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  New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions

Diener, P., Dorband, E. N., Schnetter, E., & Tiglio, M. (2007). New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions. Journal of Scientific Computing, 32(1), 109-145. doi:10.1007/s10915-006-9123-7.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4822-E Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0013-4823-C
Genre: Journal Article

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jsc32_109.pdf (Publisher version), 843KB
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 Creators:
Diener, Peter1, Author
Dorband, Ernst Nils1, Author              
Schnetter, Erik1, Author
Tiglio, Manuel, Author
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1Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24013              

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 Abstract: We construct optimized high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the truncation error on the boundary points, the spectral radius, or a combination of these. We examine in detail a set of operators that are up to tenth order accurate in the interior, and we surprisingly find that a combination of these optimizations can improve the operators’ spectral radius and accuracy by orders of magnitude in certain cases. We also construct high-order dissipation operators that are compatible with these new finite difference operators and which are semi-definite with respect to the appropriate summation by parts scalar product. We test the stability and accuracy of these new difference and dissipation operators by evolving a three-dimensional scalar wave equation on a spherical domain consisting of seven blocks, each discretized with a structured grid, and connected through penalty boundary conditions. In particular, we find that the constructed dissipation operators are effective in suppressing instabilities that are sometimes otherwise present in the restricted full norm case.

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 Dates: 2007-07
 Publication Status: Published in print
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 Identifiers: eDoc: 334779
ISI: 000247259200005
DOI: 10.1007/s10915-006-9123-7
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Title: Journal of Scientific Computing
Source Genre: Journal
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Pages: - Volume / Issue: 32 (1) Sequence Number: - Start / End Page: 109 - 145 Identifier: ISSN: 0885-7474