Heterogeneous Parallel Implementation of a Multigrid Method with Full Approximation in the Noisette Code

This article studies accelerating simulations of compressible flows on hybrid cluster systems using the full approximation scheme multigrid (FAS MG) method. The basic numerical algorithm has the following features: for spatial discretization, unstructured mixed-element meshes and schemes with the definition of mesh functions at mesh nodes are used; for temporal discretization, a fully implicit scheme is used. The aim of this study is to achieve acceleration of stationary simulations on both central and graphics processors without significant losses in parallel efficiency. We describe an approach to construct mesh levels; a technique for improving the quality of the mesh representation of the geometry of the modeled objects; and parallel implementation within the framework of complex parallelization, combining the message passing interface (MPI) for a distributed-memory parallel model, OpenMP for a shared-memory model, and OpenCL for computing on GPUs of various architectures.