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Local transparent boundary conditions for wave propagation in fractal trees (ii): error and complexity analysis
Abstract : This work is dedicated to a refined error analysis of the high-order transparent boundary conditions introduced in the companion work [8] for the weighted wave equation on a fractal tree. The construction of such boundary conditions relies on truncating the meromorphic series that represents the symbol of the Dirichlet-to-Neumann operator. The error induced by the truncation depends on the behaviour of the eigenvalues and the eigenfunctions of the weighted Laplacian on a self-similar metric tree. In this work we quantify this error by computing asymptotics of the eigenvalues and bounds for Neumann traces of the eigenfunctions. We prove the sharpness of the obtained bounds for a class of self-similar trees.
Cited literature [18 references]
https://hal.archives-ouvertes.fr/hal-02909750
Contributor : Maryna Kachanovska Connect in order to contact the contributor
Submitted on : Monday, August 3, 2020 - 7:02:49 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:04 PM
Contributor : Maryna Kachanovska Connect in order to contact the contributor
Submitted on : Monday, August 3, 2020 - 7:02:49 PM
Last modification on : Wednesday, May 11, 2022 - 12:06:04 PM
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