glaand / conjugate_gradient_with_mpi_and_openmp

Implementing a parallelized conjugate gradient algorithm using a hybrid of distributed (MPI) and shared (OpenMP) memory approach.

Parallel Conjugate Gradient algorithm with MPI plus OpenMP

An parallel implementation of the conjugate gradient algorithm using a hybrid of distributed (MPI) and shared (OpenMP) memory approach for both sparse and dense matrices. For sparse matrices, compressed row storage (CRS) is used.

MPI and OpenMP features used:

• MPI_Allreduce for dot products
• MPI_Allgatherv for matrix-vector product
• MPI_Gatherv to get solution vector
• omp parallel for and/or omp simd in matrix-vector product
• omp parallel for reduction for sub-vector dot products

Files in Hierarchical Data Format (HDF5) are used for parallel I/O and each node reads only the portion of the matrix which it needs.

Features attempted but which did not result in any performance improvements:

• omp tasks or sections to simultaneously calculate lines 15 and 16 in CG algorithm.

• Same CPU times

• omp simd vectorization instead of the OpenMP parallel for
  • Slower CPU times, same as when no simd nor parallel for
• omp parallel for simd: vectorization combined with multithreading
  • Same CPU times