Parallelization of a Class of Implicit Finite Difference Schemes in Computational Fluid Dynamics

Large-Eddy Simulation of Compressible Transitional Cascade Flows with and without Incoming Free-Stream Turbulence

“…However, when such a method was used, strong filtering was needed in order to maintain computational stability, and as a result, the resolution of the calculation in the entire region was severely degraded. Therefore, in the present study, a pipelining algorithm (22) , in which sweep is performed over all processes in each direction, is adopted to solve the band matrices.…”

Compiling Scientific Programs for Scalable Parallel Systems

“…Alternating Direction Implicit (ADI) integration is a common technique for solving partial differential equations that uses this solution style [NNN93]. Two of the NAS parallel benchmarks [BHS+95], SP and BT, use ADI integration to solve the Navier-Stokes equation in three dimensions.…”

“…Two of the NAS parallel benchmarks [BHS+95], SP and BT, use ADI integration to solve the Navier-Stokes equation in three dimensions. Fractional step methods and other solution techniques that use line sweeps are described by Naik et al [NNN93]. For this class of computations, applying a standard block partitioning to any of the spatial dimensions is problematic-recurrences along the partitioned dimension partially serialize execution.…”

An evaluation of data-parallel compiler support for line-sweep applications

“…Finally, the dHPF compiler provides novel compiler support for multipartitioning [14,15], a family of sophisticated skewed-cyclic block distributions that were originally developed for hand-coded parallelization of tightly-coupled multi-dimensional line-sweep computations [8,9,11]. Multipartitioning enables decomposition of arrays of d ≥ 2 dimensions among a set of processors so that for a line sweep computation along any dimension of an array, all processors are active in each step of the computation, load-balance is nearly perfect, and only coarse-grain communication is needed.…”

“…Line sweep computations are used to solve one-dimensional recurrences along a dimension of a multi-dimensional hyper-rectangular domain. This strategy is at the heart of a variety of numerical methods and solution techniques [8]. SP and BT employ line sweeps to perform Alternating Direction Implicit (ADI) integration-a widely-used numerical technique for solving partial differential equations such as the Navier-Stokes equation [8,9,10,11].…”