Abstract
Parallel elliptic single/multigrid solutions around an aligned and nonaligned body are presented and implemented on two multi-user and single-user shared memory multiprocessors (Sequent Symmetry and MOS) and on a distributed memory multiprocessor (a Transputer network). Our parallel implementation uses the Virtual Machine for Muli-Processors (VMMP), a software package that provides a coherent set of services for explicitly parallel application programs running on diverse multiple instruction multiple data (MIMD) multiprocessors, both shared memory and message passing. VMMP is intended to simplify parallel program writing and to promote portable and efficient programming. Furthermore, it ensures high portability of application programs by implementing the same services on all target multiprocessors. The performance of our algorithm is investigated in detail. It is seen to fit well the above architectures when the number of processors is less than the maximal number of grid points along the axes. In general, the efficiency in the nonaligned case is higher than in the aligned case. Alignment overhead is observed to be up to 200% in the shared-memory case and up to 65% in the message-passing case. We have demonstrated that when using VMMP, the portability of the algorithms is straightforward and efficient.
Highlights
The introduction of parallel computer architectures in the last years has challenged the existing serial methods such as finite differences. finite elements, and multigrid solutions of Partial Differential Equations (PDE)
Physical problems often require the solution of the corresponding Partial Differential Equations (PDE) around bodies of various shapes.lt appears that in such cases there is no simple method to map the body surface into the grid points
Another method is based on using Cartesian grids [8, 9] such that the body surface is not aligned with the grid, but we have to take into consideration its existence within the grid
Summary
The introduction of parallel computer architectures in the last years has challenged the existing serial methods such as finite differences. finite elements, and multigrid solutions of PDEs. Physical problems often require the solution of the corresponding Partial Differential Equations (PDE) around bodies of various shapes.lt appears that in such cases there is no simple method to map the body surface into the grid points. We consider two distinct cases: (1) when the body boundary is aligned with the grid and (2) when the body is not aligned with the grid so that dummy points are introduced. We consider both shared-memory and message-passing architectures and compare their performance.
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