共查询到20条相似文献,搜索用时 4 毫秒
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The multigrid method based on multi-stage Jacobi relaxation, earlier developed by the authors for structured grid calculations with Euler equations, is extended to unstructured grid applications. The meshes are generated with Delaunay triangulation algorithms and are adapted to the flow solution. 相似文献
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The recently proposed simulation framework of interface relaxation for developing multi-domain multi-physics simulation engines is considered. An experimental study of the behavior of two representative interface relaxation methods is presented. Three linear and one non-linear elliptic two-dimensional PDE problems are considered and they are coupled with both cartesian and general decompositions. The characteristics and the effectiveness of the proposed collaborative PDE solving framework in general, and of the two interface relaxation methods in particular are shown. 相似文献
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Zhencheng Fan 《Applied mathematics and computation》2010,217(8):3903-3909
We propose in this paper the discrete time waveform relaxation method for the stochastic delay differential equations and prove that it is convergent in the mean square sense. In addition, the results obtained are supported by numerical experiments. 相似文献
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We apply a Runge-Kutta-based waveform relaxation method to initial-value problems for implicit differential equations. In the implementation of such methods, a sequence of nonlinear systems has to be solved iteratively in each step of the integration process. The size of these systems increases linearly with the number of stages of the underlying Runge-Kutta method, resulting in high linear algebra costs in the iterative process for high-order Runge-Kutta methods. In our earlier investigations of iterative solvers for implicit initial-value problems, we designed an iteration method in which the linear algebra costs are almost independent of the number of stages when implemented on a parallel computer system. In this paper, we use this parallel iteration process in the Runge-Kutta waveform relaxation method. In particular, we analyse the convergence of the method. The theoretical results are illustrated by a few numerical examples. 相似文献
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For subsonic flows and upwind-discretized, linearized 1-D Euler equations, the smoothing behavior of multigrid-accelerated point Gauss-Seidel relaxation is analyzed. Error decay by convection across domain boundaries is also discussed. A fix to poor convergence rates at low Mach numbers is sought in replacing the point relaxation applied to unconditioned Euler equations, by locally implicit time-stepping applied to preconditioned Euler equations. The locally implicit iteration step is optimized for good damping of high-frequency errors. Numerical inaccuracy at low Mach numbers is also addressed.The work reported was performed in the framework of the BRITE-EURAM Aeronautics R&D Programme of the European Communities (Contract No. AER2-CT92-0040). The work was started during the second author's visit to CWI in 1993. 相似文献
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Jun Zhang 《Applied mathematics and computation》1999,100(2-3):151-168
We analyze the standard multigrid method accelerated by a minimal residual smoothing (MRS) technique. We show that MRS can accelerate the convergence of the slow residual components, thus accelerates the overall multigrid convergence. We prove that, under certain hypotheses, MRS stabilizes the divergence of certain slow residual components and thus stabilizes the divergent multigrid iteration. The analysis is customarily conducted on the two-level method. 相似文献
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We investigate some simple finite element discretizations for the axisymmetric Laplace equation and the azimuthal component of the axisymmetric Maxwell equations as well as multigrid algorithms for these discretizations. Our analysis is targeted at simple model problems and our main result is that the standard V-cycle with point smoothing converges at a rate independent of the number of unknowns. This is contrary to suggestions in the existing literature that line relaxations and semicoarsening are needed in multigrid algorithms to overcome difficulties caused by the singularities in the axisymmetric Maxwell problems. Our multigrid analysis proceeds by applying the well known regularity based multigrid theory. In order to apply this theory, we prove regularity results for the axisymmetric Laplace and Maxwell equations in certain weighted Sobolev spaces. These, together with some new finite element error estimates in certain weighted Sobolev norms, are the main ingredients of our analysis.
