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Sunday, August 2, 2020 | History

3 edition of **An assessment of linear versus non-linear multigrid methods for unstructured mesh solvers** found in the catalog.

An assessment of linear versus non-linear multigrid methods for unstructured mesh solvers

- 398 Want to read
- 19 Currently reading

Published
**2001**
by ICASE, NASA Langley Research Center, Available from NASA Center for Aerospace Information in Hampton, VA, Hanover, MD
.

Written in English

- Unstructured grids (mathematics),
- Multigrid methods.,
- Linear systems.,
- Nonlinearity.,
- Algorithms.,
- Computational grids.

**Edition Notes**

Statement | Dimitri J. Mavriplis ; prepared for Langley Research Center under contract NAS1-97046. |

Series | ICASE report -- no. 2001-12., [NASA contractor report] -- NASA/CR-2001-210870., NASA contractor report -- NASA CR-210870. |

Contributions | Institute for Computer Applications in Science and Engineering. |

The Physical Object | |
---|---|

Format | Microform |

Pagination | 1 v. |

ID Numbers | |

Open Library | OL16031851M |

For a long time, these methods have been developed concurrently, but quite independently of general-purpose Krylov subspace solvers. However, multigrid techniques, in particular algebraic multigrid (AMG) methods originally designed as standalone solvers, can be very good preconditioners for Krylov by: In this paper, we study the effect the choice of mesh quality metric, preconditioner, and sparse linear solver have on the numerical solution of elliptic partial differential equations (PDEs). We smoothe meshes on several geometric domains using various quality metrics and solve the associated elliptic PDEs using the finite element by: 2.

A simple but effective relaxation technique is proposed in multigrid prolongation procedure for solving non-linear equations. The key procedure is relaxing the corrections to be prolonged from coarse to fine grid level. The computational results of two-dimensional convective-diffusion problems indicate that it performs well for both single variable problem solvers and multi-variables coupling. I would like to hear users views on the observed differences when using direct solvers vs iterative linear solvers for highly non-linear problems in either structural or fluid dynamic problems. The more non-linear the better!!! I am fully aware of the well known academic differences of speed, memory, robustness and accuracy etc.

A Survey of Parallelization Techniques for Multigrid Solvers Edmond Chow, Robert D. Falgout, Jonathan J. Hu, roandUlrikeMeierYang This paper surveys the techniques that are necessary for constructing compu-tationally e cient parallel multigrid solvers. Both geometric and algebraicmethods areconsidered. Multigrid methods for convection di usion problems on Shishkin meshes are discussed in [21,20], where a scalable multigrid scheme is introduced. For reaction-di usion problems, most of the multigrid literature focuses on the case of a singularly perturbed problem discretized on a uniform or quasi-uniform mesh. For example, in [36], it is shown.

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Scale unstructured mesh computations, where memory is the limiting factor, non-linear m ultigrid metho ds are indeed the only viable solution strategies [13]. On the other hand, in cases where the non-linear residual ev aluation is costly, linear m ultigrid metho ds ma y b ecome more attractiv eon a cpu-time e ciency basis, since for a xed stencil, the cost of Jacobian-v.

When an exact linearization is employed, the linear and nonlinear multigrid methods asymptotically converge at identical rates and the linear method is found to Cited by: LINEAR VS NONLINEAR MULTIGRID METHODS Newton solution strategies for nonlinear problems incorporating linear multigrid solvers may fail when the initial guess is far removed from the domain of convergence of the non-linear problem, and globalization methods may be required to ensure a convergent Size: KB.

These methods can be used in a combined approach, where for example a Newton-type method can be used as smoother for a FAS and a linear or a nonlinear multigrid can be. When an approximate linearization is employed, as in the Navier-Stokes cases, the relative e ciency of the linear approach versus the non-linear approach depends both on the degree to which the linear system approximates the full Jacobian as well as the relative cost of linear versus non-linear multigrid cycles.

When an exact linearization is employed, the linear and non-linear multigrid methods converge at identical rates, asymptotically, and the linear method is found to Author: Dimitri J. Mavriplis. These include discretization methods, solution methods such as multigrid and implicit methods for steady-state and time-accurate simulations, unstructured grid generation techniques and adaptive and moving mesh strategies.

