mpi_krylov: Krylov Solver using MPI

This project provides parallel implementations of Krylov subspace solvers for sparse linear systems using MPI in C++. The solvers include Conjugate Gradient (CG), BiCGStab, GMRES, and communication avoid GMRES, with optional preconditioners such as Jacobi, Block Jacobi, and ILU0.

Setup and Installation

Ensure you have a C++17 compatible compiler and an MPI implementation installed, such as OpenMPI or MPICH. On most systems, MPI can be installed via the package manager. For example, in mac, we use brew install open-mpi.

To compile the project, navigate to the project root directory and run:

make

This will build the executable named solver. To clean compiled object files and the executable, use:

make clean

Running the Program

Since this is an MPI program, use mpirun or mpiexec to run the executable. For example, to run with four MPI processes:

mpirun -np 4 ./solver

The program performs on a small poisson dataset (can be replaced), executes all three solvers on a test sparse matrix and prints iteration counts, final residuals, and runtime for each solver. Preconditioners, if included, are applied automatically. Adjust the number of MPI processes using -np according to your system capabilities.

In my mac:

mpi_krylov % mpirun -np 2 ./solver
Solver=CG iters=4 final_res=2.8794e-12 time=0.041735 s
Solver=BiCGStab iters=4 final_res=5.01607e-07 time=0.055475 s
Solver=GMRES iters=4 final_res=8.71163e-08 time=0.039712 s

mpi_krylov % mpirun -np 4 ./solver
Solver=CG iters=6 final_res=8.52445e-11 time=0.027062 s
Solver=BiCGStab iters=6 final_res=4.13439e-07 time=0.027559 s
Solver=GMRES iters=6 final_res=8.94959e-08 time=0.017409 s