
	Where results make sense

Topic: Multigrid

Related Topics

Ordinary differential equation

Finite element method

Finite difference

Finite volume method

Partial differential equation

Numerical analysis

Difference operator

Integral equation

Computational Fluid Dynamics

Richard Courant

Elliptic partial differential equation

Fluid Dynamics

Taylor series

Fat Boy Slim

Mindfuck

In the News (Fri 12 Mar 10)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Multigrid (Site not responding. Last check: 2007-10-09)
		The multigrid methods is a group of algorithms for solving differential equations using a hierarchy of discretization.
		Multigrid Methods "An Introduction to Multigrid Methods" by Pieter Wesseling.
		MultiGrid Galerkin Hierarchical Adaptive Triangles (MGGHAT) Solve second order two dimensional elliptic partial differential equations, using adaptive refinement of second, third, or fourth order elements, and multigrid solution techniques.
	www.serebella.com /encyclopedia/article-Multigrid.html (242 words)

	Multigrid - Wikipedia, the free encyclopedia
		It has been suggested that this article or section be merged with Multigrid method.
		In mathematics, more specifically in numerical analysis, multigrid methods are a group of algorithms for solving differential equations using a hierarchy of discretizations.
		In order for the multigrid methods to be applicable, one needs to make several assumptions.
	en.wikipedia.org /wiki/Multigrid (268 words)

	Daniela Vasileva's Research, part 2 (Site not responding. Last check: 2007-10-09)
		The multigrid method is implemented in conjunction with a third-order upwind characteristics-based scheme for the discretization of the convection terms, and a fourth-order Runge-Kutta scheme for time integration.
		The multigrid acceleration is assessed in contrast to the single-grid and mesh-sequencing algorithms.
		The effects of various multigrid components on the convergence acceleration, such as prolongation operators as well as pre- and post-relaxation iterations, are also investigated.
	www.math.bas.bg /~vasileva/res2.html (377 words)

	CS267: Notes for Lecture 17, Mar 12 1996
		Multigrid is a divide-and-conquer algorithm for solving the discrete Poisson equation.
		To understand why Multigrid works so well, we need to think of the solution vector, and the error in the solution, as linear combinations of certain basis vectors, which are essentially sine-curves of different frequencies, the way one does in Fourier analysis.
		The authors explored variations on Full Multigrid, where they did varying numbers of calls to MGV (a V-cycle) within the loop of FMG, using estimates of convergence rate and parallel efficiencies to pick the optimal number of MGV calls; they were able to increase the efficiencies to.01 and.47, respectively.
	www.cs.berkeley.edu /~demmel/cs267/lecture25/lecture25.html (3578 words)

	Multigrid Workbench: Multigrid Methods (Site not responding. Last check: 2007-10-09)
		Multigrid (MG) methods are fast linear iterative solvers based on the multilevel or multi-scale paradigm.
		Multigrid does not depend on the separability of the equations or other special properties of the equation.
		In all these cases, multigrid exhibits a convergence rate that is independent of the number of unknowns in the discretized system.
	www.mgnet.org /mgnet/tutorials/xwb/mg.html (311 words)

	[No title]
		Date: 18 Oct 1999 19:33:22 GMT Newsgroups: sci.math.num-analysis Keywords: different approaches in algebraic and geometric multigrid methods Classical multigrid method, geometric multigrid method, and standard multigrid method(s) mean that a series of grids are generated and the partial differential equation is discretized on all of these grid.
		For algebraic multigrid method, you are essentially solving a linear system, you do not even have to know where the linear system come from.
		The approaches used in geometric multigrid methods, such as coarse-grid correction, full approximation scheme, or nested iterations are not fully defined in algebraic multigrid methods (with the same meanings as in geometric methods).
	www.math.niu.edu /~rusin/known-math/99/multigrid (675 words)

	MGNet Home Page
		Multigrid has the property of using linear time and space to solve a collection of interesting problems, thus making it a very fast, robust solver.
		Several multigrid conferences have a habit of publishing pre-proceedings or electronic proceedings.
		The Copper Mountain multigrid conferences (held on odd numbered years in April when the snow is still good for skiing) and the GAMM workshops on parallel multigrid (held in Germany and Austria from time to time at rather nice places) are examples of this.
	www.mgnet.org (785 words)

	Prometheus-1.x Introduction
		Prometheus is a highly parallel multigrid solver for the set of linear algebraic equations Ax=b that arise from three dimensional finite element discretizations of PDEs.
		Multigrid is known to be a highly effective method for solving the linear algebraic equations the arise from discretized analysis of partial differential equations (PDEs).
		Multigrid uses of a series of coarse grid approximations of the "fine" grid problem.
	www.cs.berkeley.edu /~madams/prom_intro.html (619 words)

	CFD Review \| How Multigrid Solver Acceleration Works
		The multigrid acceleration technique speeds up iterative solvers tremendously allowing for realistic CFD models which otherwise would not be feasible on today's computers.
		Enter the multigrid method which takes its name from the fact that it uses levels of grid coarsening to speed the solution.
		Another huge benefit of the multigrid method is that solution time is of order Nlog(N) where N is the number of points.
	www.cfdreview.com /features/01/11/28/2217256.shtml (1550 words)

