Engineering topics

Povitsky, A.

Publications and source records attributed to Povitsky, A..

3 records

NASA NTRS1998

Parallelization of the Pipelined Thomas Algorithm

In this study the following questions are addressed. Is it possible to improve the parallelization efficiency of the Thomas algorithm? How should the Thomas algorithm be formulated in order to get solved lines that are used as data for other computational tasks while processors are idle? To answer these questions, two-step pipelined algorithms (PAs) are introduced formally. It is shown that the idle processor time is invariant with respect to the order of backward and forward steps in PAs starting from one outermost processor. The advantage of PAs starting from two outermost processors is small. Versions of the pipelined Thomas algorithms considered here fall into the category of PAs. These results show that the parallelization efficiency of the Thomas algorithm cannot be improved directly. However, the processor idle time can be used if some data has been computed by the time processors become idle. To achieve this goal the Immediate Backward pipelined Thomas Algorithm (IB-PTA) is developed in this article. The backward step is computed immediately after the forward step has been completed for the first portion of lines. This enables the completion of the Thomas algorithm for some of these lines before processors become idle. An algorithm for generating a static processor schedule recursively is developed. This schedule is used to switch between forward and backward computations and to control communications between processors. The advantage of the IB-PTA over the basic PTA is the presence of solved lines, which are available for other computations, by the time processors become idle.

Povitsky, A.↗

NASA NTRS1998

Parallel Directionally Split Solver Based on Reformulation of Pipelined Thomas Algorithm

In this research an efficient parallel algorithm for 3-D directionally split problems is developed. The proposed algorithm is based on a reformulated version of the pipelined Thomas algorithm that starts the backward step computations immediately after the completion of the forward step computations for the first portion of lines This algorithm has data available for other computational tasks while processors are idle from the Thomas algorithm. The proposed 3-D directionally split solver is based on the static scheduling of processors where local and non-local, data-dependent and data-independent computations are scheduled while processors are idle. A theoretical model of parallelization efficiency is used to define optimal parameters of the algorithm, to show an asymptotic parallelization penalty and to obtain an optimal cover of a global domain with subdomains. It is shown by computational experiments and by the theoretical model that the proposed algorithm reduces the parallelization penalty about two times over the basic algorithm for the range of the number of processors (subdomains) considered and the number of grid nodes per subdomain.

Povitsky, A.↗

NASA NTRS1998

Numerical Study of Interaction of a Vortical Density Inhomogeneity with Shock and Expansion Waves

We studied the interaction of a vortical density inhomogeneity (VDI) with shock and expansion waves. We call the VDI the region of concentrated vorticity (vortex) with a density different from that of ambiance. Non-parallel directions of the density gradient normal to the VDI surface and the pressure gradient across a shock wave results in an additional vorticity. The roll-up of the initial round VDI towards a non-symmetrical shape is studied numerically. Numerical modeling of this interaction is performed by a 2-D Euler code. The use of an adaptive unstructured numerical grid makes it possible to obtain high accuracy and capture regions of induced vorticity with a moderate overall number of mesh points. For the validation of the code, the computational results are compared with available experimental results and good agreement is obtained. The interaction of the VDI with a propagating shock wave is studied for a range of initial and induced circulations and obtained flow patterns are presented. The splitting of the VDI develops into the formation of a non-symmetrical vortex pair and not in a set of vortices. A method for the analytical computation of an overall induced circulation Gamma(sub 1) as a result of the interaction of a moving VDI with a number of waves is proposed. Simplified, approximated, expressions for Gamma(sub 1) are derived and their accuracy is discussed. The splitting of the VDI passing through the Prandtl-Meyer expansion wave is studied numerically. The obtained VDI patterns are compared to those for the interaction of the VDI with a propagating shock wave for the same values of initial and induced circulations. These patterns have similar shapes for corresponding time moments.

Povitsky, A.↗