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61.
为了在低马赫数到高马赫数范围内求解可压缩Navier-Stokes方程,给出了基于预处理算法的PLU-SGS方法.将高分辨率AUSMPW格式与三阶MUSCL格式融合,将其扩展到三阶精度,并采用特征边界条件.为了验证该方法的有效性,通过求解曲线坐标系可压缩Navier-Stokes方程,对几个典型流动问题进行了数值计算.计算结果与文献计算结果或实验数据比较表明,该方法对不同马赫数Navier-Stokes方程的计算,具有较高的计算精度和收敛速度以及良好的稳定性. 相似文献
62.
R. S. Chen D. G. Fang K. F. Tsang Edward K. N. Yung 《International Journal of Infrared and Millimeter Waves》2000,21(9):1541-1560
An effective wavelet based multigrid preconditioned conjugate gradient method is developed to solve electromagnetic large matrix problem for millimeter wave scattering application. By using wavelet transformation we restrict the large matrix equation to a relative smaller matrix and which can be solved rapidly. The solution is prolonged as the new improvement for the conjugate gradient (CG) method. Numerical results show that our developed wavelet based multigrid preconditioned CG method can reach large improvement of computational complexity. Due to the automaticity of wavelet transformation, this method is potential to be a block box solver without physical background. 相似文献
63.
The computation of solution paths of large-scale continuation problems can be quite challenging because a large amount of
computations have to be carried out in an interactive computing environment. The computations involve the solution of a sequence
of large nonlinear problems, the detection of turning points and bifurcation points, as well as branch switching at bifurcation
points. These tasks can be accomplished by computing the solution of a sequence of large linear systems of equations and by
determining a few eigenvalues close to the origin, and associated eigenvectors, of the matrices of these systems. We describe
an iterative method that simultaneously solves a linear system of equations and computes a few eigenpairs associated with
eigenvalues of small magnitude of the matrix. The computation of the eigenvectors has the effect of preconditioning the linear
system, and numerical examples show that the simultaneous computation of the solution and eigenpairs can be faster than only
computing the solution. Our iterative method is based on the block-Lanczos algorithm and is applicable to continuation problems
with symmetric Jacobian matrices.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
64.
Considering matrices obtained by the application of a five-point stencil on a 2D rectangular grid, we analyse a preconditioning method introduced by Axelsson and Eijkhout, and by Brand and Heinemann. In this method, one performs a (modified) incomplete factorization with respect to a so-called ‘repeated’ or ‘recursive’ red–black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by 𝒪(n ) where n is the total number of unknowns (½ log2(√(5) − 1) = 0.153), and thus, that the total arithmetic work for the solution is bounded by 𝒪(n1.077). Our condition number estimate, which turns out to be better than standard 𝒪(log2 n) estimates for any realistic problem size, is purely algebraic and holds in the presence of Neumann boundary conditions and/or discontinuities in the PDE coefficients. Numerical tests are reported, displaying the efficiency of the method and the relevance of our analysis. © 1997 John Wiley & Sons, Ltd. 相似文献
65.
Yair Shapira Moshe Israeli Avram Sidi Uzi Zrahia 《Numerical Methods for Partial Differential Equations》1999,15(5):535-543
Spectral element schemes for the solution of elliptic boundary value problems are considered. Preconditioning methods based on finite difference and finite element schemes are implemented. Numerical experiments show that inverting the preconditioner by a single multigrid iteration is most efficient and that the finite difference preconditioner is superior to the finite element one for both definite and indefinite problems. A multigrid preconditioner is also derived from the finite difference preconditioner and is found suitable for the CGS acceleration method. It is pointed out that, for the finite difference and finite element preconditioners, CGS does not always converge to the accurate algebraic solution. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 535–543, 1999 相似文献
66.
We present robust and asymptotically optimal iterative methods for solving 2D anisotropic elliptic equations with strongly jumping coefficients, where the direction of anisotropy may change sharply between adjacent subdomains. The idea of a stable preconditioning for the Schur complement matrix is based on the use of an exotic non‐conformal coarse mesh space and on a special clustering of the edge space components according to the anisotropy behavior. Our method extends the well known BPS interface preconditioner [2] to the case of anisotropic equations. The technique proposed also provides robust solvers for isotropic equations in the presence of degenerate geometries, in particular, in domains composed of thin substructures. Numerical experiments confirm efficiency and robustness of the algorithms for the complicated problems with strongly varying diffusion and anisotropy coefficients as well as for the isotropic diffusion equations in the ‘brick and mortar’ structures involving subdomains with high aspect ratios. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
67.
