Papers › An optimization-based construction procedure for function space based...
An optimization-based construction procedure for function space based summation-by-parts operators on arbitrary grids
Jan Glaubitz, Jan Nordström, Philipp Öffner
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
We introduce a novel construction procedure for one-dimensional summation-by-parts (SBP) 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 SBP operators based on polynomial approximation and the broader class of function space SBP (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.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections