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若干非线性问题的数值解法
  • 项目名称：若干非线性问题的数值解法
  • 项目类别：重点项目
  • 批准号：10531080
  • 申请代码：A011701
  • 项目来源：国家自然科学基金
  • 研究期限：2006-01-01-2009-12-31
  • 项目负责人：余德浩
  • 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：2005
中文摘要：

随着科学技术的不断发展，科学和工程中提出的计算问题越来越复杂，特别是大量非线性问题，对计算方法的创新和发展提出了越来越高的要求和挑战。因此，针对若干具有挑战性的非线性问题，进行系统的计算方法研究不仅在理论上，而且在应用中均有重要意义。本项目选择在电磁学和复杂流动等领域有重要应用背景的的若干关键科学计算问题，应用计算数学的最新研究成果，将理论分析、算法实现和数值实验相结合，研究、构造并发展适于求解这些非线性问题的高性能计算方法，包括自然边界积分及人工边界方法、无界区域分解及多重网格方法、自适应有限元边界元并行计算方法、多尺度计算方法、谱元方法等，这些方法的综合应用是解决上述科学计算问题的重要手段，也是当前国际科学计算研究领域的前沿课题。

中文主题词： 非线性问题数值解；电磁场计算；复杂流动计算；区域分解与多重网格；自适应并行计算
结论摘要：

英文主题词Numerical solutions for nonlinear problems; electromagnetic computation; computation for complex flow; domain decomposition and multigrid; adaptive parallel computation

