Merge pull request #90 from xuanxu/figures

Use single image per figure with markdown syntax

joss_paper/paper.md

@@ -88,11 +88,7 @@ end
 
 \autoref{fig:scaling} reports the strong (left) and weak scaling (right) of GridapDistributed when applied to an standard elliptic benchmark PDE problem, namely the 3D Poisson problem. In strong form this problem reads: find $u$ such that $-{\boldsymbol{\nabla}} \cdot (\boldsymbol{\kappa} {\boldsymbol{\nabla}} u) = f$ in $\Omega=[0,1]^3$, with $u = u_{{\rm D}}$ on ${\Gamma_{\rm D}}$ (Dirichlet boundary) and $\partial_{\boldsymbol{n}} u = g_{\rm N}$ on ${\Gamma_{\rm N}}$ (Neumann Boundary); $\boldsymbol{n}$ is the outward unit normal to ${\Gamma_{\rm N}}$. The domain was discretized using the built-in Cartesian-like mesh generator in GridapDistributed. The code was run on the NCI@Gadi Australian supercomputer (3024 nodes, 2x 24-core Intel Xeon Scalable *Cascade Lake* cores and 192 GB of RAM per node) with Julia 1.7 and OpenMPI 4.1.2. For the strong scaling test, we used a fixed **global** problem size resulting from the trilinear FE discretization of the domain using a 300x300x300 hexaedra mesh (26.7 MDoFs) and we scaled the number of cores up to 21.9K cores. For the weak scaling test, we used a fixed **local** problem size of 32x32x32 hexaedra, and we scaled the number of cores up to 16.5K cores. A global problem size of 0.54 billion DoFs was solved for this number of cores.  The reported wall clock time includes: (1) Mesh generation; (2) Generation of global FE space; (3) Assembly of distributed linear system; (4) Interpolation of a manufactured solution; (5) Computation of the residual (includes a matrix-vector product) and its norm. Note that the linear solver time (GAMG built-in solver in PETSc) was not included in the total computation time as it is actually external to GridapDistributed. 
 
-![](strong_scaling.png){width=50%}
-![](weak_scaling.png){width=50%}
-\begin{figure}[!h]
-\caption{Strong (left) and weak (right) scaling of GridapDistributed when applied to 3D Poisson problem on the Australian Gadi@NCI supercomputer.\label{fig:scaling}}
-\end{figure}
+![Strong (left) and weak (right) scaling of GridapDistributed when applied to 3D Poisson problem on the Australian Gadi@NCI supercomputer.\label{fig:scaling}](strong_and_weak_scaling.png)
 
 \autoref{fig:scaling} shows, on the one hand, an efficient reduction of computation times with increasing number of cores, even far beyond a relatively small load of 25K DoFs per CPU core.
 On the other hand, an asymptotically constant time-to-solution (i.e., perfect weak scaling) when the number of cores is increased in the same proportion of global problem size with a local problem size of 32x32x32 trilinear FEs. 
@@ -109,12 +105,7 @@ For the geometrical discretization of the sphere, the software uses the so-calle
 confirms a remarkable ability of the ecosystem of Julia packages at hand to efficiently reduce computation times with increasing number of CPU cores for a complex, real-world computational model. 
 
 
-![](galewsky_visualization.png){width=35%}
-![](galewsky_scaling.png){width=55%}
-\begin{figure}[!h]
-\caption{Magnitude of the vorticity field after 6.5 simulation days with a coarser 48x48 quadrilaterals/panel cubed sphere mesh (left) and strong scaling (right) of the non-linear rotating shallow water equations solver on the Australian Gadi@NCI supercomputer.\label{fig:galewsky_scaling}}
-\end{figure}
-
+![Magnitude of the vorticity field after 6.5 simulation days with a coarser 48x48 quadrilaterals/panel cubed sphere mesh (left) and strong scaling (right) of the non-linear rotating shallow water equations solver on the Australian Gadi@NCI supercomputer.\label{fig:galewsky_scaling}](galewsky_visualization_and_scaling.png)
 
 # Acknowledgements