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科学与工程计算的方法和应用
  • 项目名称：科学与工程计算的方法和应用
  • 项目类别：创新研究群体科学基金
  • 批准号：11021101
  • 申请代码：A0117
  • 项目来源：国家自然科学基金
  • 研究期限：2011-01-01-2013-12-31
  • 项目负责人：陈志明
  • 负责人职称：研究员
  • 依托单位：中国科学院数学与系统科学研究院
  • 批准年度：2010
中文摘要：

科学计算是数学及计算机实现其在高科技领域应用的必不可少的纽带和工具，计算与理论及实验一起已成为当今世界科学活动的主要方式。本项目的研究思路是面向计算数学与科学工程计算的学科前沿，大力加强基础计算方法的研究，尤其是适应大规模科学与工程计算的需要，创造和发展有广泛应用前景的新的计算方法, 解决一些重大应用领域提出的关键模型与算法问题。本项目的研究内容是在"新型计算方法与理论研究"方面，重点研究非线性优化与结构化代数方程组的高效算法与理论、计算几何中的偏微分方程方法和动力系统保结构算法；在"材料科学中的多尺度计算"方面，重点研究第一原理计算实空间方法、多物理场关联模型与算法和拟连续介质力学方法； 在"面向复杂系统的电磁和流体自适应计算"方面，重点研究三维电磁涡流问题和散射问题以及化学反应流的高效自适应算法和实现技术。

中文主题词： 最优化算法；保结构算法；多尺度建模；自适应方法；并行计算
英文摘要：

Optimization algorithms；Structure preserving algorithm；multiscale modeling；adaptive method；parallel computing

英文主题词： Optimization algorithms；Structure preserving algorithm；multiscale modeling；adaptive method；parallel computing
结论摘要：

科学计算是数学及计算机实现其在高科技领域应用的必不可少的纽带和工具，计算与理论及实验一起已成为当今世界科学活动的主要方式。本项目面向计算数学与科学工程计算的学科前沿，大力加强基础计算方法的研究，尤其是适应大规模科学与工程计算的需要，创造和发展有广泛应用前景的新的计算方法, 解决一些重大应用领域提出的关键模型与算法问题。本项目的研究围绕新型计算方法与理论研究、材料科学中的多尺度计算和面向复杂系统的电磁和流体自适应计算开展。？主要成果包括对信号处理中经典的PCM量化方法,发现在非白噪声假定下，该方法的误差并不随着冗余度增加而减少。对多物理场耦合作用下的多尺度计算方法以及相应的数学理论提出了处理三维问题的稳定的并具有最优误差估计的跨尺度杂交耦合方法；提出了基于力场的跨尺度杂交耦合方法，基于椭圆差分方程组的正则性与基于拟差分算子的稳定性估计，对于三维无缺陷体系证明了该方法是稳定的且具有最优收敛速度;提出了大波数离散波动问题的波源转移算法，基于完美匹配层方法的误差分析理论，建立了算法在常波数情况下的最优收敛性；提出了大型变压器铁损模拟新的涡流数学模型和有效数值方法，研制了大型变压器油箱和铁芯的并行计算程序，获得了和实验数据一致的数值结果；发展了基于通量差分裂的低耗散五阶迎风紧致格式求解三维Navier-Stokes方程，发现圆球古艾特流的定常Taylor涡分叉解的新的物理现象。

