Symplectic Householder transformations for a QR-like decomposition,a geometric and algebraic approaches

The aim of this paper is to show how geometric and algebraic approaches lead us to a new symplectic elementary transformations: the 2-D symplectic Householder transformations. Their features are studied in details. Their interesting properties allow us to construct a new algorithm for computing a SR factorization. This algorithm is based only on these 2-D symplectic Householder transformations. Its new features are highlighted. The study shows that, in the symplectic case, the new algorithm is the corresponding one to the classical QR factorization algorithm, via the Householder transformations. Some numerical experiments are given.     

2.5维介质Born近似波速反演唯一性

考虑脉冲源引起的２．５维弱不均匀介质波速反演问题，利用线性化方法得到了波速的二维小扰动满足的积分方程，这是一个积分几何的问题，进而由Ｆｏｕｒｉｅｒ变换和脉冲函数的性质将此二维积分方程化为单变量的积分方程，最后用压缩映象理论证明了积分方程解的唯一性。本文给出了二给波速反演的一种新算法。同时，唯一性结果证明了已有的迭代算法的合理性。     

二维波动方程部分Dirichlet边界控制正则性的数值分析

通过数值方法,研究边界充分(逐段)光滑区域上的二维波动方程在部分Dirichlet边界控制下的正则性问题.数值结果表明:在所选条件下,系统是Salamon-Weiss意义下正则的.     

二维柱坐标系辐射输运方程保球对称的离散纵标格式

 离散纵标格式是计算辐射输运方程的常用格式之一. 但是, 传统的离散纵标格式求解二维柱坐标系辐射输运方程模拟一维球对称问题时, 会出现明显的非对称现象, 球对称性被破坏. 针对该问题, 本文分析了传统离散纵标格式不能够保持球对称性的原因, 提出了空间基于柱坐标系、方向基于球坐标系的辐射输运方程, 并对该方程设计了新的离散纵标格式, 从理论上证明了当空间网格取球对称剖分时该离散格式能够保持一维球对称性的充分必要条件. 通过对真空球区域辐射输运、与物质耦合辐射输运等球对称算例的数值模拟, 验证了该格式的保球对称性, 球对称误差能够达到机器精度. 非对称辐射驱动模型以及非对称网格剖分条件下的数值模拟等算例也取得了较好的结果.     

Fuzzy-2D-HMMS算法及其收敛性

通过对Dat Tran和Michael Wagner等提出的FCM-FE-HMMS算法研究,并把它与2维隐马氏模型联系起来,提出了Fuzzy-2D-HMMS算法,得出在给定初值的情况下该算法将收敛到一个局部最优解.     

MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS

In this paper we propose the well-known Fourier method on some non-tensor productdomains in R~d, inclding simplex and so-called super-simplex which consists of (d 1)!simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a parallelhexagon and a parallel quadrilateral dodecahedron, respectively. We have extended mostof concepts and results of the traditional Fourier methods on multivariate cases, such asFourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm(FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT)and related fast algorithms over a simplex. The relationship between the basic orthogonalsystem and eigen-functions of a Laplacian-like operator over these domains is explored.     

A quadratic b-spline based isogeometric analysis of transient wave propagation problems with implicit time integration method

A uniform quadratic b-spline isogeometric element is exclusively considered for wave propagation problem with the use of desirable implicit time integration scheme. A generalized numerical algorithm is proposed for dispersion analysis of one-dimensional (1-D) and two-dimensional (2-D) wave propagation problems where the quantified influence of the defined CFL number on wave velocity error is analyzed and obtained. Meanwhile, the optimal CFL (Courant–Friedrichs–Lewy) number for the proposed 1-D and 2-D problems is suggested. Four representative numerical simulations confirm the effectiveness of the proposed method and the correctness of dispersion analysis when appropriate spatial element size and time increment are adopted. The desirable computation efficiency of the proposed isogeometric method was confirmed by conducting time cost and calculation accuracy analysis of a 2-D numerical example where the referred FEM was also tested for comparison.     

Efficient boundary element methods for three-dimensional exterior viscous flows

An efficient numerical algorithm for partial differential equations in complicated three-dimensional (3-D) geometries is developed in case of exterior viscous flows. The algorithm essentially consists of a boundary element method, where the resulting algebraic system is solved with a multigrid procedure. Our investigation covers and exact mathematical foundation, a detailed analysis of the discretization error, and some numerical tests with reasonable physical examples.     

Convergence of the point vortex method for the 3-D euler equations

We prove consistency, stability, and convergence of a point vortex approximation to the 3-D incompressible Euler equations with smooth solutions. The 3-D algorithm we consider here is similar to the corresponding 3-D vortex blob algorithm introduced by Beale and Majda; see [3]. We first show that the discretization error is second-order accurate. Then we show that the method is stable in l^p norm for the particle trajectories and in w^?1.p norm for discrete vorticity. Consequently, the method converges up to any time for which the Euler equations have a smooth solution. One immediate application of our convergence result is that the vortex filament method without smoothing also converges.     

