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71.
Sven Beuchler 《Numerical Linear Algebra with Applications》2003,10(8):721-732
From the literature it is known that the conjugate gradient method with domain decomposition preconditioners is one of the most efficient methods for solving systems of linear algebraic equations resulting from p‐version finite element discretizations of elliptic boundary value problems. One ingredient of such a preconditioner is a preconditioner related to the Dirichlet problems. In the case of Poisson's equation, we present a preconditioner for the Dirichlet problems which can be interpreted as the stiffness matrix Kh,k resulting from the h‐version finite element discretization of a special degenerated problem. We construct an AMLI preconditioner Ch,k for the matrix Kh,k and show that the condition number of C Kh,k is independent of the discretization parameter. This proof is based on the strengthened Cauchy inequality. The theoretical result is confirmed by numerical examples. Copyright © 2003 John Wiley & Sons, Ltd. 相似文献
72.
Hoonjoo Kim Sung‐Jin Lee Hae‐Soo Oh 《Numerical Methods for Partial Differential Equations》2003,19(3):399-420
The method of auxiliary mapping (MAM), introduced by Babu?ka and Oh, was proven to be very successful in dealing with monotone singularities arising in two‐dimensional problems. In this article, in the framework of the p‐version of FEM, MAM is presented for one‐dimensional elliptic boundary value problems containing singularities. Moreover, in order to show the effectiveness of MAM, a detailed proof of an error estimate is also presented, which gives a sharp error bound of MAM. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 399–420, 2003. 相似文献
73.
Based on the Rytov approximation of light propagation in weak turbulent atmosphere,the closed-form expressions of field and average irradiance of each one of the four fundamental families of Helmholtz-Gauss (HzG)beams:cosine-Gauss beams,stationary Mathieu-Gauss beams,stationary parabolic-Gauss beams,and Bessel-Gauss beams,which are propagating in weak turbulent atmosphere,are obtained.The results show that the field and average irradiance can be written as the product of four factors:complex amplitude depending on the z-coordinate only,a Ganssian beam.a factor of complex phase perturbation induced by atmospheric turbulence,and a complex scaled version of the transverse shape of the non-diffracting beam.The effect of weak atmospheric turbulence on irradiance distribution of the HzG beam can be ignored. 相似文献
74.
We study the uniform approximation of boundary layer functions for , , by the and versions of the finite element method. For the version (with fixed mesh), we prove super-exponential convergence in the range . We also establish, for this version, an overall convergence rate of in the energy norm error which is uniform in , and show that this rate is sharp (up to the term) when robust estimates uniform in are considered. For the version with variable mesh (i.e., the version), we show that exponential convergence, uniform in , is achieved by taking the first element at the boundary layer to be of size . Numerical experiments for a model elliptic singular perturbation problem show good agreement with our convergence estimates, even when few degrees of freedom are used and when is as small as, e.g., . They also illustrate the superiority of the approach over other methods, including a low-order version with optimal ``exponential" mesh refinement. The estimates established in this paper are also applicable in the context of corresponding spectral element methods.
75.
We consider the numerical approximation of singularly perturbed elliptic boundary value problems over nonsmooth domains. We use a decomposition of the solution that contains a smooth part, a corner layer part and a boundary layer part. Explicit guidelines for choosing mesh‐degree combinations are given that yield finite element spaces with robust approximation properties. In particular, we construct an hp finite element space that approximates all components uniformly, at a near exponential rate. © 1999 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 15: 63–89, 1999 相似文献
76.
提出了一个MCNP-3a的微机版本,它具有绘图功能、用户界面发好,介绍了这个微机版本的结构和实现办法,所有例题的计算结果正确。 相似文献
77.
In terms of the coherent state evolution in phase space, we present a quantum mechanical version of the classical Liouville theorem. The evolution of coherent state from |z〉to |sz-rz*〉angle corresponds to the motion from a point z(q,p) to another point sz-rz* with |s|2-|r|2=1. The evolution is governed by the so-called Fresnel operator U(s,r) recently proposed in quantum optics theory, which classically corresponds to the matrix optics law and the optical Fresnel transformation and obeys the group product rules. In another word, we can recapitulate the Liouville theorem in the context of quantum mechanics by virtue of coherent state evolution in phase space, which seems to be a combination of quantum statistics and quantum optics. 相似文献
78.
本文针对带有随机杨氏模量和荷载的平面线弹性问题,提出了一类随机弱Galerkin有限元方法.先利用Karhunen-Loève展开把随机项参数化,将方程转化为一个确定性问题;再采用弱Galerkin有限元法和k-/p-型方法分别离散空间区域和随机场.在弱Galerkin离散中,用分片s(s≥1)和s+1次多项式逼近单元... 相似文献
79.
An experimental approach to the study of the sedimentation of dispersed particles in a centrifugal field 总被引:1,自引:0,他引:1
Summary On the basis of an especially developed centrifuge, a PC-controlled separation analyser has been assembled for the continuous
registration of particles' sedimentation process in a fluid, caused by centrifugal acceleration. The system enables the parallel
investigation of up to eight samples. During the centrifugation, the radial and temporal variation of light transmission through
the samples is registered by means of a CCD line detector. Experiments were carried out with the separation analyser on manipulated
rigid and sphered red blood cells for the verification of an established one-dimensional mixture fluid model. In particular,
the influence of particle volume concentration as well as of the angular velocity on the sedimentation process was investigated.
Justification could be furnished for the one-dimensional model based on the theory of kinematic waves and shocks. In addition,
an algorithm has been developed for the experimental determination of the suspension's effective or apparent viscosity.
Received 20 March 2001; accepted for publication 23 August 2001
RID="
ID=" This work is an abridged version of a part of the first author's PhD thesis. The study was supported in part by the
German Federal Ministry of Education and Research (project 03 TOU 2063) and the foundation Deutsche Forschungsgemeinschaft
(project Le 734/1–2). 相似文献
80.
Hae‐Soo Oh Bongsoo Jang Yichung Jou 《Numerical Methods for Partial Differential Equations》2003,19(3):301-326
Recently Babus?ka‐Oh introduced the method of auxiliary mapping (MAM) which efficiently handles elliptic boundary value problems containing singularities. In this paper, a special weighted residue method, the Weighted Ritz‐Galerkin Method (WRGM), is investigated by introducing special weight functions. Together with this method, MAM is modified to yield highly accurate finite element solutions to general elliptic boundary value problems on the exterior of bounded domains at low cost. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 301–326, 2003. 相似文献