalty function,namely,whether there exists a sufficiently large penalty parameter so that the penalty problem shares the optimal solution set with the original *** this paper,we consider a class of MPGCCs that are of multi-affine objective *** problem class finds applications in various fields,e.g.,the multi-marginal optimal transport problems in many-body quantum physics and the pricing problems in network *** first provide an instance from this class,the exactness of whose l_(1)penalty function cannot be derived by existing *** then establish the exactness results under rather mild *** results cover those existing ones for MPCC and apply to multi-block contexts.

关键词： Mathematical program with generalized complementarity constraints l_(1)penalty function Exact penalty Multi-affine objective function Error bound

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Efficient and scalable methods for dual-porosity/permeability models in fractured reservoir simulations

Efficient and scalable methods for dual-porosity/permeabilit...

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SPE Asia Pacific Oil and Gas Conference and Exhibition 2016

作者： Cui, Tao Wang, Kun Liu, Hui Luo, Jia Chen, Zhangxin State Key Laboratory of Scientific and Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences China University of Calgary Canada

ISBN: (纸本)9781510835849

In this paper, the multi-stage preconditioners are modified and applied to dual-porosity/permeability (DPDK) model problems. Employed as the first step of the multi-stage preconditioning processes, two modified decoupling processes for DPDK problems are developed. In a DPDK model, mass transfer both between fractures and between matrices is allowed, which means that the pressure both in fractures and matrix behaves as an elliptic property, so it is natural to employ two preconditioning stages solving the fracture pressure system and the matrix pressure, respectively, which draws the first type of a multi-stage preconditioner in this paper. Since the transmisibility between fracture blocks is much higher than that between matrices, the elliptic property of the fracture pressure is much stronger. Hence, we remove the stage of solving the matrix pressure system in the second type of a multi-stage preconditioner. Moreover, an extra stage of the ILU preconditioning process is added to the above multi-stage preconditioners in order to improve their efficiency, which results in another two multi-stage preconditioners. Combination of the modified decoupling processes and four new multi-stage preconditioners are studied and compared by large-scale reservoir simulation problems. Based on these numerical experiments, the optimal method to solve the DPDK model problems is concluded. © 2016 Society of Petroleum Engineers. All rights reserved.

关键词： Fracture

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A Riemannian Exponential Augmented Lagrangian Method for computing the Projection Robust Wasserstein Distance 37

A Riemannian Exponential Augmented Lagrangian Method for Com...

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37th Conference on Neural Information Processing Systems, NeurIPS 2023

作者： Jiang, Bo Liu, Ya-Feng Ministry of Education Key Laboratory of NSLSCS School of Mathematical Sciences Nanjing Normal University Nanjing210023 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

ISBN: (纸本)9781713899921

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently reformulating the computation of the PRW distance as an optimization problem over the Cartesian product of the Stiefel manifold and the Euclidean space with additional nonlinear inequality constraints, we propose a Riemannian exponential augmented Lagrangian method (REALM) for solving this problem. Compared with the existing Riemannian exponential penalty-based approaches, REALM can potentially avoid too small penalty parameters and exhibit more stable numerical performance. To solve the subproblems in REALM efficiently, we design an inexact Riemannian Barzilai-Borwein method with Sinkhorn iteration (iRBBS), which selects the stepsizes adaptively rather than tuning the stepsizes in efforts as done in the existing methods. We show that iRBBS can return an Ε-stationary point of the original PRW distance problem within O(Ε-3) iterations, which matches the best known iteration complexity result. Extensive numerical results demonstrate that our proposed methods outperform the state-of-the-art solvers for computing the PRW distance. © 2023 Neural information processing systems foundation. All rights reserved.

关键词： Constrained optimization

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A New Multi-point Stepsize Gradient Method for Optimization 5th

A New Multi-point Stepsize Gradient Method for Optimization

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5th International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOV 2020

作者： Huang, Yakui Dai, Yu-Hong Liu, Xin-Wei Institute of Mathematics Hebei University of Technology Tianjin300401 China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

ISBN: (纸本)9783030720391

The Barzilai-Borwein (BB) gradient method, which employs two-point stepsizes computed by the information of two consecutive iterations, is efficient in solving large-scale unconstrained optimization. In this paper, motivated by the success of BB method and the multi-point stepsize proposed by Dai and Fletcher (Mathematical Programming, 2006, 106: 403–421), we develop a new efficient gradient method, called MPSG, which adaptively uses the Dai-Fletcher long stepsize and Dai-Fletcher short stepsize. The R-linear convergence of MPSG for general n-dimensional strictly convex quadratic functions is established. By making use of two modified multi-point stepsizes and nonmonotone line searches, MPSG is extended to solve general unconstrained optimization. Moreover, the proposed MPSG method is further generalized for solving extreme eigenvalue problems. Numerical experiments on quadratic optimization, general unconstrained optimization and extreme eigenvalue problems demonstrate the efficiency of our method. © 2021, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Gradient methods

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