共查询到19条相似文献,搜索用时 359 毫秒
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块三对角线性方程组不完全分解预条件的一种一维区域分解并行化方法 总被引:1,自引:0,他引:1
对块三对角线性方程组,不完全分解是最有效的预条件之一,但它本质上是一个串行计算过程,难以有效并行化.基于一维重叠区域分解,对局部不完全分解得到的上、下三角因子分别各自进行组合,构造一类全局的并行不完全分解型预条件.在具体实现时,给出两种具体途径,其中一种基于所有重叠部分对应分量的交换.之后,在仔细对其中的计算过程进行分析的基础上,给出一种只需要一条网格线上分量通信的实现算法,大大减少了通信量,且通信不随重叠度的增加而增加.这种并行化方法可以应用于块三对角线性方程组的任何不完全分解型预条件.实验结果表明,文中提出的并行化方法普遍优于加性Schwarz并行化方法. 相似文献
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利用块三对角矩阵的嵌套局部块分解构造了一个不完全分解预条件子,并考虑了其修正型变种,分析了两者的存在性及若干性质.针对标准七点差分矩阵,给出了预条件后的实际条件数.结果表明,采用局部块分解预条件时条件数与矩阵阶数的2/3次幂成正比,而采用修正型预条件时条件数与矩阵阶数的立方根成正比.最后考虑了预条件的高效实现并在主频为550MHz、内存为256M的微机上作了若干数值实验,并与其它较有效的预条件方法进行了比较. 相似文献
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非定常Navier-Stokes方程基于完全重叠型区域分解的有限元并行算法 总被引:1,自引:0,他引:1
基于完全重叠型区域分解技巧,提出三种求解非定常Navier-Stokes方程的有限元并行算法.其基本思想是首先对空间施行完全重叠区域分解,然后各个处理器使用向后Euler格式独立并行求解关于时间t的常微分方程;对于非线性的对流项,分别采用半隐格式和全隐格式进行处理.算法中每个处理器所负责的子问题是一个全局问题,它定义在整个求解区域上,但绝大部分自由度来自其所负责的子区域,从而使得算法实现简单,通信需求少.数值算例验证了算法的有效性及其良好的并行性能. 相似文献
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众所周知, 风场分解与重构最有效的方法就是引入速度势和流函数, 其一般通过求解两个Poisson 方程得到. 由于速度势和流函数在边界上的耦合性质,有限区域风场分解是不唯一的, 这对风场分解带来了很大困难. 本文采用变分伴随结合正则化方法来克服风场分解的不唯一性, 其核心是把速度势和流函数的边值作为控制变量来反演. 目标泛函由两部分组成, 一是衡量重构风场误差大小的观测项; 二是保证风场分解问题适定的正则化项, 其目的在于寻求具有气象意义的稳定正则化解. 数值试验结果表明, 在正确选取正则化参数后, 利用变分伴随结合正则化方法进行有限区域风场分解与重构是有效可行的. 相似文献
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提出了无界区域波动方程的区域分解算法,基于自然边界归化,分别研究了重叠型与非重叠型区域分解算法,首先将控制方程对时间进行离散化,得到关于时间步长离散化格式,对每一时间步长给出了Dirichlet-Neumann和Schwartz交替算法,对Schwartz交替算法,给出了算法的收敛性,对圆外区域研究了压缩因子,并给出了数值例子。 相似文献
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基于几何型扩展有限元离散方法,研究含静态裂缝线弹性问题的高效区域分解预条件算法。为了构造Schwarz型预条件算法,采用一种特殊的裂尖型区域分解策略,将计算区域分解为包含所有分支增强自由度的裂尖子区域和仅包含标准有限元自由度与Heaviside增强自由度的常规子区域。基于该区域分解策略,推导一类高效的乘性和限制型乘性Schwarz区域分解预条件子,对裂尖子问题进行精确求解,而对常规子问题则非精确求解。数值实验验证了算法的有效性。 相似文献
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Long Yuan & Qiya Hu 《advances in applied mathematics and mechanics.》2013,5(6):791-808
An interesting discretization method for Helmholtz equations was
introduced in B. Després [1]. This method is based on the
ultra weak variational formulation (UWVF) and the wave shape
functions, which are exact solutions of the governing Helmholtz
equation. In this paper we are concerned with fast solver for the
system generated by the method in [1]. We propose a new
preconditioner for such system, which can be viewed as a combination
between a coarse solver and the block diagonal preconditioner
introduced in [13]. In our numerical experiments, this
preconditioner is applied to solve both two-dimensional and
three-dimensional Helmholtz equations, and the numerical results
illustrate that the new preconditioner is much more efficient than
the original block diagonal preconditioner. 相似文献
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Tsung-Ming Huang Wei-Jen Chang Yin-Liang Huang Wen-Wei Lin Wei-Cheng Wang Weichung Wang 《Journal of computational physics》2010,229(23):8684-8703
To explore band structures of three-dimensional photonic crystals numerically, we need to solve the eigenvalue problems derived from the governing Maxwell equations. The solutions of these eigenvalue problems cannot be computed effectively unless a suitable combination of eigenvalue solver and preconditioner is chosen. Taking eigenvalue problems due to Yee’s scheme as examples, we propose using Krylov–Schur method and Jacobi–Davidson method to solve the resulting eigenvalue problems. For preconditioning, we derive several novel preconditioning schemes based on various preconditioners, including a preconditioner that can be solved by Fast Fourier Transform efficiently. We then conduct intensive numerical experiments for various combinations of eigenvalue solvers and preconditioning schemes. We find that the Krylov–Schur method associated with the Fast Fourier Transform based preconditioner is very efficient. It remarkably outperforms all other eigenvalue solvers with common preconditioners like Jacobi, Symmetric Successive Over Relaxation, and incomplete factorizations. This promising solver can benefit applications like photonic crystal structure optimization. 相似文献
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本文提出了一种基于新的五维多环多翼超混沌系统的数字图像加密方法.首先,将明文图像矩阵和五条混沌序列分别通过QR分解法分解成一个正交矩阵和一个上三角矩阵,将混沌系统产生的五条混沌序列分别通过LU分解法分解成一个上三角矩阵和一个下三角矩阵,分别将两个上三角矩阵和一个下三角矩阵相加,得到五个离散后的混沌序列;其次,将明文图像矩阵分解出来的正交矩阵与五个混沌序列分解出来的五个正交矩阵相乘,同时把明文图像矩阵分解出来的上三角矩阵中的元素通过混沌序列进行位置乱,再将操作后的两个矩阵相乘;最后,将相乘后的矩阵通过混沌序列进行比特位位置乱,再用混沌序列与其进行按位“异或”运算,得到最终加密图像.理论分析和仿真实验结果表明该算法的密钥空间远大于10^200,密钥敏感性强,能够有效地抵御统计分析和灰度值分析的攻击,对数字图像的加密具有很好的加密效果. 相似文献
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Completeness of the system of eigenvectors of off-diagonal operator matrices and its applications in elasticity theory
