位置：立项数据库 > 立项详情页
偏微分方程数值求解中的自适应网格方法研究
  • 项目名称：偏微分方程数值求解中的自适应网格方法研究
  • 项目类别：重点项目
  • 批准号：10431050
  • 申请代码：A011701
  • 项目来源：国家自然科学基金
  • 研究期限：2005-01-01-2008-12-31
  • 项目负责人：孙家昶
  • 负责人职称：研究员
  • 依托单位：中国科学院软件研究所
  • 批准年度：2004
中文摘要：

网格是偏微分方程数值解法的基础，直接关系到计算结果的精度，甚至影响计算的成败。网格方法的研究经历了从结构化到非结构化、从单一网格到混合网格的过程，而近三十年来兴起的自适应网格方法引起了国际学术界和各类应用部门的高度重视，并成为网格方法研究的热点问题。尽管偏微分方程数值求解中的自适应网格方法研究取得了一些进展，但是面向应用、针对具体问题深入研究自适应网格方法的工作还开展得远远不够。本项目将对椭圆型方程等一类与时间无关问题的数值网格生成方法及相关的网格性质、抛物型方程和非定常流体力学方程数值求解中的移动网格方法、计算流体力学中的自适应坐标变换方法进行深入研究；并从应用层面上对一类应用问题的自适应网格和非匹配网格上的多重网格法、新一代油藏数值模拟器中的网格方法以及多介质大变形流动问题的网格变换方法进行考察和研究。

中文主题词： 偏微分方程数值解法;自适应网格加密;移动网格方法;自适应坐标
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
  • 74
  • 31
  • 0
  • 0
  • 1
期刊论文
一类六边形网格上拉普拉斯4 点差分格式及其预条件子
An efficient and effective nonlinear solver in a parallel software for large scale petroleum reservo
Robin transmission conditions for overlapping additive Schwarz method applied to linear elliptic pro
Approximate eigen-decomposition preconditioners for solving numerical PDE problems
Multivariate Fourier transform methods over simplex and super-simplex domains
Convergence and stability of a numerical method for micromagnetics
Burgers 方程的声速点故障问题
Convergence of inner iterations scheme of the discrete ordinate method in spherical geometry
基于Riemann 解的二维流体力学 Lagrange 有限点无网格方法
SPH 方法中的Riemann 解与人工粘性
A general Riemann solver for Euler equations
A cell-centered lagrangian scheme in two- dimensional cylindrical geometry
有限点方法研究
TVD finite point method for two-dimensional conservation equation
Computation of length scales for second-order laminated microstructure with surface energy
An averaging scheme for macroscopic numerical simulation of minimization problems
Numerical solution of nonlinear elasticity problems with Lavrentiev phenomenon
Computation of the lower semicontinuous envelope of integral functionals and non-homogeneous micr
Upwind isoparametric interpolation finite point method for 2D scalar conservation equation
Dynamic PDE parametric curves
Local oscillations in finite difference solutions of hyperbolic conservation laws
A regularized mesh transformation method for the computation of crystalline microstructures
A truncation method for detecting singular minimizers involving the Lavrentiev phenomenon
Accurate calculation of Green's functions of Schroedinger equations in block layered potentials
Higher-order accurate Runge-Kutta discontinuous Galerkin methods for a nonlinear Dirac model
非线性Dirac 方程的数值研究
理想磁流体的散度自由移动网格方法
An adaptive moving mesh method for multidimensional ideal magnetohydrodynamics
An efficient adaptive mesh redistribution method for a nonlinear Dirac equation
Discrete Fourier analysis on a dodecahedron and a tetrahedron
Interaction for the solitary waves of a nonlinear Dirac model
On the sonic point glitch
Robust and efficient adaptive moving mesh solution of the 2-D Euler equations
A moving mesh method for the Euler flow calculations using a directional monitor function
On a kind of special bivariate spline
Fast Fourier transform on hexagon
Discrete Fourier analysis, cubature and interpolation on a hexagon and a triangle
Numerical methods for energy flux of temperature diffusion equation on unstructured meshes
Computing non-smooth minimizers with the mesh transformation method
Interaction of solitary waves with a phase shift in a nonlinear Dirac model
Generalzied Fourier transform on an arbitrary triangular domain
Edge-oriented hexagonal elements
A new class of three-variable orthogonal polynomials and their recurrences relations
High resolution schemes for conservation laws and convection-diffusion equations with varying time a
On convergence of a domain decomposition method for hyperbolic conservation laws
A class of high resolution difference schemes for nonlinear Hamilton-Jacobi equations with varying t
A note on the conservative schemes for the Euler equations,
A numerical iterative scheme for computing finite order rank-one convex envelopes
Non-conforming finite element and artificial boundary in multi-atomic Young measure approximatio
Parallel preconditioners for large scale partial difference equation systems
On Construction of difference schemes and finite elements over hexagon partitions
An irregular grid for numerical solution of linear elliptic PDE
Super spectral viscosity method for nonlinear conservation law
Hexagonal spectral methods for two-dimensional incompressible flows
A Runge-Kutta discontinuous Galerkin method for the Euler equations
The mesh transformation method and optimal finite element solutions.
