piosson-solver

A C++ based implementation of a Poisson Equation solver performing Gauss-Seidel, Gauss-Seidel Red-Black or Jacobi methods. All the methods come with a sequential and parallel implementation. For the parallel implementations the code leverages the APIs from FastFlow C++ library.

Requirements

• C++11 compiler, e.g GNU g++ / Intel icc. In my experiments I used the Intel compiler for perfomance reasons.

• FastFlow, a library offering high-performance parallel patterns and building blocks in C++.

Installation

By default, Makefile make use of GNU g++ compiler, but if you prefer using Intel icc compiler to also reproduce results, make sure to provide the name of the chosen C++11 compiler and the home directory to FastFlow, and enable the related compiler options, check CXX and OPTIMIZE_FLAGS. In that repo, find the latter as a submodule, so no worries. Run make all to compile the code for all the configurations configurations and version of the source code. Instead, if you want to build the binary for a specific method run make <SOLVER>, eg for sequential Jacobi method, do make jacobi_seq. See below for full list of options.

Make options

Sequential:

• Jacobi jacobi_seq
• Gauss-Seidel gauss_seq
• Gauss-Seidel Red-Black gaussrb_seq

Parallel:

• Jacobi jacobi_par
• Gauss-Seidel gauss_par
• Gauss-Seidel Red-Black gaussrb_par

Basic usage

Once the code has been compiled, the generated binary code can be run provided with the following arguments ./solver <n> <m> <eps> <nw> <sc> <bx> <by>, where n and m represent the height and width of the grid for the discretized poisson equation, eps is the error tolerance. In the parallel versions, the option nw represents the number of threads, and sc is the FastFlow schedule type (ie data distribution policy), and bx and by are the sizes for the blocked version of the stencils in order to run blocked loops and thus optimize cache accesses.

To help you, the repo comes with run_poisson_solver.sh shell script, to easily build and run the desired solver.

Theory

For further informations about the math background on the implemented numerical solvers and the obtained results, you can find a copy of the slides I made for the High Performance Scientific Computing class @ University of Pisa.