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Implement matrix-free version with ghost points #2
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JamieJQuinn
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NOT WORKING It builds and runs but the residual is massive. Clearly not correct.
…es original version.
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This PR implements SPMV, SYMGS and the prolongation and restriction operators using a matrix-free method that manually applies the stencil encoded in the associated sparse matrix with extended for loops, instead of using the matrix directly. This is intended to remove the overhead of accessing the sparse matrix and the indirect memory accesses of the input vector. Things that are working:
arch=Linux_Serialarch=GCC_OMPand multiple OpenMP threadsarch=Linux_MPIand running with one MPI processThings that are still sketchy, broken or untested:
Previous matrix-free implementations manually handle the boundaries of the domain using generated code. This implementation uses ghost points at the edge of the boundary to incorporate known boundary values outside the domain, allow the use of one single loop over the entire domain. This reduces the complexity and size of the code, however we perform O(x^2) more FLOPs. Since the algorithm scales with O(x^3) this should be negligible and the preliminary performance testing reported below shows the tradeoff is acceptable.
Initial performance for MPI (single process) version is: