In many fields of applications such as reactive transport or ocean-atmosphere coupling, models with very different spatial and time scales have to be coupled. Optimized Schwarz Waveform Relaxation methods (OSWR), appl...
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In this article, we carry out the convergence analysis of the dual-mixed hybridized finite volume scheme proposed in (Marco Brera et al., Comput. Methods Appl. Mech. Eng., in press, 2010) for the numerical approximati...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
In this article, we carry out the convergence analysis of the dual-mixed hybridized finite volume scheme proposed in (Marco Brera et al., Comput. Methods Appl. Mech. Eng., in press, 2010) for the numerical approximation of transport problems in symmetrizable form. Using the results of (Micheletti et al., SIAM J. Sci. Comput., 23-1:245-270, 2001;Brezzi et al., Discretization of semiconductor device problems (i), Elsevier North-Holland, Amsterdam, 2005) optimal error estimates are obtained for the scalar unknown and the flux in the appropriate graph norm, while using the techniques and analysis of (Arnold and Brezzi, Math. Modeling Numer. Anal., 19-1:7-32, 1985;Brezzi and Fortin, Mixed and Hybrid Finite Element Methods, Springer, New York, 1991) the superconvergence of the hybrid variable and of its post-processed (nonconforming) reconstruction are proved. Numerical experiments are included to support the theoretical conclusions.
We apply a recently proposed [5] robust overlapping Schwarz method with a certain spectral construction of the coarse space in the setting of element agglomeration algebraic multigrid methods (or agglomeration AMGe) f...
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ISBN:
(纸本)9783642113031
We apply a recently proposed [5] robust overlapping Schwarz method with a certain spectral construction of the coarse space in the setting of element agglomeration algebraic multigrid methods (or agglomeration AMGe) for elliptic problems with high-contrast coefficients. Our goal is to design multilevel iterative methods that converge independent of the contrast in the coefficients. We present simplified bounds for the condition number of the preconditioned operators. These bounds imply convergence that is independent of the contrast. In the presented preliminary numerical tests, we use geometric agglomerates;however, the algorithm is general and offers some simplifications over the previously proposed spectral agglomerate AMGe methods (cf., [2, 3]).
Schwarz waveform relaxation methods have been studied for a wide range of scalar linear partial differential equations (PDEs) of parabolic and hyperbolic type. They are based on a space-time decomposition of the compu...
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ISBN:
(纸本)9783642113031
Schwarz waveform relaxation methods have been studied for a wide range of scalar linear partial differential equations (PDEs) of parabolic and hyperbolic type. They are based on a space-time decomposition of the computational domain and the subdomain iteration uses an overlapping decomposition in space. There are only few convergence studies for non-linear PDEs. We analyze in this paper the convergence of Schwarz waveform relaxation applied to systems of semi-linear reaction-diffusion equations. We show that the algorithm converges linearly under certain conditions over long time intervals. We illustrate our results, and further possible convergence behavior, with numerical experiments.
We present a new class of coarse spaces for two-level additive Schwarz preconditioners that yield condition number bound independent of the contrast in the media properties. These coarse spaces are an extension of the...
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ISBN:
(纸本)9783642113031
We present a new class of coarse spaces for two-level additive Schwarz preconditioners that yield condition number bound independent of the contrast in the media properties. These coarse spaces are an extension of the spaces discussed in [3]. Second order elliptic equations are considered. We present theoretical and numerical results. Detailed description of the results and numerical studies will be presented elsewhere.
Motivated by the numerical simulation of particulate flow with slip boundary conditions at the interface fluid/particles, our goal, in this publication, is to discuss a fictitious domain method for the solution of lin...
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In this study, we present the details of a Legendre series truncation method where the stream function and vorticity are expanded in terms of associated Legendre functions to calculate the secondary currents induced b...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
In this study, we present the details of a Legendre series truncation method where the stream function and vorticity are expanded in terms of associated Legendre functions to calculate the secondary currents induced by a vibrating spherical particle. The time-dependent differential equations which result from the expansions are solved using a Crank-Nicolson numerical scheme.
In this paper the numerical study of a simplified model of airflow through glot- tal region of the human vocal tract is addressed and the self-oscillating vocal fold is modelled. The main attention is paid to comparis...
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In the numerical simulation of electromagnetic wave radiation from an antenna, the antenna is assumed to be a perfectly conducting obstacle. It was shown numerically that the antenna can be effectively modeled by a hi...
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ISBN:
(纸本)9783642113031
In the numerical simulation of electromagnetic wave radiation from an antenna, the antenna is assumed to be a perfectly conducting obstacle. It was shown numerically that the antenna can be effectively modeled by a highly conducting region occupied by it. The Finite Difference Time Domain method combined with Perfectly Matched Layer gives a flexible numerical methodology for this problem. We apply the method to analyze several radiation problems with different types of antennas such as a birdcage and the Yagi types where the delta gap type power supply model is adopted. For treating an unbounded outer region numerically, we apply a newly developed technique to discretize the PML region with little artificial reflection. Theoretical justification of this procedure for a 1D case was presented in DD17, and effectiveness of this technique was also demonstrated numerically for 2D and 3D cases. We observe a good 3D numerical performance of the method and confirm its usefulness though theoretical justification remains as a future problem.
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