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Consider a time dependent pde(i.e u(x,t)).I know when only space-coarsening is used the standard multigrid performance can be applied but what if instead we use only time-coarsening?Can we apply the standard multigrid for solving the spatial problem in order to take one time step(i.e going from t1 to t2)?

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  • $\begingroup$ Yes. That is, for example, the algorithm used in the XBraids library. $\endgroup$ – Wolfgang Bangerth Nov 10 '19 at 19:14
  • $\begingroup$ So to be crystal clear.By applying a time-coarsening techique we can use multigrid to coarse space dimension in order to take a time step right? $\endgroup$ – spyros Nov 10 '19 at 22:22
  • $\begingroup$ Yes, that is correct. Search for "multigrid in time". $\endgroup$ – Wolfgang Bangerth Nov 11 '19 at 4:07
  • $\begingroup$ I did.One last question since you seem to have a solid knowledge on this topic and I am a little bit confused.The FCF-relaxation on temporal mesh(solving a block jacobi) leading to an another linear system(spatial system Φ*u_i=u_i-1 in you use an implicit scheme) .So I want to know if you have to solve this system "exactly" using for example a multigrid method in space in order to i-1 to i or just to use few iteration of GS for example and go on with FCF relaxation.In some examples they find the "exact" solution in every time step for all grid and i got confused.Thank you for your help! $\endgroup$ – spyros Nov 16 '19 at 0:46
  • $\begingroup$ I don't actually know. What I stated above is roughly the extent of my knowledge :-) $\endgroup$ – Wolfgang Bangerth Nov 16 '19 at 3:25

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