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This paper deals with off-diagonal operator matrices and their applications in elasticity theory.Two kinds of completeness of the system of eigenvectors are proven,in terms of those of the compositions of two block operators in the off-diagonal operator matrices.Using these results,the double eigenfunction expansion method for solving upper triangular matrix differential systems is proposed.Moreover,we apply the method to the two-dimensional elasticity problem and the problem of bending of rectangular thin plates on elastic foundation. 相似文献
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A Newton–Krylov method is developed for the solution of the steady compressible Navier–Stokes equations using a discontinuous Galerkin (DG) discretization on unstructured meshes. Steady-state solutions are obtained using a Newton–Krylov approach where the linear system at each iteration is solved using a restarted GMRES algorithm. Several different preconditioners are examined to achieve fast convergence of the GMRES algorithm. An element Line-Jacobi preconditioner is presented which solves a block-tridiagonal system along lines of maximum coupling in the flow. An incomplete block-LU factorization (Block-ILU(0)) is also presented as a preconditioner, where the factorization is performed using a reordering of elements based upon the lines of maximum coupling. This reordering is shown to be superior to standard reordering techniques (Nested Dissection, One-way Dissection, Quotient Minimum Degree, Reverse Cuthill–Mckee) especially for viscous test cases. The Block-ILU(0) factorization is performed in-place and an algorithm is presented for the application of the linearization which reduces both the memory and CPU time over the traditional dual matrix storage format. Additionally, a linear p-multigrid preconditioner is also considered, where Block-Jacobi, Line-Jacobi and Block-ILU(0) are used as smoothers. The linear multigrid preconditioner is shown to significantly improve convergence in term of number of iterations and CPU time compared to a single-level Block-Jacobi or Line-Jacobi preconditioner. Similarly the linear multigrid preconditioner with Block-ILU smoothing is shown to reduce the number of linear iterations to achieve convergence over a single-level Block-ILU(0) preconditioner, though no appreciable improvement in CPU time is shown. 相似文献
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We present some rigorous sharp lower and upper bounds for the integrated phonon density of states and for the phonon specific heat of various types of two-dimensional disordered systems of masses and springs which are placed on triangular lattices. The bounds are given by quadrature formulas involving the first moments of the underlying probability distribution. We compare the results obtained for random systems up to the fourth order in moments with exact expressions corresponding to ordered systems with the same dimension and lattice structure. 相似文献
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A preconditioning technique to accelerate the simulation of steady-state problems using the single-relaxation-time (SRT) lattice Boltzmann (LB) method was first proposed by Guo et al. [Z. Guo, T. Zhao, Y. Shi, Preconditioned lattice-Boltzmann method for steady flows, Phys. Rev. E 70 (2004) 066706-1]. The key idea in this preconditioner is to modify the equilibrium distribution function in such a way that, by means of a Chapman–Enskog expansion, a time-derivative preconditioner of the Navier–Stokes (NS) equations is obtained. In the present contribution, the optimal values for the free parameter γ of this preconditioner are searched both numerically and theoretically; the later with the aid of linear-stability analysis and with the condition number of the system of NS equations. The influence of the collision operator, single- versus multiple-relaxation-times (MRT), is also studied. Three steady-state laminar test cases are used for validation, namely: the two-dimensional lid-driven cavity, a two-dimensional microchannel and the three-dimensional backward-facing step. Finally, guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the Reynolds and Mach numbers. The new optimally preconditioned MRT method derived is shown to improve, simultaneously, the rate of convergence, the stability and the accuracy of the lattice Boltzmann simulations, when compared to the non-preconditioned methods and to the optimally preconditioned SRT one. Additionally, direct time-derivative preconditioning of the LB equation is also studied. 相似文献
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为了解决光子晶体波导出射端光场控制, 同时解决二维三角晶格光子晶体波导出射光辐射困难的问题。利用二维三角晶格光子晶体设计了一种新型光子晶体波导出射口结构。在二维三角晶格光子晶体波导出射端引入两个微腔, 通过光波与微腔发生共振, 形成类似于三个点光源干涉的出射光, 同时进一步提出波导出射端喇叭口干涉出射光定向辐射的设计。通过这种微腔喇叭口设计, 利用时域有限差分法分析结果表明光波实现很好的定向辐射, 并且辐射距离显著提高。 相似文献