Parallelizing across time when solving time-dependent partial differential equations
The standard numerical algorithms for solving time-dependent partial differential equations (PDEs) are inherently sequential in the time direction. This paper describes algorithms for the time-accurate solution of certain classes of linear hyperbolic and parabolic PDEs that can be parallelized in both time and space and have serial complexities that are proportional to the serial complexities of the best known algorithms. The algorithms for parabolic PDEs are variants of the waveform relaxation multigrid method (WFMG) of Lubich and Ostermann where the scalar ordinary differential equations (ODEs) that make up the kernel of WFMG are solved using a cyclic reduction type algorithm. The algorithms for hyperbolic PDEs use the cyclic reduction algorithm to solve ODEs along characteristics. 43 refs.
- Research Organization:
- Oak Ridge National Lab., TN (United States)
- Sponsoring Organization:
- DOE; USDOE, Washington, DC (United States)
- DOE Contract Number:
- AC05-84OR21400
- OSTI ID:
- 6026480
- Report Number(s):
- ORNL/TM-11963; ON: DE92003733
- Country of Publication:
- United States
- Language:
- English
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