An approach to solving systems of equations by projecting the problem from a fine scale representation onto a coarser one. A coarse representation generally has fewer unknowns, making it faster to solve than the original problem. The coarse solution can then be projected back onto the finer problem as an initial guess of the solution to the finer problem.
Questions tagged [multigrid]
103 questions
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Is it usual to have no convergence checking in Multigrid?
I just read Chapter 3 in "A Multigrid Tutorial" by Briggs/Henson/McCormick, link.
The text is about Multigrid cycles such as V-cycle, mu-cycle, FMG. What caught my eye: In most iterative procedures one checks whether it has converged to the desired…
Michael
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How exactly does the *full* multigrid algorithm run?
So I understand (or at least I believe I do) how a V-cycle runs. I've written in Matlab the 1-D, recursive version of a V-cycle. However, when I ran my code for FMG, my solution wasn't converging. I believe my trouble lies in my understanding of the…
TheRealFakeNews
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10
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3 answers
FAS-multigrid slower than linear defect correction?
I have implemented a V-Cycle multigrid solver using both a linear defect correction (LDC) and full approximation scheme (FAS).
My problem is the following: Using LDC the residual is reduced by a factor of ~0.03 per cycle. The FAS implementation does…
Silpion
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9
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Multigrid on "not perfectly rectangular" grid
Multigrid introductions normally use a rectangular grid. Interpolation of values is then straight forward: Just interpolate linearly on the edge between two adjacent nodes of the coarse grid to find the value of the fine grid node on that edge.
For…
Michael
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7
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2 answers
How to use grid sizes that are not powers of two in Geometric Multigrid
I am trying to solving a poisson equation in structured grid with Geometric Multigrid method. However, when coarsening the fine grid, I simply double the grid spacing at each successive level. That means that the number of points on the finest…
Anyang
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3
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Full Multigrid convergence is too slow. What could possibly be causing it?
I've coded full multigrid in Matlab and it doesn't seem to be converging fast enough. When I increase the number of grids or the number of iterations, it converges to the analytical solution. But FMG shouldn't need that many iterations and it should…
TheRealFakeNews
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Why post-smoothing in MG is needed?
In pre-smoothing we eliminate high frequencies,but what about post-smoothing?Is it used for the remain high frequencies that pre-smoothing didn't eliminate?
spyros
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3
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Can I use multigrid to solve linear algebra problems that do not arise from a differential equation?
Can the Multigrid method be applied to solve a linear system of equations in the form $Ax=b$, that is not necessarily related to differential equations?
3
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1 answer
Can F-cycle substitue FMG for update of existent solution?
I have a nicely working multigrid solver, which I use for solving the Poisson equation from an electrostatic problem. I solve this equation first without any charges, and then many times with a slowly changing charge distribution.
Right now, I do a…
Thomas Klimpel
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coarsening coefficient matrixes (A2h, A4h...) for geometric multigrid method in 2-D/3-D
I am learning about multigrid methods from the textbook section 6.3 Multigrid Methods, which shows a geometric multigrid algorithm for 1-D examples in detail, including how to build restriction/interpolation matrices (i.e., eqs.1, 3) and how to get…
Freewill
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How coarsening rate affects MG convergence?
If we use an aggresive coarsening how does this affect the convergence of a MG cycle?Is the convergence slower?Do we need more cycles in this case?
spyros
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Differences between Two-Grid Correction and V-Cycle Scheme
I found in A Multigrid Tutorial: Second Edition by William L. Briggs, Van Emden Henson, Steve F. (here) the following Schemes:
Two-Grid Correction Scheme, p. 37:
And V-Cycle Scheme, p. 40
I want to check that I understood it correctly, Two-Grid…
ChaosPredictor
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