Amdahl’s law is a very famous law in parallel programing that states that the speed-up S of a parallel algorithm is bound by the sequential part (Tseq):

S (∞) = 1 / Tseq

To be efficient, aim is to achieve at least 99% parallelism.

So, everything needs to be parallelized efficiently! The table below gives some speedup according to the % of parallelism and the number of processors (P):

Open

2 approaches

• Graph Partitioning

  • Based on element connectivities

  • Several popular libraries: Metis, Scotch, …

• Geometrical decomposition

  • Based on spacial criteria

  • Few packages (Zoltan)

Metis

• Current algorithm used in OpenRadioss

• Quality & speed of decomposition

• Possibility to optimize load-balancing and communication

• Multi-constraints : load-balancing using several criteria

• Trade-off between number of constraints and quality of decomposition

• Static decomposition

Open

Domain Splitting

• General idea

  • Domain decomposition is done by a separate process (Starter)

  • Local data is built before the start of the MPI processes

• Purposes

  • Compute local entities from global data and domain decomposition scheme (with help of OpenMP parallelization)

  • Local renumbering

    • Local structures are renumbered inside every MPI domain, eg: nodes from 1 to NUMNOD_L(P)

    • Renumbering is needed to avoid indirection of type: N_L = NUMNOD_LOC(I)

    • Renumbering improves locality: based on element connectivities of every local domain

  • Optimize start-up time and memory consumption of MPI processes

    • Parallel read from every MPI process

    • Memory allocation based on local memory requirement only

Here is described the general workflow between Starter and Engine processes which allows parallel reading

Here is the pseudo code of an explicit code like it is programmed in OpenRadioss in routine https://github.com/OpenRadioss/OpenRadioss/blob/main/engine/source/engine/resol.F