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This and speed up for the whole simulation, using the assembly- would give a scaled percentage run time of: optimised code. This perhaps The graph of the scaled results are shown in Fig. As expected, can be expected, as DG assembly does not rely on any MPI com- DG assembly has a much shorter absolute run time: at 96 cores, munication, which can be expected to dominate the rest of the there is a 3.
Case Min. Imbalance Mean Standard dev.
Pre-optimisation 6. This severe load imbalance resulted in smaller partitions wait- ing on blocking MPI communications e. The code with the enhanced load balanc- ing brought the imbalance down to 2. Mesh reordering Finite element calculations require the calculation of integrals over the computational mesh, leading to the construction of sparse matrices or vectors.
These latter local integrals use data for the element consid- ered, and typically also use data for neighbouring elements. How- ever mesh generators may create meshes which are sub-optimal for such calculations. A pre-processing tool was written to reorder mesh data. The mesh vertices are similarly reordered based upon a reordering of the Fig. Note that a more advanced al- scaled by relative run time for each case.
An example speed up is 3. Some subroutines independent of the assem- of the mesh reordering functionality is presented in Fig.
Load balancing and decomposition 7. Performance evaluation We observed that the meshes generated and used by Fluidity are not well ordered. For this type of simulation Fluidity extrudes To evaluate the performance of all the optimisations under- the 2D mesh representing open boundaries and coastlines down- taken a more realistic test case is considered, chosen to be as close wards into a 3D mesh matching the bathymetry of the simulation as possible as to the type of simulation the code has been opti- being undertaken.
By re-ordering the numbering of mesh elements mized for: ie. This was developed from a on the 2D mesh see mesh reordering section , we can ensure that pre-existing prototype of the Sound of Islay, spanning This means that an ini- culations on a given element.
The simulation was set to run for timesteps; there were This improvement allows the code to more effectively balance two Picard iterations for each timestep, which means the DG as- mesh sizes across subdomains, even when there are spatially vari- sembly code is called times. To track the improvements that able numbers of element layers.
Subdomain mesh sizes from the each section of optimisation work made to performance, the model tidal test case before and after this improvement are shown in was benchmarked at four stages of development: i the code with Table 4. The elements are coloured according to their element number indexed from zero.
Sound of Islay overview. Table 6 Fig. Graph of speed-ups for tidal case with cores. Values for speed-ups from successive optimisations for tidal mod- elling case with cores. Running the 2D mesh re- Case n Run time min Speed-up ordering increases the performance over the pre-optimised code to Pre-optimisation 80 - 1.
Table 6 and Fig. Summary misation on the performance of Fluidity on the tidal case. Surv Geo- phys ; Large eddy simulation runtime to less than one third of the run time of the original code.
Int J Heat Fluid Flow ; Such improvements can enable new science by allowing much  Creech A. A Large eddy simulation of an energetic tidal site: the sound of Islay.
CAIMS annual meeting; Nonlin Processes Geophys same amount of computational resources.
The source code devel- ; Turbul Heat Mass Transfer ;7. Power P, de Oliveira C. Three-dimensional unstructured mesh ocean modelling.
AJ adapting unstructured meshes. Int J Numer Methods Fluids 20 08; 03— Technical report, dCSE. J Comput Phys ; 2 — Ocean Modell ;— J Comput Phys ;— The available adaptivity with applications in numerical ocean modelling. Ocean Modell power from tidal stream turbines in the Pentland Firth. Proc R Soc A Renewable Energy ; Part I: model formulation. Mon Weather Rev ;— A Eng ;79 11 — J Hydraul Eng ; Spud 1. Harmful Algae ;53 3 — Geosci Model Dev ;— General circulation experiments with the primitive equations.
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