2019
DOI: 10.5802/afst.1600
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Transparent numerical boundary conditions for evolution equations: Derivation and stability analysis

Abstract: The aim of this article is to propose a systematic study of transparent boundary conditions for finite difference approximations of evolution equations. We try to keep the discussion at the highest level of generality in order to apply the theory to the broadest class of problems.We deal with two main issues. We first derive transparent numerical boundary conditions, that is, we exhibit the relations satisfied by the solution to the pure Cauchy problem when the initial condition vanishes outside of some domain… Show more

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Cited by 8 publications
(25 citation statements)
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“…As in all numerical approximation problems, a crucial feature for the efficiency of the numerical scheme is stability. Following the general result of [15], the DTBC for the leap-frog scheme on a half-space do not meet the strongest possible stability properties because the leap-frog scheme exhibits glancing wave packets (even in one space dimension). On a half-space, the exact DTBC meet some kind of neutral stability which calls for special care since a slight modification in the numerical boundary conditions may yield violent instabilities.…”
Section: S537mentioning
confidence: 98%
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“…As in all numerical approximation problems, a crucial feature for the efficiency of the numerical scheme is stability. Following the general result of [15], the DTBC for the leap-frog scheme on a half-space do not meet the strongest possible stability properties because the leap-frog scheme exhibits glancing wave packets (even in one space dimension). On a half-space, the exact DTBC meet some kind of neutral stability which calls for special care since a slight modification in the numerical boundary conditions may yield violent instabilities.…”
Section: S537mentioning
confidence: 98%
“…For later use and also for the ease of reading, we first go back to the corresponding one-dimensional problem in Section 3. We adapt the general strategy of [3,18], which was recently generalized in [15], to the particular case of the leap-frog scheme. Some of the tools used in [15] are complemented here by some explicit expansions, based on Legendre polynomials, which were already used in [3,12,18].…”
Section: S537mentioning
confidence: 99%
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