Parallelization & Optimization of Poisson Equation Solvers

This program is used for solving Poisson Equation.

1.Poisson Equation Solvers

Poisson Equation is first solved by 3 methods.

• Jacobi method
• SOR method
• Conjugate Gradient method

2.CSR & Profiling

CSR(Compressed Sparse Row) matrix is used to CG method

• At new 'CSR' branch

3.OpenMP & MKL

OpenMP technique is applied to each method except SOR

• At new branch 'OpenMP' branch

  • Jacobi method is parallelized
  • Conjugate gradient method is parallelized

• At 'CSR' branch

  • MKL libraries are used
    • to calculate matrix vector product, vector vector product, norm2
    • and also tested with changing OPEN_NUM_THREADS

4.MPI

MPI technique is applied to each method

• At new branch 'MPI' branch
• MPI is used to solve Poisson equation using Conjugate gradient method
• MPI is also used to solve Poisson equation using Jacobi and SOR method to
  • SOR is modified to red-black SOR because MPI cannot be applied to SOR.
• This case, CG method is based on the dense matrix
• MPI I/O is applied to make the results of Conjugate gradient method