Applications of summation-by-parts operators
Oskar Ålund
Nov 2020 · Linköping Studies in Science and Technology. Dissertations Book 2106 · Linköping University Electronic Press
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Numerical solvers of initial boundary value problems will exhibit instabilities and loss of accuracy unless carefully designed. The key property that leads to convergence is stability, which this thesis primarily deals with. By employing discrete differential operators satisfying a so called summation-by-parts property, it is possible to prove stability in a systematic manner by mimicking the continuous analysis if the energy has a bound. The articles included in the thesis all aim to solve the problem of ensuring stability of a numerical scheme in some context. This includes a domain decomposition procedure, a non-conforming grid coupling procedure, an application in high energy physics, and two methods at the intersection of machine learning and summation-by-parts theory.
Numerical solvers of initial boundary value problems will exhibit instabilities and loss of accuracy unless carefully designed. The key property that leads to convergence is stability, which this thesis primarily deals with. By employing discrete differential operators satisfying a so called summ...
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