成果综合统计
成果类型
数量
  • 期刊论文
  • 会议论文
  • 专利
  • 获奖
  • 著作
  • 96
  • 7
  • 0
  • 0
  • 0
期刊论文
A Source Transfer Domain Decomposition Method For Helmholtz Equations in Unbounded Domain
Stochastic Multi-symplectic Integrator for Stochastic Nonlinear Schroedinger Equation
LOD-MS for Gross-Pitaevskii Equation in Bose-Einstein Condensates
Numerical Investigation of Wavy and Spiral Taylor-Gortler Vortices in Medium Spherical Gaps
Modulus-based Synchronous Multisplitting Iteration Methods for Linear Complementarity Problems
Parallel Construction of Hamiltonian Paths for Conforming Tetrahedral Meshes
An Adaptive Anisotropic Perfectly Matched Layer Method for 3-D Time Harmonic Electromagnetic Scatter
Inversion of Electron Tomography Images Using L2-Gradient Flows--Computational Methods
Analysis on a Superlinearly Convergent Augmented Lagrangian Method
A Counter-Example to a Conjecture of Ben-Tal, Nemirovski and Roos
A Trust Region Method Based on a New Affine Scaling Technique for Simple Bounded Optimization
Finite Element Computation of KPP Front Speeds in Cellular and Cat's Eye Flows
球头体激波诱导燃烧问题的移动网格计算
Reverse Time Migration for Extended Obstacles: Acoustic Waves
Reverse Time Migration for Extended Obstacles: Electromagnetic Waves
Target Detection and Characteriztion from Electromagnetic Induction Data
An Aanisotropic Perfectly Matched Layer Method for Helmholtz Scattering Problems with Discontinuous
Symplectic and Multisymplectic Numerical Methods for Maxwell’s Equations
A New Approach to Construct Runge-Kutta Type Methods and Geometric Numerical Integrators
Comparison of Two Equivalent Multisymplectic Numerical Methods for Nonlinear Wave Equations
Enhanced HBVMs for the Numerical Solution of Hamiltonian Problems with Multiple Invariants
On an Integrable Discretisation of the Lotka-Volterra System
On the Meany Inequality with Applications to Convergence Analysis of Several Row-action Iteration me
On Nonsingularity of Block Two-by-Two Matrices
Rotated Block Triangular Preconditioning Based on PMHSS
Symplectic structure- preserving integrators for the two-dimensional Gross-Pitaevskii equation for B
Mean-square Convergence of Numerical Approximations for a Class of Backward Stochastic Differential
An Efficient Multigrid Method for Molecular Mechanics Modeling in Atomic Solids
A Multiscale Approach for Optimal Control Problems of Linear Parabolic Equations
Multiscale Asymptotic Method for Steklov Eigenvalue Equations in Composite Media
Multiscale Computation of a Steklov Eigenvalue Problem with Rapidly Oscillating Coefficients
Multiscale Analysis and Computation for Parabolic Equations with Rapidly Oscillating Coefficients in
Multiscale Asymptotic Analysis and Computation of Optimal Control for Elliptic Systems with Constrai
A Finite Difference Real Ghost Fluid Method on Moving Meshes with Corner-transport Upwind Interpolat
A Runge-Kutta Discontinuous Galerkin Method for Detonation Wave Simulation
On Approximated ILU and UGS Preconditioning Methods for Linearized Discretized Steady Incompressible
A Cone Constrained Convex Program: Structure and Algorithms
Optimality Conditions and a Smoothing Trust Region Newton Method for Nonlipschitz Optimization
A Regularized Newton Method for Monotone Nonlinear Equations and its Application
Finite Element Approximations of Nonlinear Eigenvalue Problems in Quantum Physics
A Symmetry-Based Decomposition Approach to Eigenvalue Problems
Finite Element Computation of KPP Front Speeds in 3D Cellular and ABC Flows
Postprocessed Two-scale Finite Element Discretizations,Part I
Remark About Orthogonal Matching Pursuit Algorithms
A Unified Method for Hybrid Subdivision Surface Design Using Geometric Partial Differential Equation
Computational Inversion of Electron Micrographs Using L2-gradient Flows—convergence Analysis
