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Fast Time and Space Parallel Algorithms for Solution of Parabolic Partial Differential Equations
| Content Provider | Semantic Scholar |
|---|---|
| Author | Fijany, Amir |
| Copyright Year | 1993 |
| Abstract | ing this paper, fast timeand space-parallel algorithms for solution of linear parabolic PDEs are developed. It is shown that the seemingly strictly serial iterations of the time-stepping procedure for solution of the problem can be completely decoupled. This decoupling is achieved by using a transformation based on the eigenvalue-eigenvector decompositions of the matrices involved in the iterations and results in time-parallel algorithms that enable the solution for all the time steps to be computed in parallel. The time-parallel algorithms also allow a massively parallel solution of the problem through exploitation of parallelism in space. With a sufficient number of processors, parallelism in both time and space can be fully exploited, leading to a computational complexity of max(O(Log N),O(Log M)) + O(Log N) !. a both time-and space-parallel solution of the problem where M and N stand the number of time steps and the size of grid. However, for many practical cases, the complexity of time-parallel algorithms is independent of M. The for for time-parallel algorithms have a highly decoupled structure and hence can be efficiently implemented on the emerging massively parallel MIMD architectures with a minimum communication and synchronization overhead. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://techreports.jpl.nasa.gov/1993/93-0410.pdf |
| Alternate Webpage(s) | https://trs.jpl.nasa.gov/bitstream/handle/2014/34955/93-0410.pdf?isAllowed=y&sequence=1 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
