This paper deals with the aim of coupling multigrid generation of boundary-fitted grids with an effective full multigrid technique. For the last years we have been developing the generation of structured grids by the ...
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This paper deals with the aim of coupling multigrid generation of boundary-fitted grids with an effective full multigrid technique. For the last years we have been developing the generation of structured grids by the definition of specific elliptic systems and the application of multigrid computation to their solution. In this paper we present a Full-fas multigrid algorithm for the generation of curvilinear coordinate systems on physical domains. We adopt standard central differencing for the approximation of the nonlinear generating 2D and 3D systems, full approximation storage (fas) algorithms to solve the resulting discrete equations and Full multigrid computation to obtain a better initial guess for the already developed multigrid algorithms. In the paper we introduce the elliptic grid generation models, the multigrid computation and the full multigrid algorithm, based on the nested iteration technique. Then we detail the multigrid components, and therefore the available forms, of the basic Full-fas algorithm and we comment numerical results with the help of figures. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.
A numerical method is presented in order to analyze steady viscoelastic fluid flows. A finite difference technique has been introduced on a non-uniform staggered grid system by adopting an upwind scheme to discretize ...
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A numerical method is presented in order to analyze steady viscoelastic fluid flows. A finite difference technique has been introduced on a non-uniform staggered grid system by adopting an upwind scheme to discretize the constitutive equations where the stress tenser can be decomposed into Newtonian and non-Newtonian parts. In both, the fas (Full Approximation Storage) multigrid algorithm is used, The performance of this method is investigated for the stick-slip and the four-to-one abrupt plane contraction problems. We have selected Oldroyd B and Phan Thien-Tanner fluid models for the calculations. Some results prove that the Oldroyd model is not totaly appropriate. (C) 2001 Elsevier Science B.V. All rights reserved.
A computationally efficient multigrid algorithm for upwind edge-based finite element schemes is developed for the solution of the two-dimensional Euler and Navier-Stokes equations on unstructured triangular grids. The...
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A computationally efficient multigrid algorithm for upwind edge-based finite element schemes is developed for the solution of the two-dimensional Euler and Navier-Stokes equations on unstructured triangular grids. The basic smoother is based upon a Galerkin approximation employing an edge-based formulation with the explicit addition of an upwind-type local extremum diminishing (LED) method. An explicit time stepping method is used to advance the solution towards the steady state. Fully unstructured grids are employed to increase the flexibility of the proposed algorithm. A full approximation storage (fas) algorithm is used as the basic multigrid acceleration procedure. Copyright (C) 1999 John Wiley & Sons, Ltd.
A finite volume, time-marching for solving time-dependent viscoelastic flow in two space dimensions for Oldroyd-B and Phan Thien-Tanner fluids, is presented. A non-uniform staggered grid system is used. The conservati...
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A finite volume, time-marching for solving time-dependent viscoelastic flow in two space dimensions for Oldroyd-B and Phan Thien-Tanner fluids, is presented. A non-uniform staggered grid system is used. The conservation and constitutive equations are solved using the finite volume method with an upwind scheme for the viscoelastic stresses and an hybrid scheme for the velocities. To calculate the pressure field, the semi-implicit method for the pressure linked equation revised method is used. The discretized equations are solved sequentially, using the tridiagonal matrix algorithm solver with under-relaxation. In both, the full approximation storage multigrid algorithm is used to speed up the convergence rate. Simulations of viscoelastic flows in four-to-one abrupt plane contraction are carried out. We will study the behaviour at the entrance corner of the four-to-one planar abrupt contraction. Using this solver, we show convergence up to a Weissenberg number We of 20 for the Oldroyd-B model. No limiting Weissenberg number is observed even though a Phan Thien-Tanner model is used. Several numerical results are presented. Smooth and stable solutions are obtained for high Weissenberg number. Copyright (C) 2002 John Wiley Sons, Ltd.
This paper deals with the task of pricing European basket options in the p-resence of transaction costs. We develop a model that incorporates the illiquidity of the market into the classical two-assets Black-Scholes f...
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This paper deals with the task of pricing European basket options in the p-resence of transaction costs. We develop a model that incorporates the illiquidity of the market into the classical two-assets Black-Scholes framework. We perform a nu-merical simulation using finite difference method. We consider a nonlinear multigrid method in order to reduce computational costs. The objective of this paper is to inves-tigate a deterministic extension for the Barles' and Soner's model and to demonstrate the effectiveness of multigrid approach to solving a fully nonlinear two dimensional Black-Scholes problem.
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