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Agns Tourin 《Numerical Methods for Partial Differential Equations》2006,22(2):381-396
We explain how the exploitation of several kinds of operator splitting methods, both local and global in time, lead to simple numerical schemes approximating the solution of nonlinear Hamilton‐Jacobi equations. We review the existing local methods which have been used since the early 80's and we introduce a new method which is global in time. We show some numerical experiments. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006 相似文献
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Imanol Garcia-Beristain Lakhdar Remaki 《Numerical Methods for Partial Differential Equations》2023,39(1):329-355
Time efficiency is one of the more critical concerns in computational fluid dynamics simulations of industrial applications. Extensive research has been conducted to improve the underlying numerical schemes to achieve time process reduction. Within this context, this paper presents a new time discretization method based on the Adomian decomposition technique for Euler equations. The obtained scheme is time-order adaptive; the order is automatically adjusted at each time step and over the space domain, leading to significant processing time reduction. The scheme is formulated in an appropriate recursive formula, and its efficiency is demonstrated through numerical tests by comparison to exact solutions and the popular Runge–Kutta-discontinuous Galerkin method. 相似文献
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Yeping Li 《Journal of Mathematical Analysis and Applications》2008,342(2):1107-1125
In this paper, we investigate a multidimensional nonisentropic hydrodynamic (Euler-Poisson) model for semiconductors. We study the convergence of the nonisentropic Euler-Poisson equation to the incompressible nonisentropic Euler type equation via the quasi-neutral limit. The local existence of smooth solutions to the limit equations is proved by an iterative scheme. The method of asymptotic expansion and energy methods are used to rigorously justify the convergence of the limit. 相似文献
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We prove existence of solutions to the two-dimensional Euler equations with vorticity bounded and with velocity locally bounded but growing at infinity at a rate slower than a power of the logarithmic function. We place no integrability conditions on the initial vorticity. This result improves upon a result of Serfati which gives existence of a solution to the two-dimensional Euler equations with bounded velocity and vorticity. 相似文献
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Hao Chen Chengjian Zhang 《Applied mathematics and computation》2011,218(6):2619-2630
New and effective quadrature rules generated by boundary value methods are introduced. We employ the introduced quadrature rules to construct quadrature methods for the second kind Volterra integral equations and Volterra integro-differential equations. These methods are shown to be effective and possess excellent convergence properties. The nonlinear multigrid method is applied to solve the discrete systems derived from the introduced numerical scheme. Numerical simulations are presented and confirm the efficiency and accuracy of the methods. 相似文献
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XIAO Ling LI Fucai & WANG Shu Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China Department of Mathematics Nanjing University Nanjing China College of Applied Sciences Beijing University of Technology Beijing China 《中国科学A辑(英文版)》2006,49(2):255-266
We establish the convergence of the Vlasov-Poisson-Fokker-Planck system to the incompressible Euler equations in this paper. The convergence is rigorously proved on the time interval where the smooth solution to the incompressible Euler equations exists. The proof relies on the compactness argument and the so-called relative-entropy method. 相似文献
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We study a random Euler scheme for the approximation of Carathéodory differential equations and give a precise error analysis. In particular, we show that under weak assumptions, this approximation scheme obtains the same rate of convergence as the classical Monte–Carlo method for integration problems. 相似文献
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Dongho Chae 《Mathematische Zeitschrift》2007,257(3):563-580
We consider systems of deformed system of equations, which are obtained by some transformations from the system of incompressible
Euler equations. These have similar properties to the original Euler equations including the scaling invariance. For one form
of deformed system we prove that finite time blow-up actually occurs for ‘generic’ initial data, while for the other form
of the deformed system we prove the global in time regularity for smooth initial data. Moreover, using the explicit functional
relations between the solutions of those deformed systems and that of the original Euler system, we derive the condition of
finite time blow-up of the Euler system in terms of solutions of one of its deformed systems. As another application of those
relations we deduce a lower estimate of the possible blow-up time of the 3D Euler equations.
This research was supported partially by the KOSEF Grant no. R01-2005-000-10077-0 相似文献