Operator-Based Preconditioning of Stiff Hyperbolic Systems

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We introduce an operator-based scheme for preconditioning stiff components encoun- tered in implicit methods for hyperbolic systems of partial differential equations posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a char- acteristic decomposition of the resulting directional parts. This approach allows for solution to any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydro- dynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where ... continued below

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Daniel R. Reynolds, Ravi Samtaney, and Carol S. Woodward February 9, 2009.

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We introduce an operator-based scheme for preconditioning stiff components encoun- tered in implicit methods for hyperbolic systems of partial differential equations posed on regular grids. The method is based on a directional splitting of the implicit operator, followed by a char- acteristic decomposition of the resulting directional parts. This approach allows for solution to any number of characteristic components, from the entire system to only the fastest, stiffness-inducing waves. We apply the preconditioning method to stiff hyperbolic systems arising in magnetohydro- dynamics and gas dynamics. We then present numerical results showing that this preconditioning scheme works well on problems where the underlying stiffness results from the interaction of fast transient waves with slowly-evolving dynamics, scales well to large problem sizes and numbers of processors, and allows for additional customization based on the specific problems under study.

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  • Report No.: PPPL-4377
  • Grant Number: DE-AC02-09CH11466
  • Office of Scientific & Technical Information Report Number: 950693
  • Archival Resource Key: ark:/67531/metadc925564

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  • February 9, 2009

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  • Nov. 13, 2016, 7:26 p.m.

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  • Dec. 13, 2016, 12:16 p.m.

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Daniel R. Reynolds, Ravi Samtaney, and Carol S. Woodward. Operator-Based Preconditioning of Stiff Hyperbolic Systems, report, February 9, 2009; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc925564/: accessed August 17, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.