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

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dc.creatorDiener, Peter
dc.creatorDorband, Ernst Nils
dc.creatorSchnetter, Erik
dc.creatorTiglio, Manuel
dc.date2005-11-30
dc.date.accessioned2026-07-07T11:04:23Z
dc.date.available2026-07-07T11:04:23Z
dc.descriptionWe construct new, efficient, and accurate 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.
dc.description16 pages, 9 figures. The files with the coefficients for the derivative and dissipation operators can be accessed by downloading the source code for the document. The files are located in the "coeffs" subdirectory
dc.identifierhttps://arxiv.org/abs/gr-qc/0512001
dc.identifierhttp://arxiv.org/abs/gr-qc/0512001
dc.identifierJ.Sci.Comput.32:109-145,2007
dc.identifierdoi:10.1007/s10915-006-9123-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/188872
dc.subjectGeneral Relativity and Quantum Cosmology
dc.titleNew, efficient, and accurate high order derivative and dissipation operators satisfying summation by parts, and applications in three-dimensional multi-block evolutions
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