2 edition of study of multigrid methods with application to convection-diffusion problems found in the catalog.
study of multigrid methods with application to convection-diffusion problems
|Statement||Dafik ; supervised by D.J. Silvester.|
|Contributions||Silvester, D. J., Mathematics.|
In this paper, we propose an extrapolation full multigrid (EXFMG) algorithm to solve the large linear system arising from a fourth-order compact difference discretization of two-dimensional (2D) convection diffusion equations. A bi-quartic Lagrange interpolation for the solution on previous coarser grid is used to construct a good initial guess on the next finer grid for V- or W-cycles. On Adaptive Eulerian-Lagrangian Method for Linear Convection-Diffusion Problems X. Hu, Y.-J. Lee, J. Xu and C. Zhang J. Sci. Comput., 58(1), () A Parallel Auxiliary Grid Algebraic Multigrid Method for Graphic Processing Units.
Algebraic multigrid (AMG) is a very efficient algorithm for solving large problems on unstructured grids. While much of it can be parallelized in a straightforward way, some components of the classical algorithm, particularly the coarsening process and some of the most efficient smoothers, are highly sequential, and require new parallel approaches. Here we briey review the multigrid method for solving boundary value problems (BVPs),as wellas the relevant fea-tures of modern graphics architectures. Boundary value problems and the multigrid algorithm Many physical problems require solving boundary value problems (BVPs) of the form: Lf = f (1) where L is some operator acting on an.
1. Introduction. Convection-diffusion problems describe important physical processes such as contaminant transport. The numerical solution of such problems, in particular in the case of dominating convection, has attracted much attention, and it is now widely appreciated what role stabilization techniques have to play. Nonlocal convection-diffusion problems and finite element approximations with H. Tian and L. Ju, Comp. Meth. Appl. Mech. Eng., , 60–78, Robust discretization of nonlocal models related to peridynamics, with X. Tian, in Meshfree Methods for Partial Differential Equations VII, Lecture Notes in Computational Science and Engineering.
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The algebraic variational multiscale–multigrid method is then particularly analyzed for convection–diffusion problems. The present initial study focuses on exploiting the methodical aspects of the new framework by developing a fine-scale discontinuity Cited by: One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.).
The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other problems. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.).
The book also contains a complete presentation of the multi-grid method of the second kind, which has important applications to integral equations (e.g. the "panel method") and to numerous other : Springer-Verlag Berlin Heidelberg. A multigrid method based on graph matching for convection-diffusion equations; H.
Kim, J. Xu, and L. Zikatanov Numer. Linear Algebra Appl. 10 () Successive subspace correction method for singular system of equations. In the literature, there are many different algebraic multigrid methods that have been developed from different perspectives.
In this paper we try to develop a unified framework and theory that can be used to derive and analyse different algebraic multigrid methods in a coherent by: Extrapolation cascadic multigrid method and multiscale multigrid computation.
The resulting sparse linear system from the FOC scheme can be solved by iterative methods. One of the most efficient ones for elliptic partial differential equations is multigrid methods since its convergence rate is independent of the grid basic idea of multigrid methods is to use coarse grid.
The fast multigrid solution of an optimal control problem governed by a convection–diffusion partial-integro differential equation is investigated. This optimization problem considers a cost functional of tracking type and a constrained distributed control.
The optimal control sought is characterized by the solution to the corresponding optimality system, which is approximated. Yongbin Ge and Fujun Cao, Multigrid method based on the transformation-free HOC scheme on nonuniform grids for 2D convection diffusion problems.
Often, this problem can be solved analytically. Multigrid methods are solvers for linear system of equations that arise, e.g., in the discretization of partial di erential equations. For this reason, discretizations of () will be considered: a nite di erence method and a nite element method.
MULTIGRID METHODS c Gilbert Strang For the larger problem on the ﬁne grid, iteration converges slowly to. MULTIGRID METHODS c Gilbert Strang the low frequency smooth part of the solution u. The multigrid method transfers the current residual rh = b − Auh to the coarse grid. We iterate a few times on that 2h.
A partial semi-coarsening multigrid method based on the high order compact (HOC) difference scheme on nonuniform grids is developed to solve the two dimensional (2D) convection-diffusion problems.
Multigrid methods are often used for solving partial differential equations. This book introduces and analyzes the multigrid approach. The approach used here applies to both test problems on rectangular grids and to more realistic applications with complicated grids and.
For linear convection equation, it can predict whether the solution will grow or damp but it may have some problem when the solution is having multiple wave number.
I personally don't agree with the linear spectral analysis of RK methods. If you like it, you can improve this analysis. I have carried a small case study on this analysis.
Fujun Cao, Yongbin Ge and Hai-Wei Sun, Partial semi-coarsening multigrid method based on the HOC scheme on nonuniform grids for the convection–diffusion problems, International Journal of Computer Mathematics, 94, 12, (), (). Multigrid Method Matlab Example. The use of the multigrid method (MGM) with the STS-based smoothers for solving convection–diffusion problems has been studied in.
The convergence of the MGM with the STS-based smoothers has also been proved in this research. The local Fourier analysis of the MGM with the triangular skew-symmetric smoothers has been performed in.
The results. A STUDY of multigrid smoothers used in compressible CFD based on the convection diffusion equation Birken, Philipp LU; Bull, Jonathan and Jameson, Antony () 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2.
p Mark; Abstract. We look at multigrid methods for unsteady viscous compressible flows. 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 ingredients of such a preconditioner are a preconditioner for the Schur complement, a.
This chapter concerns iterative methods for solution of discrete convection–diffusion equations. It discusses Krylov subspace methods, principally the generalized minimum residual method, together with preconditioning strategies and multigrid methods, including convergence analysis of these methods.
Competing numerical methods include the Jacobian-free Newton-Krylov scheme that Wang et al. [15, 16] used with primitive variables to examine linear stability of natural convection for axially and laterally heated cylinders.
The geometric multigrid method (GMG) is applied for this study and the. An iterative solution method, in the form of a preconditioner for a Krylov subspace method, is presented for the Helmholtz equation. The preconditioner is based on a Helmholtz-type differential operator with a complex term. A multigrid iteration is used for approximately inverting the preconditioner.in theory and application of important values, but also innovative, advanced and applied.
In book, Kovarik, K. sets his sights on reviewing the whole group of numerical methods from the oldest (the finite differences method), and discusses the basic equations of a groundwater flow and of the transport of pollutants in a porous medium.Coupling p-multigrid to geometric multigrid for discontinuous Galerkin formulations of the convection–diffusion equation Journal of Computational Physics, Vol.No.
10 Implicit LU-SGS algorithm for high-order methods on unstructured grid with p-multigrid strategy for solving the steady Navier–Stokes equations.