Thanks for your reply Peter, The matrix-free run is basic same as in step-75 except I substitute coarse grid solver. For fe_degree=6 without GMG and fe_degree in each level decrease by 1 for pMG, the solve_system() function runtime is 24.1s. It's decomposed to *MatrixFree MG operators construction*(1.36s), MatrixFree MG transfers(2.73s), KLU coarse grid solver(5.7s), *setting smoother_data and compute_inverse_diagonal for level matrices*(3.4s) CG iteration(9.8s).
The two bold texts cost a lot more(133s and 62s, respectively) in matrix-based multigrid case. I noticed just as in step-16, the finest level matrix is assembled twice(one for system_matrix and one for mg_matrices[maxlevel]) so assembling time cost more. Best, Wayne 在2022年10月19日星期三 UTC+8 17:10:27<[email protected]> 写道： > Hi Wayne, > > your numbers make totally sense. Don't forget that you are running for > high order: degree=6! The number of non-zeroes per element-stiffness matrix > is ((degree + 1)^dim)^2 and the cost of computing the element stiffness > matrix is even ((degree + 1)^dim)^3 if I am not mistaken (3 nested loop: i, > j and q). Higher orders are definitely made for matrix-free algorithms! > > Out of curiosity: how large is the setup cost of MG in the case of the > matrix-free run? As a comment: don't be surprised that the setup costs are > relatively high compared to the solution process: you are probably setting > up a new Triangulation-, DoFHander-, MatrixFree-, ... -object per level. In > many simulations, you can reuse these objects, since you don't perform AMR > every time step. > > Peter > > On Wednesday, 19 October 2022 at 10:38:34 UTC+2 yy.wayne wrote: > >> Hello everyone, >> >> I modified step-75 a little bit and try to test it's runtime. However the >> result is kind of inexplainable from my point of view, especially on >> *disproportionate >> assemble time and solve time*. Here are some changes: >> 1. a matrix-based version of step75 is contructed to compare with >> matrix-free one. >> 2. no mesh refinement and no GMG, and fe_degree is constant across all >> cells within every cycle. Fe_degree adds one after each cycle. I make this >> setting to compare runtime due to fe_degree. >> 3. a direct solver on coareset grid. I think it won't affect runtime >> since coarest grid never change >> >> For final cycle it has fe_degree=6 and DoFs=111,361. >> For matrix-based method, overall runtime is 301s where setup system(84s) >> and solve system(214s) take up most. In step-75 solve system actually did >> both multigrid matrices assembling, smoother construction, and CG solving. >> Runtime of this case is shown: >> [image: matrix-based.png] >> On each level I print time assembling level matrix. *The solve system is >> mostly decomposed to MG matrices assembling(83.9+33.6+...=133s), smoother >> set up(65s), coarse grid solve(6s) and CG solve(2.56).* My doubt is why >> actual CG solve only takes 2.56 out of 301 seconds for this problem? The >> time spent on assembling and smoother construction account too much that >> they seems a burden. >> >> For matrix-free method however, runtime is much smaller without >> assembling matrices. Besides, CG solve cost more because of more >> computation required by matrix-free I guess. But *smoother construction >> time reduces significantly* as well is out of my expectation. >> [image: matrix-free.png] >> >> Matrix-free framework saves assembling time but it seems too efficient to >> be real. The text in bold are my main confusion. May someone share some >> experience on matrix-free and multigrid methods' time consumption？ >> >> Best, >> Wayne >> >> -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/58dae75e-644e-49d8-bee2-e212c5184e1cn%40googlegroups.com.