An adaptive ghost fluid finite volume method for compressible gas-water simulations
曲率与运动界面发展
平行六边形区域非均匀节点快速傅立叶变换
非结构网格上温度扩散方程的能流计算方法
MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS
推进方式的参考Jacobian网格优化方法
Burgers方程的声速点故障问题
非线性Dirac方程的数值研究
复杂区域上的一种结构网格生成方法
A POSTERIORI ERROR ESTIMATES OF A NON-CONFORMING FINITE ELEMENT METHOD FOR PROBLEMS WITH ARTIFICIAL BOUNDARY CONDITIONS
一个磁流体力学中心型数值通量的耗散控制器（英文）
HIGH RESOLUTION SCHEMES FOR CONSERVATION LAWS AND CONVECTION-DIFFUSION EQUATIONS WITH VARYING TIME AND SPACE GRIDS
会议论文
Error estimates of spectral approximations by using polynomials on a disc and a triangle
On PDE approach to three-variable orthogonal polynomials
On two and three variables trigonometric surface and orthogonal polynomials over some irregular doma
三维分片四面体造型数学上的本质困难与对策
An adaptive ghost fluid finite volume method and its applications
Numerical methods for crystalline microstructure - - - Young measure and scaling law
On finite element methods over 2-D hexagon and 3-D dodecahedron partitions
Finite point method for partial differential equations
Adaptive coordinate transformation method for 2D Euler equation,
Approximate eigen-decomposition preconditioners,
Multi-atomic Young measure and artificial boundary in approximation of micromagnetics
On constructive orthogonal bases over 3-D domains with 4-direction partitions
A fully tensorial rational spectral element method on the triangle and the tetrahedron
Mesh transformation method for computation of microstructures and phase boundary
二维可压缩流体计算中Lagrangian方法的研究进展
Adaptive coordinate transformation method for fluid dynamics computation
Parallel preconditioners for large scale partial difference equation systems
Optimal error estimates for polynomial approximation on the triangle
On the sonic point glitch
A Lagrangian finite point method solving two-dimensional fluid dynamic problem,
Numerical simulation of micromagnetics
A PDE approach in multivariate approximation over non-traditional structured partition
Numerical analysis and computation of multi-order laminated microstructure
Numerical methods for crystalline microstructure
Mesh transformation method for computation of microstructures and phase boundary
Optimal error estimates in Jacobi-weighted Sobolev spaces for polynomial approximations on the trian
A fully coupled implicit solver for shallow water equations on the cubed-sphere
Spectral simulation of 2-D isotropic turbulence by using hexagonal grids
An adaptive phase field method for the mixture of two incompressible fluids
高分辨自适应移动网格方法及其CFD应用
Adaptive coordinate transformation methods for multimaterial fluid dynamics
著作
非传统区域Fourier变换与正交多项式
相关项目
自适应移动网格方法模拟有限时间爆破解的理论研究和应用
期刊论文 13
移动网格方法在双曲守恒律和辐射扩散方程中的应用
期刊论文 1
自适应移动非结构网格方法及其在计算流体力学中的应用
期刊论文 3
求解时间分数阶偏微分方程自适应移动网格方法
期刊论文 8
爆轰驱动的多流体系统数值模拟及应用研究
期刊论文 27 著作 1
孙家昶的项目
提高分布式并行数值软件性能的若干关键技术研究
2008 北京“高性能科学计算中的逼近问题”国际会议
分布式并行系统大型迭代算法研究与并行实现
非规则区域数据快速变换及并行算法研究与应用
期刊论文 14 会议论文 13 著作 1
三维数据多面体组合网格与快速算法
期刊论文 7 会议论文 1
非规则区域傅氏与小波变换及其在图形图像处理中的应用
第三届中意计算与应用数学研讨会