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          Institute: MPI für Gravitationsphysik     Collection: Astrophysical Relativity     Display Documents



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ID: 334779.0, MPI für Gravitationsphysik / Astrophysical Relativity
New, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
Authors:Diener, Peter; Dorband, Ernst Nils; Schnetter, Erik; Tiglio, Manuel
Date of Publication (YYYY-MM-DD):2007-07
Title of Journal:Journal of Scientific Computing
Volume:32
Issue / Number:1
Start Page:109
End Page:145
Review Status:not specified
Audience:Not Specified
Abstract / Description: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.
External Publication Status:published
Document Type:Article
Communicated by:Bernhard F. Schutz
Affiliations:MPI für Gravitationsphysik/Astrophysical Relativity
Identifiers:ISI:000247259200005 [ID No:1]
ISSN:0885-7474 [ID No:2]
DOI:10.1007/s10915-006-9123-7
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