The objective of this paper is to explain the principles of the design of a coarse space in a simplified way and by pictures. The focus is on ideas rather than on a more historically complete presentation. That can be...
A mixed multiscale finite element method (MsFEM) for wave equations is presented. Global information is used in the mixed MsFEM to construct multiscale basis functions. The solution of the wave equation smoothly depen...
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ISBN:
(纸本)9783642113031
A mixed multiscale finite element method (MsFEM) for wave equations is presented. Global information is used in the mixed MsFEM to construct multiscale basis functions. The solution of the wave equation smoothly depends on the global information. We investigate the relation between the smoothness of the global information and convergence rate of the mixed MsFEM.
A scalable FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithm for the Stokes problem is developed and analyzed. Advantages of this approach are a coarse problem without primal pressure unknowns...
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ISBN:
(纸本)9783642113031
A scalable FETI-DP (Dual-Primal Finite Element Tearing and Interconnecting) algorithm for the Stokes problem is developed and analyzed. Advantages of this approach are a coarse problem without primal pressure unknowns and the use of a relatively cheap lumped preconditioner. Especially in three dimensions, these advantages provide a more robust and faster FETI-DP algorithm. In three dimensions, the velocity unknowns at subdomain corners and the averages of velocity unknowns over common faces are selected as the primal unknowns in the FETI-DP formulation. A condition number bound of the form C(H/h) is established, where C is a positive constant which is independent of any mesh parameters and H/h is the number of elements across individual subdomains.
We consider a family of two-weight finite difference schemes for a time-dependent advection-diffusion problem. For a given uniform grid-spacing in time and space, and for a fixed value of advection and diffusion param...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
We consider a family of two-weight finite difference schemes for a time-dependent advection-diffusion problem. For a given uniform grid-spacing in time and space, and for a fixed value of advection and diffusion parameters, we demonstrate how to optimally choose these weights by means of the notion of an equivalent differential equation. We also provide a geometric interpretation of the weights. We present numerical results that demonstrate that the approach is superior to other commonly used methods that also fit into the framework of a two-weight scheme.
We present a refinement of a model due to Mondal and Mazumder [7] for dispersion of fine particles in an oscillatory turbulent flow. The model is based on the time-dependent advection-diffusion equation posed on a sem...
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ISBN:
(数字)9783642196652
ISBN:
(纸本)9783642196645
We present a refinement of a model due to Mondal and Mazumder [7] for dispersion of fine particles in an oscillatory turbulent flow. The model is based on the time-dependent advection-diffusion equation posed on a semi-infinite strip, whose solution represents the concentration of particles over time and down-stream distances. The problem is solved by first mapping to a finite domain and then, using a monotone finite difference method on a tensor product, piecewise uniform mesh. The numerical results obtained for the related steady-state problem are compared with experimental data.
Tissue stiffness is one of the qualitative properties to distinguish abnormal tissues from normal tissues, and the stiffness changes are generally described in terms of the Lamé coefficient. In this paper, an all...
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Nonlinear singularly perturbed interior layer problems are examined. Numerical results are presented for a numerical method consisting of a monotone scheme on a Shishkin mesh refined around the approximate location of...
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ISBN:
(纸本)9783642196645
Nonlinear singularly perturbed interior layer problems are examined. Numerical results are presented for a numerical method consisting of a monotone scheme on a Shishkin mesh refined around the approximate location of the interior layer.
Adaptive solvers are now widely used in numerical simulations of lots of problems for better accuracy with minimal computational cost. The reasons for choosing adaptive method for the problem (1) are two-folded. First...
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