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科学计算中的线性与非线性数值代数问题研究
  • 项目名称：科学计算中的线性与非线性数值代数问题研究
  • 项目类别：重点项目
  • 批准号：10731060
  • 申请代码：A011705
  • 项目来源：国家自然科学基金
  • 研究期限：2008-01-01-2011-12-31
  • 项目负责人：王兴华
  • 负责人职称：教授
  • 依托单位：浙江大学
  • 批准年度：2007
中文摘要：

数值代数是计算数学的基础，计算数学是科学计算的核心。实际工程计算所对应的偏微分方程通过有限元，或有限差分等方法离散以后都化为相应的线性或非线性数值代数问题。数值代数格式的好坏以及计算的效率直接影响着实际工程计算问题的数值求解与数值模拟的成败。 本项目将对数值代数领域中的大规模线性和非线性方程组、代数特征值问题的数值求解中的若干问题展开研究。我们将研究新的自适应非协调多重网格法严格的数学理论，并从数值实验上来验证此方法的有效性；研究与飞行器外部流场相关的按照区域剖分单元分块而形成的非线性代数方程组的求解；研究不依赖于具体迭代法的收敛性不变量的概念和统一的判定法则，并将实计算理论与数值泛函的框架理论以及微分方程理论结合起来；我们还将研究二次特征值问题和其反问题的数值计算方法。本项目可作为973"高性能科学计算研究"在数值代数领域的延伸和补充。

中文主题词： 大规模计算、线性和非线性代数方程组、代数特征值问题
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  • 期刊论文
  • 会议论文
  • 专利
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  • 著作
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期刊论文
Convergence criterion of Newton’s method for singular systems with constant rank derivative
The King-Werner method for solving nonsymmetric algebraic Riccati equation.
Generic well-posedness for perturbed optimization problems in Banach spaces,
Newton’s method for sections on Riemannian manifolds: Generalized covariant -theory,
Interative algorithms for nonexpansive mapping in Hadamard manifolds.
Generalizations of Hölder’s and some related inequalities
带有爆破现象的反应扩散方程的移动网格方法
Kantorovich-type convergence criterion for inexact Newton methods.
Smale's α-theory for inexact Newton methods under the γ-condition
A multilevel preconditioner for the mortar method for nonconforming P1 finite element
Subdifferentials of perturbed distance functions in Banach spaces
Bregman distance, approximate compactness and convexity of Chebyshev sets in Banach
Anisotropic best c-approximation in normed spaces
Nearest and farthest points in spaces of curvature bounded below
Guaranteed descent conjugate gradient methods with modified secant condition
下降的非线性共轭梯度法及其全局收敛性
Two-grid?algorithms?for?linear?and?nonlinear?elliptic?problems?based?on?HSS?iteration?method
Standard and economical cascadic multigrid methods for the Mortar element methods
The Crouzeix- - Raviart FE on nonmatching grids with an approximate mortar condition,
On the computation of an element of Clarke generalized Jacobian for a vector-valued max function
On the local convergence of a family of Euler-Halley type iterations with a parameter
Gauss-Newton methods for convex composite optimization on Riemannian manifolds
A generalization of Muller's iteration method based on standard information
Convergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theory
Convergence of the family of Euler-Halley type methods on Riemannian manifolds under the γ-ondition
Local multilevel methods for adaptive finite element methods for nonsymmetric and indefinite ellipti
A topological approach to the existence of solutions for nonlinear differential equations with piece
Convergence and quasi-optimality of adaptive nonconforming finite element methods for some nonsymmet
A Ulm-like method for inverse eigenvalue problems
Kantorovich's theorems of Newton's method for mappings and optimization problems on Lie groups
Smale’s point estimate theory for Newton’s method on Lie groups
Monotone and accetive vector fields on Riemannian manifolds
Optimized Schwarz methods with Robin transmission conditions for parabolic problems
On the convergence rate of a parallel nonoverlapping domain decomposition method
Self-excitation of neurons leads to multiperiodicity of discrete-time neural networks with distribut
The patch recovery for finite element approximation of elasticity problems under quadrilateral meshe
Title: Two-grid algorithms for some linear and nonlinear elliptic systems
Constraint qualifications for extended Farkas's lemmas and Lagrangian dualities in convex infinite
Accurate solutions of M-matrix Sylvester equations
Some new residual-based a posteriori error estimators for the mortar finite element methods
A robust WENO type finite volume solver for steady Euler equations on unstructured grids
Sharp a Posteriori Error Estimate for Elliptic Equation with Singular Data
An Efficient NRxx Method for Boltzmann-BGK Equation
An $h$-Adaptive Mesh Method for Boltzmann-BGK/Hydrodynamics Coupling
Numerical Regularized Moment Method of Arbitrary Order for Boltzmann-BGK Equation
Numerical Regularized Moment Method for High Mach Number Flow
AN ITERATION METHOD WITH GENERALLY CONVERGENT PROPERTY FOR CUBIC POLYNOMIALS
A Robust High-order Residual Distribution Type Scheme for Steady Euler Equations on Grids
Local convergence of inexact methods under the H?lder condition
A new semi-local convergence theorem for the inexact Newton methods
带有爆破现象的反应扩散方程的移动网格方法,
On matrix and determinant identities for composite functions
Stable and total Fenchel duality for convex optimization problems in locally convex spaces
Stable and Total Fenchel Duality for DC Optimization Problems in Locally Convex Spaces.
Constraint qualifications for optimality conditions and total Lagrangian duality in convex infinite
Subdifferential Calculus Rules for Supremum Functions in Convex Analysis
An iteration method with maximal order based on standard information
Moving mesh method for problems with blow-up on unbounded domains
Efficient Chebyshev Spectral Method for Solving Linear Elliptic PDEs Using Quasi-Inverse Technique
A new divergence-free interpolation operator with applications to the Darcy-Stokes- Brinkman equatio
Optimality of local multilevel methods on adaptively refined meshes for elliptic boundary value prob
Spectral Analysis of Dirichlet- Neumann Operators and Optimized Schwarz Methods with Robin Transmiss
Constraint qualifications for convex inequality systems with applications in constrained optimizatio
NRxx Simulation of Microflows with Shakhov Model
An inexact Newton-type method for inverse singular value problems
On a quadratic inverse eigenvalue problem
A new eigenvalue embedding approach for finite element model updating
Stable Solutions of Linear Systems Involving Long Chain of Matrix Multiplications,
Perturbation of partitioned Hermitian definite generalized eigenvalue problems
The formulation and numerical method for partial quadratic eigenvalue assignment problems
Accurate solutions of M-matrix algebraic Riccati equations
带移动奇异源热方程的移动网格方法
一个求解障碍问题的非光滑迭代算法（英文）
著作
控制论中的矩阵计算
王兴华的项目
非线性问题的并行算法及其整体复杂性
数值方法的分析和构造与实计算理论
期刊论文 21
非线性数值计算与数值逼近及其应用