We are also interested in design optimization methods, and the efficient solution of coupled fluid-structural problems. 3 Outline 1. Typical design of CFD solvers 2. Methods for Solving Linear Systems of Equations 3.

Geometric Multigrid 4. Algebraic MultigridFile Size: KB. [Show full abstract] directly, a linear multigrid method which is used to solve the linear system arising from a Newton linearization of the non-linear system, and a hybrid scheme which is based.

An Assessment of Linear Versus Nonlinear Multigrid Methods for Unstructured Mesh Solvers Journal of Computational Physics, Vol. No. 1 An assessment of linear versus non-linear multigrid methods for unstructured meshCited by: Abstract The efficiency of three multigrid methods for solving highly non‐linear diffusion problems on two‐dimensional unstructured meshes is examined.

The three multigrid methods differ mainly in. Dimitri J. Mavriplis, An assessment of linear versus nonlinear multigrid methods for unstructured mesh solvers, Journal of Computational Physics, v n.1, p, January 1, L.

Botti, A choice of forcing terms in inexact Newton iterations with application to pseudo-transient continuation for incompressible fluid flow computations Cited by: Get this from a library.

An assessment of linear versus non-linear multigrid methods for unstructured mesh solvers. [Dimitri Mavriplis; Institute for. Mavriplis DJ () An assessment of linear versus nonlinear multigrid methods for unstructured mesh solvers.

J Comput Phys (1)– MathSciNet CrossRef zbMATH Google Scholar Merkle CL, Choi Y-H () Computation of low-speed compressible flows with time marching by: 1. To clarify, geometric multigrid actually discretizes the problem on a series of grids whereas algebraic multigrid simply works with the linear system.

When working with unstructured grids it is really difficult to define a series of meshes for geometric multigrid so algebraic multigrid. The rest of this blog post will focus on discussing the main ideas behind multigrid methods, as they are the most powerful of methods.

Why Multigrid Methods Are Necessary In order to introduce you to the basic ideas behind this solution method, I will present you with numerical experiments exposing the intrinsic limitations of iterative methods. Effects of Flow Instabilities on the Linear Analysis of Turbomachinery Aeroelasticity.

Developing and Using a Geometric Multigrid, Unstructured Grid Mini-Application to Assess Many-Core Architectures. An assessment of linear versus non-linear multigrid methods for unstructured by: Multigrid methods use several grids of different grid size covering the same computational fluid domain.

Iterative solvers determine in each iteration (relaxation) a better approximation to the exact solution. The difference between the exact solution and the approximation is called residual (error). the non-linear full approximation scheme (FAS) developed by Brandt in [2]. InHoppe developed a solver for obstacle problems which employs a multigrid method to solve reduced linear algebraic systems in [13].

A later multigrid approach for obstacle problems was called the monotone multigrid method, developed by Kornhuber in [19]. McAdams et al. / A parallel multigrid Poisson solver for ﬂuids simulation on large grids ample, [MCP09,KFCO06,FOK05,ETK07] use conform-ing tetrahedralizations to accurately enforce boundary con-ditions, [LGF04] uses adaptive octree-based discretization, and [CFL07] makes use of tetrahedralized volumes for free surface Size: 2MB.

Introduction to Multigrid Methods Given a linear system TΔxu = f construct sequence um →u Now recall the following deﬁnitions The Good The solution is deﬁned by TΔxu = f Mesh widths (step size) ℎ and H, respectively Introduction to Multigrid Methods – p/the non-linear residual in a given number of grid sweeps, but that the linear solver is more efficient in cpu time due to the lower cost of linear versus non-linear grid sweeps.

Key words, non-linear, unstructured, multigrid Subject classification. Applied and Numerical Mathematics 1. Introduction.tive mesh reﬁnement and an optimal multigrid solver to achieve this efﬁciency. The novel contribution of this work lies in the manner in which these two techniques are combined.

In particular the multigrid solver provides a natural and simple method of handling grid .