	Research
		The research project is devoted to the development and analysis of a new multigrid method for solving systems of linear equations as they arise from discretisations of boundary value problems on complicated domains.
		The efficiency of multigrid methods is based on a multiscale discretisation of the problem.
		During this project, the convergence of multigrid methods with composite finite elements should be investigated and generalized to interesting problems as the Stokes equation and the biharmonic equation.
	www.math.unizh.ch /index.php?assi-forschung&no_cache=1&L=1&no_cache=1&key1=133&no_cache=1 (186 words)

	MGNet Codes
		This is a full multigrid method for the solution of an optimality system arising from optimal control of the solid fuel ignition model.
		Multigrid V or W cycles which use point, line(s), or planar relaxation and fully weighted residual restriction are available for algorithm tuning to obtain optimal multigrid performance.
		UG is a flexible software library for the development of adaptive multigrid methods on unstructured meshes in two or three spatial dimensions.
	www.cerfacs.fr /~douglas/mgnet-codes.html (1772 words)

	Multigrid Methods and Parallel Computation
		Multigrid techniques are among the most efficient, advanced methods for solving large scale problems arising in scientific and engineering computation.
		The theory and analysis of basic multigrid techniques is presented to set the direction of the course.
		Various multigrid and multilevel techniques are introduced and the performance of these methods is analyzed theoretically, where possible, and demonstrated numerically.
	home.gwu.edu /~mmg/math234.htm (482 words)

	MUDPACK: Multigrid Software for Elliptic Partial Differential Equations
		Multigrid iteration (see [12,13,15,17,18,20]) combines classical iterative techniques, such as Gauss-Seidel line or point relaxation, with subgrid refinement procedures to yield a method superior to the iterative techniques alone.
		Multigrid iteration requires less storage and computation than direct methods for nonseparable elliptic PDEs (e.g., see [7]) and is competitive with direct methods such as cyclic reduction [5,14,24,25] for separable equations.
		A conversation with Achi Brandt affirmed that the default multigrid options in MUDPACK are a good choice and that the use of deferred corrections in obtaining fourth-order approximations with multigrid is a reasonable strategy.
	www.scd.ucar.edu /css/software/mudpack (2421 words)

	Papers of Jürgen Fuhrmann (Site not responding. Last check: 2007-10-09)
		Incomplete factorizations and linear multigrid algorithms for the semiconductor device equations.
		A multigrid method for the solution of a convection - diffusion equation with rapidly varying coefficients.
		Multigrid FAS methods for the solution of systems of nonlinear partial differential equations occuring in semiconductor device simulation.
	www.wias-berlin.de /people/fuhrmann/papers.html (788 words)

	CFD Books Guide - An Introduction to Multigrid Methods
		Topics such as the basic multigrid principle, smoothing methods and their Fourier analysis, course grid approximation, multigrid cycles and results of multigrid theory are treated.
		Multigrid methods have developed rapidly over the past 25 years and are now a powerful tool for the efficient solution of elliptic and hyperbolic partial differential equations.
		The impact of multigrid methods on computational fluid dynamics and computational physics is considerable.
	www.cfd-online.com /Books/show_book.php?book_id=129 (360 words)

	An Algebraic Multigrid Solver for Analytical Placement With Layout Based Clustering
		We apply the algebraic multigrid method to solve the linear equations that arise from the analytical placement.
		A layout based clustering scheme is put forward to generate coarsening levels for the multigrid method.
		The experimental results show that the algebraic multigrid solver is promising for analytical placement.
	www.gigascale.org /pubs/477.html (313 words)

	Montreal Scientific Computing Days Feb 2005 (Site not responding. Last check: 2007-10-09)
		Multigrid methods are a class of numerical techniques to solve linear systems arising from discretization of PDEs using a heirarchy of discretization grids.
		The optimal complexity of multigrid has brought within the reach of simulation many scientific problems previously thought to be of intractable size.
		In the first part, we will see the mechanics of multigrid methods and explain why it leads to optimal algorithms, illustrating it on simple examples.
	www.math.mcgill.ca /humphries/research/scdays/SC05.html (274 words)

	9.7.1 Introduction
		In the multigrid method, a smoothed problem is projected to a coarser grid.
		In the full multigrid method, a coarser grid is also used to compute an initial guess for the multigrid iteration on a finer grid.
		Multigrid methods are best understood for elliptic problems, that is, the Poisson equation, stationary reaction-diffusion equations, implicit time-steps in parabolic problems, and so on.
	www.netlib.org /utk/lsi/pcwLSI/text/node215.html (422 words)

	MGNet Digest V3N07
		Mavriplis Three-dimensional unstructured multigrid for the {E}uler equations, AIAA J., 30 (1992), pp.
		Smith and A. Weiser Semicoarsening multigrid on a hypercube, SIAM J. Sci.
		The algorithm is a variant of the multigrid waveform relaxation method where the scalar ordinary differential equations that make up the kernel of computation are solved using a cyclic reduction type algorithm.
	www.tat.physik.uni-tuebingen.de /~mgnet/mgnet/digests.html/V3N07.html (1289 words)

