OpenACC Parallelisation for Diffusion Problems, Applied to Temperature Distribution on a Honeycomb Around the Bee Brood: A Worked Example Using BiCGSTAB

Abstract

We discuss a simple OpenACC implementation of the iterative BiCGSTAB algorithm for linear systems. Problems of this type arise in the numerical solution of diffusion-reaction problems, where the linear solver constitutes the most computationally expensive component of the simulation ($\sim$80 % of time spent) and therefore has often been the primary target for parallelization. We deploy and test this method on a desktop workstation with two supported GPUs, one targeted for high performance computing, one a consumer level GPU, to compute the temperature distribution on a honeycomb around the bee brood. The paper is written from a user’s, not from a GPU computing expert’s perspective and aims to fill a gap we noticed between real world application problems and the simple problems solved in introductory OpenACC tutorials or in benchmarking studies.

Appendices

Appendix

OpenACC Fortran Code-stubs

The following code stubs are provided for illustration only. They are copied from the source codes used here but changed to reflect the notation in the text. The authors do not guarantee their proper working if copied from here and do not assume responsibility for any damages this might cause.

Matrix-vector product $y:=Ax$ for sparse diagonal format. In the following code, $d$ is the number of diagonals, sparse matrix $A$ is an $n \times d$ array, ioff contains the offsets of the sub-diagonals. $A,x,d, ioff$ are handed over to the subroutine, $y$ is returned.

Scalar product $ddt:= x^T y$. In the following code stub $x,y$ are $n$-arrays handed over to the function, the real variable ddt is returned.