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Some notes on summation by parts time integration methods
Results in Applied Mathematics, 2019 Some properties of numerical time integration methods using summation by parts (SBP) operators and simultaneous approximation terms are studied. These schemes can be interpreted as implicit Runge-Kutta methods with desirable stability properties such as ...
Hendrik Ranocha
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Hybridized Summation-by-Parts Finite Difference Methods [PDF]
Journal of Scientific Computing, 2021 26 pages, 6 figures, 3 ...
Jeremy E. Kozdon +2 more
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On an Eigenvalue Property of Summation-By-Parts Operators [PDF]
Journal of Scientific Computing, 2022 AbstractSummation-By-Parts (SBP) methods provide a systematic way of constructing provably stable numerical schemes. However, many proofs of convergence and accuracy rely on the assumption that the SBP operator possesses a particular eigenvalue property. In this note, three results pertaining to this property are proven.
Viktor Linders
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Summation-By-Parts in Time: The Second Derivative
SIAM Journal on Scientific Computing, 2016 Summary: We analyze the extension of summation-by-parts operators and weak boundary conditions for solving initial boundary value problems involving second derivatives in time. A wide formulation is obtained by first rewriting the problem on first order form.
Jan Nordström, Tomas Lundquist
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Properties of Runge-Kutta-Summation-By-Parts methods
Journal of Computational Physics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Viktor Linders +2 more
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A Framework for Simultaneous Approximation Terms for Multi-Dimensional Summation-by-Parts Operators [PDF]
Journal of Scientific Computing, 2016 This paper is concerned with the accurate, conservative, and stable imposition of boundary conditions and inter-element coupling for multi-dimensional summation-by-parts (SBP) finite-difference operators. More precisely, the focus is on diagonal-norm SBP operators that are not based on tensor products and are applicable to unstructured grids composed ...
David C. Del Rey Fernández +2 more
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Eigenvalue Analysis for Summation-by-Parts Finite Difference Time Discretizations
SIAM Journal on Numerical Analysis, 2020 Diagonal norm finite difference based time integration methods in summation-by-parts form are investigated.
Andrea Alessandro Ruggiu, Jan Nordström
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Steady-State Computations Using Summation-by-Parts Operators
Journal of Scientific Computing, 2005 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Magnus Svärd +2 more
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Summation-by-Parts Operators for Non-Simply Connected Domains
SIAM Journal on Scientific Computing, 2018 A new combination of summation-by-parts operators (SBP-SAT) is constructed which can be applied to partial differential equations on non-simply connected multidimensional geometries. The authors consider as a prototype problem rectangles with rectangular holes inside, where the holes are not part of the computational domain.
Samira Nikkar, Jan Nordström
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Probability-theoretical approach to the accuracy of the component assembly of multilink mechanisms [PDF]
E3S Web of Conferences, 2021 The technological process, ensuring the accuracy of mechanism assembly is formally a sequential summation of primary manufacturing errors and an analysis of obtained, generalized values to develop and implement specific technological methods to meet ...
Shekikhachev Yuri +4 more
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