High Performance Programming for Soft Computing

55

GPU-based Conjugated GPU-based Conjugated

Gradient Solution for Phase Gradient Solution for Phase

Field Models Field Models

Juan J. Tapia* and Rigoberto Alvarado

ABSTRACT

This chapter presents a GPU-based solution for the Allen-Cahn

differential equation which describes a phase fi eld model. The proposed

algorithm is based in the conjugate gradient method. CUDA and its

libraries CUSPARSE and CUBLAS for sparse matrix operations and

linear algebra operations respectively, are used to implement the

solution. The proposed implementation uses the Fletcher-Reeves

version of the nonlinear conjugate gradient method.

5.1 Introduction

The nonlinear problems ...