	Multigrid (Site not responding. Last check: 2007-10-09)
		The multigrid methods is a group of algorithms for differential equations using a hierarchy of discretization.
		It is ideal for someone interested in multigrid methods but who doesn't want to get lost i...
		Multigrid Methods II: Proceedings of the 2nd European Conference on Multigrid Methods Held at Cologne, October 1-4, 1985 (Lecture Notes in Mathemati)
	www.freeglossary.com /Multigrid (243 words)

	deal.II library: Multigrid< VECTOR > Class Template Reference
		It is not clear, whether the paradigm of local smoothing we use is applicable to continuous elements with hanging nodes; in fact, most people you meet on conferences seem to deny this.
		The function which starts a multigrid cycle on the finest level is cycle().
		Perform a multigrid cycle with a vector which is already a level vector.
	www.dealii.org /developer/doxygen/deal.II/classMultigrid.html (835 words)

	Multigrid Methods
		Multigrid method: Solution method for linear systems based on restricting and extrapolating solutions between a series of nested grids.
		An analysis of multigrid methods is relatively straightforward in the case of simple differential operators such as the Poisson operator on tensor product grids.
		Many multigrid methods can be shown to have an (almost) optimal number of operations, that is, the work involved is proportional to the number of variables.
	www.netlib.org /linalg/html_templates/node129.html (514 words)

	[No title]
		Multigrid solvers for the Dirac equations arising in quantum field theory.
		Multigrid Monte-Carlo approaches for solving the high-dimensional (several-particle) Schrodinger equation by real-time path integrals.
		Multigrid methods for integral transforms and integro-differential equations, on adaptable grids, with applications to tribology.
	www.wisdom.weizmann.ac.il /~achi/gaussctr.html (514 words)

	Recent Development Of Multigrid Algorithms For Mixed And Nonconforming Methods For Second Order Elliptic Problems ... (Site not responding. Last check: 2007-10-09)
		Abstract: Multigrid algorithms for nonconforming and mixed finite element methods for second order elliptic problems on triangular and rectangular finite elements are considered.
		The construction of several coarse-to-fine intergrid transfer operators for nonconforming multigrid algorithms is discussed.
		6 The analysis of multigrid algorithms for nonconforming and m..
	citeseer.ist.psu.edu /24655.html (542 words)

	A Nonconforming Multigrid Method Using Conforming Subspaces - Lee (ResearchIndex) (Site not responding. Last check: 2007-10-09)
		Multigrid And Multilevel Methods For Nonconforming Rotated Q1..
		Equivalence Between and Multigrid Algorithms for Mixed and..
		Lee, A nonconforming multigrid method using conforming subspaces, Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, N. Melson et al., eds., NASA Conference Publication 3224, Part 1, 1993, 317--330.
	citeseer.ist.psu.edu /lee93nonconforming.html (481 words)

	Computer Science Colloquium (Site not responding. Last check: 2007-10-09)
		Multigrid computational techniques are known to be amongst the most efficient methods for the numerical solution of several classes of problems.
		Originally developed for partial differential equations in the 1970's, multigrid (more generally, multi-level) algorithms are currently employed, in academia and industry, as efficient solvers for an ever increasing variety of linear and nonlinear problems involving many variables.
		In this talk, the multigrid approach will be introduced for a toy example, followed by a presentation of a few of our recent developments and applications for problems in image analysis and processing, as time allows.
	www.cs.technion.ac.il /~colloq/20040323_14_30_Irad.html (173 words)

	[No title] (Site not responding. Last check: 2007-10-09)
		If anyone > could help me, I would really appreciate what you are after is known as "algebraic multigrid" and here come some papers: there are many papers on this subject, but typically also in these papers there is background of discretization methods involved, since otherwise the whole concept makes little sense.
		Furthermore, we apply these results to a multigrid version of the replacement process approach developed by Sumita and Rieders.
		The theory applies to algebraic multigrid processes, as well as to the usual geometric multigrid.
	www.math.niu.edu /~rusin/known-math/01_incoming/alg_multigrid (516 words)

	Multigrid iterative algorithm using pseudo-compressibility for three-dimensional mantle convection with strongly ... (Site not responding. Last check: 2007-10-09)
		Multigrid iterative algorithm using pseudo-compressibility for three-dimensional mantle convection with strongly variable viscosity
		Equations for conservation of mass and momentum for highly viscous and incompressible uids are solved iteratively by a multigrid method in combination with pseudo-compressibility and local time stepping techniques.
		This algorithm is suitable for large-scale three-dimensional numerical simulations, because (i) memory storage for any additional matrix is not required and (ii) vectorization and parallelization are straightforward.
	www.es.jamstec.go.jp /esc/research/Solid/members/kameyama/papers/kamejcp1abs.html (218 words)

Try your search on: Qwika (all wikis)