Elena I. Zakharova Andrey T. Proshin Mikhail Y. Monakov Alexander M. Dudchenko 《Molecules (Basel, Switzerland)》2021,26(23)
We have previously suggested a key role of the hippocampus in the preconditioning action of moderate hypobaric hypoxia (HBH). The preconditioning efficiency of HBH is associated with acoustic startle prepulse inhibition (PPI). In rats with PPI > 40%, HBH activates the cholinergic projections of hippocampus, and PNU-282987, a selective agonist of α7 nicotinic receptors (α7nAChRs), reduces the HBH efficiency and potentiating effect on HBH of its solvent dimethyl sulfoxide (DMSO, anticholinesterase agent) when administered intraperitoneally. In order to validate the hippocampus as a key structure in the mechanism of hypoxic preconditioning and research a significance of α7nAChR activation in the hypoxic preconditioning, we performed an in vivo pharmacological study of intrahippocampal injections of PNU-282987 into the CA1 area on HBH efficiency in rats with PPI ≥ 40%. We found that PNU-282987 (30 μM) reduced HBH efficiency as with intraperitoneal administration, while DMSO (0.05%) still potentiated this effect. Thus, direct evidence of the key role of the hippocampus in the preconditioning effect of HBH and some details of this mechanism were obtained in rats with PPI ≥ 40%. The activation of α7nAChRs is not involved in the cholinergic signaling initiated by HBH or DMSO via any route of administration. Possible ways of the potentiating action of DMSO on HBH efficiency and its dependence on α7nAChRs are discussed. 相似文献
68.
This article concerns the spectral analysis of matrix‐sequences which can be written as a non‐Hermitian perturbation of a given Hermitian matrix‐sequence. The main result reads as follows. Suppose that for every n there is a Hermitian matrix Xn of size n and that {Xn}n~λf, that is, the matrix‐sequence {Xn}n enjoys an asymptotic spectral distribution, in the Weyl sense, described by a Lebesgue measurable function f; if with ‖·‖2 being the Schatten 2 norm, then {Xn+Yn}n~λf. In a previous article by Leonid Golinskii and the second author, a similar result was proved, but under the technical restrictive assumption that the involved matrix‐sequences {Xn}n and {Yn}n are uniformly bounded in spectral norm. Nevertheless, the result had a remarkable impact in the analysis of both spectral distribution and clustering of matrix‐sequences arising from various applications, including the numerical approximation of partial differential equations (PDEs) and the preconditioning of PDE discretization matrices. The new result considerably extends the spectral analysis tools provided by the former one, and in fact we are now allowed to analyze linear PDEs with (unbounded) variable coefficients, preconditioned matrix‐sequences, and so forth. A few selected applications are considered, extensive numerical experiments are discussed, and a further conjecture is illustrated at the end of the article. 相似文献
69.
K. F. Tsang L. Mo Z. B. Ye 《International Journal of Infrared and Millimeter Waves》2003,24(6):1005-1022
In this paper, both fast Fourier transformation (FFT) and preconditioned CG technique are introduced into method of lines (MOL) to further enhance the computational efficiency of this semi-analytic method. Electromagnetic wave scattering by an infinite plane metallic grating is used as the examples to describe its implementation. For arbitrary incident wave, Helmholz equation and boundary condition are first transformed into new ones so that the impedance matrix elements are calculated by FFT technique. As a result, this Topelitz impedance matrix only requires O(N) memory storage for the conjugate gradient FFT method to solve the current distribution with the computational complexity O(N log N) . Our numerical results show that circulate matrix preconditioner can speed up CG-FFT method to converge in much smaller CPU time than the banded matrix preconditioner. 相似文献
70.
Janos Karatson 《Applications of Mathematics》2005,50(3):277-290
A mesh independent bound is given for the superlinear convergence of the CGM for preconditioned self-adjoint linear elliptic problems using suitable equivalent operators. The results rely on K-condition numbers and related estimates for compact Hilbert-Schmidt operators in Hilbert space.This research was supported by the Hungarian National Research Fund OTKA under grant No. T043765. 相似文献