An Optimization-Based Construction Procedure for Function Space-Based Summation-by-Parts Operators on Arbitrary Grids
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10915_2025_Article_3062.pdf
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Author(s)
Glaubitz, Jan
Nordström, Jan
Öffner, Philipp
Date Issued
November 6, 2025
Journal
Journal of Scientific Computing
Publisher
Springer US
Citation
Glaubitz, J., Nordström, J. & Öffner, P. An Optimization-Based Construction Procedure for Function Space-Based Summation-by-Parts Operators on Arbitrary Grids. J Sci Comput 105, 83 (2025).
Version
Final published version
Abstract
We introduce a novel construction procedure for one-dimensional function space summation-by-parts (FSBP) operators. Existing construction procedures for FSBP operators of the form D = P - 1 Q proceed as follows: Given a boundary operator B, the norm matrix P is first determined and then in a second step the complementary matrix Q is calculated to finally get the FSBP operator D. In contrast, the approach proposed here determines the norm and complementary matrices, P and Q, simultaneously by solving an optimization problem. The proposed construction procedure applies to classical summation-by-parts (SBP) operators based on polynomial approximation and the broader class of FSBP operators. According to our experiments, the presented approach yields a numerically stable construction procedure and FSBP operators with higher accuracy for diagonal norm difference operators at the boundaries than the traditional approach. Through numerical simulations, we highlight the advantages of our proposed technique.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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DOI of Published Version
https://doi.org/10.1007/s10915-025-03062-1