An H-ψ Formulation for the Three-Dimensional Eddy Current Problem in Laminated Structures
Recent Advances in Numerical Methods for Nonlinear Equations and Nonlinear Least Sqaures
Stability and Allocation in a Three-player Game
Adaptive Perfectly Matched Layer Method for Multiple Scattering Problems
An Inner-constrained Separation Technique for 3-D Finite-element Modeling of Grain-oriented Silicon
Local Multilevel Methods for Second-order Elliptic Problems with Highly Discontinuous Coefficients
An Efficient Eddy Current Model for Nonlinear Maxwell Equations with Laminated Conductors
A Kohn-Sham Equation Solver Based on Hexahedral Finite Elements
压缩感知
The Regularity of Refinable Functions
On B-spline Framelets Derived From the Unitary Extension Principle
Gradient-flow-based Semi-implicit Finite-element Method and Its Convergence Analysis for Image Recon
Convergence of a Force-based Hybrid Method in Three Dimensions
Ghost Force Influence of a Quasicontinuum Method in Two Dimension
An Efficient High Order Heterogeneous Multiscale Method for Elliptic Problems
Adaptive Hp-finite Element Computations for Timeharmonic Maxwell’s Equations
一种可扩展的三维半导体器件并行数值模拟算法
三维结构分析并行自适应有限元软件PHG-Solid
Time Finite Element Methods: A Unified Framework for Numerical Discretizations of ODEs
Energy-preserving numerical methods for Landau-Lifshitz equation
Preconditioned MHSS Iteration Methods for a Class of Block Two-by-two Linear Systems with Applicatio
A Delta-regularization Finite Element Method for a Double Curl Problem with Divergence-free Constrai
Numerical Solution of Acoustic Scattering by an Adaptive DtN Finite Element Method
A Source Transfer Domain Decomposition Method For Helmholtz Equations in Unbounded Domain, Part II:
Hohenberg-Kohn Theorem for Coulomb Type Systems and Its Generalization
七方程可压缩多相流模型的HLLC格式及应用
Uniform Convergence of Adaptive Multigrid Methods for Elliptic Problems and Maxwell';s Equations
Modulus-based Synchronous Two-stage Multisplitting Iteration Methods for Linear Complementarity Prob
Low Complexity Interference Alignment Algorithms for Desired Signal Power Maximization Problem of MI
Solvability of Concatenated Runge-Kutta Equations for Second-order Nonlinear PDEs
A Novel Geometric Flow Approach for Quality Improvement of Multi-Component Tetrahedral Meshes
An Overfilled Cavity Problem for Maxwell';s Equations
Convergence Issues in Using High-resolution Schemes and Lower–upper Symmetric Gauss–Seid
A Fast Classification Method for Single-Particle Projections with a Translation and Rotation Invaria
Long-Time Stability and Convergence of the Uniaxial Perfectly Matched Layer Method for Time-Domain A
The Performance of PCM Quantization under Tight Frame Representations
Multi-symplectic Algorithms for Hamiltonian Partial Differential Equations
A Geometric Flow Approach for Region-based Image Segmentation
G1连续的细分几何偏微分方程曲面设计
THE PERFORMANCE OF ORTHOGONAL MULTI-MATCHING PURSUIT UNDER THE RESTRICTED ISOMETRY PROPERTY
会议论文
A Novel Geometric Flow-Driven Approach for Quality Improvement of Segmented Tetrahedral Meshes
A Fast Classification Method for Single-Particle Projections
Solvability of the Central Box Scheme for a Kind of Nonlinear Partial Differential Equations
Adaptive Finite Element Analysis Based on Perturbation Arguments
The Well-posedness of a Special Partial Differential Equation
Stochastic Multisymplectic Integrator for Stochastic KdV Equation
Biomedical Image Interpolation Based on Multi-resolution Transformations
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陈志明的项目
科学与工程计算的方法和应用
期刊论文 7
控制、偏微分方程与科学计算国际会议
偏微分方程的多尺度分析与计算
　适应于千万亿次科学计算的新型计算模式
计算数学与科学工程计算
宏观超导模型及其自适应计算
非线性偏微分方程的计算方法研究
　高性能科学计算研究
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