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
  • 78
  • 13
  • 0
  • 1
  • 0
期刊论文
无界区域KPZ方程的自然边界元和有限元的耦合算法(英文)
Resolving the shock-induced combustion by an adaptive mesh redistribution method
Spectral Element Viscosity Methods for Nonlinear Conservation Laws on the Semi-Infinite Interval
A numerical comparison of outflow boundary conditions for spectral element simulations of incompress
Finite difference/spectral approximations for the time-fractional diffusion equation
A regularized domain decomposition method with Lagrange multiplier
Optimal superconvergence results for delay integro-differential equations of pantograph type
Fast iterative schemes for nonsymmetric algebraic Riccati equations arising from transport theory
隐式重新启动精化Lanczos双对角化方法
龙格库塔间断有限元方法在计算爆轰问题中的应用
关于Wielandt-Hoffman不等式的简化证明及其推广
A Coupled Legendre-Laguerre Spectral-Element Method for the Navier-Stokes Equations in Unbounded Dom
一类特殊矩阵的逆特征值问题
Boundary integral formulas for elastic plane problem of exterior circular domain
Domain decomposition with nonmatching grids for exterior transmission problems via FEM and DTN mappi
Natural boundary element method for three dimensional exterior harmonic problem with an inner prolat
A Spectral Element/Laguerre Coupled Method to the Elliptic Helmholtz Problem on the Half Line
Stability Analysis of Large Time-Stepping Methods for Epitaxial Growth Models
Symmetric super compact difference scheme of the Navier-Stokes equation and its parallel algorithm
Stabilization Methods for Spectral Element Computations of Incompressible Flows
圆外平面弹性问题的边界积分公式
Nonlinear inexact Uzawa algorithms for linear and nonlinear saddle-point problems
An adaptive finite element method for the eddy current model with circuit/field couplings
THE ELLIPSOID ARTIFICIAL BOUNDARY METHOD FOR THREE-DIMENSIONAL UNBOUNDED DOMAINS
Solution of exterior problem using ellipsoidal artificial boundary
Generalized Extrapolation for Computation of Hypersingular Integrals in Boundary Element Methods
Flux-difference splitting-based upwind compact schemes for the incompressible Navier-Stokes equation
On optimal message vector length for block single parallel partition algorithm in a three-dimensiona
Spectral Vanishing Viscosity for Large-Eddy Simulations by Spectral Element Methods
自适应有限元常用标记策略及其在 PHG 中的并行实现
A parallel algorithm for adaptive local refinement of tetrahedral meshes using bisection
Approximation BFGS methods for nonlinear image restoration
Transient Thermal Response of a Partially Insulated Crack in an Orthotropic Functionally Graded Stri
The Artificial Boundary Method for a Nonlinear Interface Problem on Unbounded Domain
A FEM-BEM formulation for an exterior quasilinear elliptic problem in the plane
A non-overlapping domain decomposition for low-frequency time-harmonic Maxwell's equations in unboun
A P_N x P_N Spectral Element Projection Method for the Unsteady Incompressible Navier-Stokes Equatio
Numerical approximation of acoustic waves by spectral element methods
A Laguerre/Legendre Spectral Method for the Stokes Problem in a Semi-Infinite Channel
Generalized Normal Derivatives and Their Applications in DDMs with Nonmatching Grids and DG Methods
A mortar edge element method with nearly optimal convergence for three-dimensional Maxwell's equatio
A note on the spectral for real Hankel matrices
The Coupling Method of Natural Boundary Element and Mixed Finite Element for Stationary Navier-Stoke
Structures of circulant inverse M-matrices
An invert-free Arnoldi method for computing interior eigenpairs of large matrices
Maximum inverse positive matrices
一类矩阵的逆奇异值问题
一种加权的Simpler GMRES算法
关于双曲守恒型方程式黎曼问题解的核心判别位置的确定
无界区域Stokes问题非重叠型区域分解算法及其收敛性
MULTIGRID ALGORITHM FOR THE COUPLING SYSTEM OF NATURAL BOUNDARY ELEMENT METHOD AND FINITE ELEMENT METHOD FOR UNBOUNDED DOMAIN PROBLEMS
Spectral Element Viscosity Methods for Nonlinear Conservation Laws onthe Semi-Infinite Interval
一类非线性Schrodinger方程的差分／Legendre谱元法
THE ELLIPSOID ARTIFICIAL BOUNDARY METHOD FOR THREE-DIMENSIONAL UNBOUNDED DOMAINS
An Implicitly Restarted Block Arnoldi Method in a Vector-Wise Fashion
对称双随机矩阵逆特征值问题
基于张量乘积的快速谱元算法
NATURAL BOUNDARY ELEMENT METHOD FOR THREE DIMENSIONAL EXTERIOR HARMONIC PROBLEM WITH AN INNER PROLATE SPHEROID BOUNDARY
DOMAIN DECOMPOSITION WITH NONMATCHING GRIDS FOR EXTERIOR TRANSMISSION PROBLEMS VIA FEM AND DTN MAPPING
隐式重新启动的Lanczos算法在模型降阶中的应用
一类非线性Schrodinger方程的守恒差分法与Fourier谱方法
具有位数3和4的双随机循环矩阵中的素元
添加近似误差的重新启动的simpler GMRES方法
非线性Kundu方程的弱守恒差分格式
无界区域KPZ方程的自然边界元和有限元的耦合算法
A IPN× IPN Spectral Element Projection Method for the Unsteady Incompressible Navier-Stokes Equations
广义块Toeplitz特征值问题的基于sine变换的预处理子
虚拟流体方法中界面处Riemann问题定义方式的改进
会议论文
A note on the spectral for real Hankel matrices
A New Kind of Multilevel Solver for Second Order Steklov-Poincaré Operators
Approximation BFGS methods for nonlinear image restoration
Preconditioned Lanczos method for generalized Toeplitz eigenvalue problems
THE ELLIPSOID ARTIFICIAL BOUNDARY METHOD FOR THREE-DIMENSIONAL UNBOUNDED DOMAINS
A note on solving real linear systems with the complex schur decompositon
On Perturbation bounds for HR decomposition
A Third-Order Upwind Compact Scheme on Curvilinear Meshes for the Incompressible Navier-Stokes Equat
Dynamic load balancing on adaptive unstructured meshes
Efficient parallel adaptive computation of 3D time-harmonic Maxwell's equations using the toolbox PH
求解Maxwell线性元鞍点系统的基于HX预条件子的Uzawa算法
基于几何非协调分解的Lagrange乘子区域分解方法
A SADDLE POINT APPROACH TO THE COMPUTATION OF HARMONIC MAPS
获奖
人工边界方法与偏微分方程数值解
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余德浩的项目
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