From 0ca074e02c818a538561daf1425ea5613e41331e Mon Sep 17 00:00:00 2001 From: Timo Heister Date: Sun, 10 May 2020 10:20:00 -0400 Subject: [PATCH] step-50: fix references - update funding source - fix paper references --- doc/doxygen/references.bib | 23 +++++++++++++++++++++++ examples/step-50/doc/intro.dox | 6 +++--- 2 files changed, 26 insertions(+), 3 deletions(-) diff --git a/doc/doxygen/references.bib b/doc/doxygen/references.bib index 1a07590727..b0a4497779 100644 --- a/doc/doxygen/references.bib +++ b/doc/doxygen/references.bib @@ -315,6 +315,21 @@ journal = {Computer Methods in Applied Mechanics and Engineering} } +% ------------------------------------ +% Step 50 +% ------------------------------------ + +@article{karakashian2003posteriori, + title={A posteriori error estimates for a discontinuous Galerkin approximation of second-order elliptic problems}, + author={Karakashian, Ohannes A and Pascal, Frederic}, + journal={SIAM Journal on Numerical Analysis}, + volume={41}, + number={6}, + pages={2374--2399}, + year={2003}, + publisher={SIAM} +} + % ------------------------------------ % Step 51 % ------------------------------------ @@ -701,3 +716,11 @@ year = {2008}, Number = {91-279}, Url = {citeseer.ist.psu.edu/saad93flexible.html} } + +@Article{clevenger_par_gmg, + Title = {A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM}, + Author = {Thomas C. Clevenger and Timo Heister and Guido Kanschat and Martin Kronbichler}, + Journal = {submitted}, + Year = {2019}, + Url = {https://arxiv.org/abs/1904.03317} +} diff --git a/examples/step-50/doc/intro.dox b/examples/step-50/doc/intro.dox index 1263229b40..5d289f95a1 100644 --- a/examples/step-50/doc/intro.dox +++ b/examples/step-50/doc/intro.dox @@ -4,7 +4,7 @@ This program was contributed by Thomas C Clevenger and Timo Heister.
This material is based upon work partly supported by the National -Science Foundation Award DMS-1901529, OAC-2015848, EAR-1925575, by the Computational +Science Foundation Award DMS-2028346, OAC-2015848, EAR-1925575, by the Computational Infrastructure in Geodynamics initiative (CIG), through the NSF under Award EAR-0949446 and EAR-1550901 and The University of California -- Davis. @@ -36,7 +36,7 @@ for 2D and a Fichera corner for 3D) with $\epsilon = 1$ if $\min(x,y,z)>-\frac{1 $\epsilon = 100$ otherwise. The boundary conditions are $u=0$ on the whole boundary and the right-hand side is $f=1$. We use continuous Q2 elements to discretize $V_h$ and use a residual-based, cell-wise a posteriori error estimator -$e(K) = e_{\text{cell}}(K) + e_{\text{face}}(K)$ from _CITE EST PAPER_ with +$e(K) = e_{\text{cell}}(K) + e_{\text{face}}(K)$ from @cite karakashian2003posteriori with @f{align*} e_{\text{cell}}(K) = h^2 \| f + \epsilon \triangle u \|_K^2, \qquad e_{\text{face}}(K) = \sum_F h_F \| [ \epsilon \nabla u \cdot n ] \|_F^2. @@ -116,7 +116,7 @@ The value MGTools::workload_imbalance()$= 1/\mathbb{E}$ then represents the fact in timings we expect for GMG methods (vmults, assembly, etc.) due to the imbalance of the mesh partition. -_CITE MG PAPER_ contains a full discussion of the partition efficiency model +@cite clevenger_par_gmg contains a full discussion of the partition efficiency model and the effect the imbalance has on the GMG V-cycle timing. In summary, the value of $\mathbb{E}$ is highly dependent on the degree of local mesh refinement used and has an optimal value $\mathbb{E} \approx 1$ for globally refined meshes. Typically for adaptively -- 2.39.5