Abstract
An algorithm which solves the multidimensional diffusion equation on complex shapes to fourth-order accuracy and is asymptotically stable in time is presented. This bounded-error result is achieved by constructing, on a rectangular grid, a differentiation matrix whose symmetric part is negative definite. The differentiation matrix accounts for the Dirichlet boundary condition by imposing penalty-like terms. Numerical examples in 2-D showthatthe method is effective even where standard schemes, stable by traditional definitions, fail. The ability of the paradigm to be applied to arbitrary geometric domains is an important feature of the algorithm.
Original language | English |
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Pages (from-to) | 279-288 |
Number of pages | 10 |
Journal | Journal of Computational Physics |
Volume | 133 |
Issue number | 2 |
DOIs | |
State | Published - 15 May 1997 |
Externally published | Yes |
Bibliographical note
Funding Information:1This research was supported by the National Aeronautics and Space Administration under NASA Contract NAS1-19480 while the authors were in the residence of the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA. S. Abarbanel was also supported in part by the Air Force Office of Scientific Research under Grant AFOSR-F49620-95-1-0074, and by the Department of Energy under Grant DOE-DE-FG02-95ER25239.
Funding
1This research was supported by the National Aeronautics and Space Administration under NASA Contract NAS1-19480 while the authors were in the residence of the Institute for Computer Applications in Science and Engineering (ICASE), NASA Langley Research Center, Hampton, VA. S. Abarbanel was also supported in part by the Air Force Office of Scientific Research under Grant AFOSR-F49620-95-1-0074, and by the Department of Energy under Grant DOE-DE-FG02-95ER25239.
Funders | Funder number |
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ICASE | |
Institute for Computer Applications in Science and Engineering | |
NASA Langley Research Center, Hampton | |
U.S. Department of Energy | DOE-DE-FG02-95ER25239 |
National Aeronautics and Space Administration | NAS1-19480 |
Air Force Office of Scientific Research | AFOSR-F49620-95-1-0074 |