From 608c5c6b69544655c985eaeff5e15916ac97c56e Mon Sep 17 00:00:00 2001 From: Martin Kronbichler Date: Tue, 14 May 2019 10:40:33 +0200 Subject: [PATCH] Fix some typos in results of step-59 --- examples/step-59/doc/results.dox | 28 +++++++++++++++------------- 1 file changed, 15 insertions(+), 13 deletions(-) diff --git a/examples/step-59/doc/results.dox b/examples/step-59/doc/results.dox index 2c3ebd4a07..d85f116caa 100644 --- a/examples/step-59/doc/results.dox +++ b/examples/step-59/doc/results.dox @@ -210,20 +210,22 @@ because higher polynomial degrees often yield a vastly better solution, but especially also when having matrix-based schemes in mind where the denser coupling at higher degree leads to a monotonously decreasing throughput (and a drastic one in 3D, with $k=4$ being more than ten times slower than -$k=1$!). For higher degres, the throughput decreases a bit, which is both due +$k=1$!). For higher degrees, the throughput decreases a bit, which is both due to an increase in the number of iterations (going from 12 at $k=2,3,4$ to 19 at $k=10$) and due to the $\mathcal O(k)$ complexity of operator evaluation. Nonetheless, efficiency as the time to solution would be still -better at higher degrees because they have better convergence rates (at least -for problems as simple as this one). For $k=12$, we reach roundoff accuracy -already at 1 million Dofs (solver time less than a second), whereas for $k=8$ +better for higher polynomial degrees because they have better convergence rates (at least +for problems as simple as this one): For $k=12$, we reach roundoff accuracy +already with 1 million DoFs (solver time less than a second), whereas for $k=8$ we need 24 million DoFs and 8 seconds. For $k=5$, the error is around -$10^{-9}$ at 57m DoFs and thus still far away from roundoff, despite taking 16 +$10^{-9}$ with 57m DoFs and thus still far away from roundoff, despite taking 16 seconds. -Note that the above numbers are a bit pessimistic because they -include the time it takes the Chebyshev smoother to compute an eigenvalue -estimate, which is around 10 percent of the solver time. +Note that the above numbers are a bit pessimistic because they include the +time it takes the Chebyshev smoother to compute an eigenvalue estimate, which +is around 10 percent of the solver time. If the system is solved several times +(as e.g. common in fluid dynamics), this eigenvalue cost is only paid once and +faster times become available.

Evaluation of efficiency of ingredients

@@ -316,7 +318,7 @@ FEFaceEvaluation::integrate_scatter(). The data in the table shows that not using MatrixFree::DataAccessOnFaces -increases timings by around 10% for higher polynomial degrees. For lower +increases costs by around 10% for higher polynomial degrees. For lower degrees, the difference is obviously less pronounced because the volume-to-surface ratio is more beneficial and less data needs to be exchanged. The difference is larger when looking at the matrix-vector product @@ -334,9 +336,9 @@ the effectiveness of these basis functions. As mentioned in the introduction, the fast diagonalization method is tied to a Cartesian mesh with constant coefficients. If we wanted to solve variable-coefficient problems, we would need to invest a bit more time in the -design of the smoother parameters by selecting better values. +design of the smoother parameters by selecting proper generalizations (e.g., +approximating the inverse on the nearest box-shaped element). Another way of extending the program would be to include support for adaptive -meshes, for which an interface operation at edges of different refinement -level becomes necessary, as discussed in step-39. - +meshes, for which interface operations at edges of different refinement +level become necessary, as discussed in step-39. -- 2.39.5