# A GPU implementation of the Discontinuous Galerkin method for simulation of diffusion in brain tissue

## TL;DR

This paper presents a GPU-accelerated Discontinuous Galerkin method for simulating water diffusion in brain tissue, enabling efficient approximation of the covariance matrix in diffusion studies.

## Contribution

It introduces a parallel GPU implementation of the Discontinuous Galerkin method tailored for brain tissue diffusion simulation, improving computational efficiency.

## Key findings

- GPU implementation achieves significant speedup
- Numerical results validate the method in 2D cases
- Method accurately approximates covariance matrices

## Abstract

In this work we develop a methodology to approximate the covariance matrix associated to the simulation of water diffusion inside the brain tissue. The computation is based on an implementation of the Discontinuous Galerkin method of the diffusion equation, in accord with the physical phenomenon. The implementation in in parallel using GPUs in the CUDA language. Numerical results are presented in 2D problems.