Finite Volume Element Methods for Two-Dimensional Three-Temperature Radiation Diffusion Equations

Two-dimensional three-temperature (2-D 3-T) radiation diffusion equations are widely used to approximately describe the evolution of radiation energy within a multi-material system and explain the exchange of energy among electrons, ions and photons. Their highly nonlinear, strong discontinuous and tightly coupled phenomena always make the numerical solution of such equations extremely challenging. In this paper, we construct two finite volume element schemes both satisfying the discrete conservation property. One of them can well preserve the positivity of analytical solutions, while the other one does not satisfy this property. To fix this defect, two as repair techniques are designed. In addition, as the numerical simulation of 2-D 3-T equations is very time consuming, we also devise a mesh adaptation algorithm to reduce the cost. Numerical results show that these new methods are practical and efficient in solving this kind of problems.     

Anisotropic mesh refinement for finite element methods based on error reduction

In this paper, we propose an anisotropic adaptive refinement algorithm based on the finite element methods for the numerical solution of partial differential equations. In 2-D, for a given triangular grid and finite element approximating space V, we obtain information on location and direction of refinement by estimating the reduction of the error if a single degree of freedom is added to V. For our model problem the algorithm fits highly stretched triangles along an interior layer, reducing the number of degrees of freedom that a standard h-type isotropic refinement algorithm would use.     

Resolution of the incompressible inverse problem by singularities perturbation: Theory and industrial applications

Several inverse design methods using conformai mapping in 2-D have been developed, which, however, do not permit an extension in 3-D. The present 2-D inverse design method involves a linearized system resulting from small perturbations of a 2-D direct calculation procedure. The feasibility of this method is demonstrated by examples taken from industrial applications. The principles involved make possible an extension in 3-D.     

求解二维波动方程正演反演问题的半离散方法

本文用半离散方法将二维波动方程离散为一维耦合波动方程组．给出了离散的收敛性及波动方程组的适定性．利用这种方法可以求解波动方程系数及演问题．     

DERIVATION AND ANALYSIS OF A NEW RECONSTRUCTION FORMULA FROM CONE-BEAM PROJECTIONS

A new method to compute the first derivative of 3-D Radon transform is given for cone-beam data taken from any orbit. Smith [Ⅰ1] and Grangeat [5] even derived cone-beam inversion formulas which are the basic work in fully 3-D image reconstruction algorithm and are used extensively now. In this paper we will give a new inversion formula and a simple necessary and sufficient condition which guarantees the complete reconstruction algorithm.     

分布式系统上并行矩阵乘法

1．引言矩阵乘法是最简单的数学问题,同时由于其计算量大而通常被用来对计算机的浮点运算速度进行测试,尤其是对于并行计算机,其并行效率的好坏可通过这个简单的问题反应出来,如果在这个问题上都不能取得很好的效果,对于其它问题就更不可能．此外,为了提高计算性能,对求解数值代数中的问题最终会归结到有矩阵乘法的计算,如LAPACK,ScaLAPACK等,因此有效地并行计算矩阵乘法在实际应用中是非常重要的．矩阵乘法是做C＝A×B,其中A是m×k阵,B是k×n阵,C是m×n阵．设矩阵A,B可以分成p×p块矩阵,即A＝（Ai,j）p×p,B＝（B…     

The computation of transient 2-D eddy current problem by domain decomposition algorithms

A combination of domain decomposition method and a time discretization for the solution of transient 2-D eddy current problem is considered. A domain decomposition algorithm suitable for parallelization is described and convergence is established. Numerical experiments on a shared memory multiprocessor are presented.     

2—D奇异系统正则观测器的设计

本文讨论了一类２－Ｄ奇异系统正则观测器的设计问题。为此，首先将２－Ｄ奇异系统等价为降阶正则系统和一纯代数等式的组合，在此基础上，从理论上解决了２－Ｄ奇异系统的一类正则观测器的设计问题。     

The implementation of the finite-volume dynamical core in the community atmosphere model

A distributed memory message-passing parallel implementation of a finite-volume discretization of the primitive equations in the community atmosphere model (CAM) 3.0 is presented. These 3-D equations can be decoupled into a set of 2-D equations by the introduction of a floating vertical coordinate, resulting in considerable potential parallelism. Subsequent analysis of the data dependencies—in particular those arising from the polar singularity of the latitude-longitude coordinate system—suggests that two separate domain decompositions should be employed, each tailored for a different part of the model. The implementation requires that data be periodically redistributed between these two decompositions. Furthermore, data from nearest neighbors are kept in halo regions, which are updated between iterations. These data movements are optimized through one-sided communication primitives and multithreading. The resulting algorithm is shown to scale to very large machine configurations, even for relatively coarse resolutions.     

Torus data flow for parallel computation of missized matrix problems

A data-flow approach is used to solve dense symmetric systems of equations on a torus-connected 2-D mesh of processors. A torus mapping of the matrix onto this processor array allows the Cholesky decomposition to be completed in 3n − 2 time steps using only n²/4 processors (less than half the number needed in previously reported results). New definitions for missized problems and parallel algorithm performance are given along with various time-step, efficiency, and processor utilization plots.