README.md

Poisson-Solver

This repository contains a solver for the the modified Poisson-equation

-Δu(x) + αu(x) = f(x), x∈Ω, ∂Ω = 0, α >0

where the domain Ω is either square or cubic.

The solver discretizes this equation using central finite differences to get a linear system and then runs the preconditioned conjugate gradient method to solve this system. For the preconditioner we use a tridiagonal matrix that we can efficiently invert using Cuda on a Nvidia graphic card.

I developed this code for my Bachelor thesis but did not look at it since then. It still seems to compile though. Maybe someone has a use for it.

Directory structure

├── README.md
├── cublas_wrapper.h          # wrapper functions around some cublas functions
├── makefile
├── misc.h                    # some small helper functions
├── preconditioner.h          # Cuda kernels that solve solve the linear system for the preconditioner
├── solver.h                  # functions that apply the preconditioned conjugate gradient to solve the problem
└── test.cu                   # demonstrates how to use the given code and runs tests for the different implementations.