Superconvergence of the Strang splitting when using the Crank-Nicolson scheme for parabolic PDEs with Dirichlet and oblique boundary conditions

Autor: Guillaume Bertoli, Christophe Besse, Gilles Vilmart

Publikováno v: Mathematics of Computation
Mathematics of Computation, 2021, 90 (332), pp.2705-2729
Mathematics of computation, Vol. 90, No 332 (2021) pp. 2705-2729

International audience; We show that the Strang splitting method applied to a diffusion-reaction equation with inhomogeneous general oblique boundary conditions is of order two when the diffusion equation is solved with the Crank-Nicolson method, whi

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::97c53a03dff21a5ce8e56c02ab1a5315
https://hal.science/hal-02992821

Discrete transparent boundary conditions for the two-dimensional leap-frog scheme: approximation and fast implementation

Autor: Christophe Besse, Jean-François Coulombel, Pascal Noble

Publikováno v: ESAIM: Mathematical Modelling and Numerical Analysis
ESAIM: Mathematical Modelling and Numerical Analysis, 2021, 55, pp.S535-S571. ⟨10.1051/m2an/2020052⟩
ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2021, 55, pp.S535-S571. ⟨10.1051/m2an/2020052⟩

International audience; We develop a general strategy in order to implement approximate discrete transparent boundary conditions for finite difference approximations of the two-dimensional transport equation. The computational domain is a rectangle e

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1bad6bd77d178189bf3947d7b698d2ba
https://hal.science/hal-03154036

A conservation law with spatially localized sublinear damping

Autor: Rémi Carles, Sylvain Ervedoza, Christophe Besse

Publikováno v: Annales de l'Institut Henri Poincaré C, Analyse non linéaire
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, 2020, 37 (1), pp.13-50. ⟨10.1016/j.anihpc.2019.03.002⟩
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis
Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, Elsevier, 2020, 37 (1), pp.13-50. ⟨10.1016/j.anihpc.2019.03.002⟩

International audience; We consider a general conservation law on the circle, in the presence of a sublinear damping. If the damping acts on the whole circle, then the solution becomes identically zero in finite time, following the same mechanism as

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0fd47a4d972b830da8c0ef063481436c
https://hal.science/hal-01741189

Well-suited and adaptive post-processing for the visualization of hp simulation results

Autor: Christophe Besse, Vincent Mouysset, Matthieu Maunoury, Pol-André Haas, Sébastien Pernet

Publikováno v: Journal of Computational Physics
Journal of Computational Physics, Elsevier, 2018, 375, pp.1179-1204. ⟨10.1016/j.jcp.2018.09.017⟩
Journal of Computational Physics, 2018, 375, pp.1179-1204. ⟨10.1016/j.jcp.2018.09.017⟩

International audience; While high order methods became very popular as they allow to perform very accurate solutions with low computational time and memory cost, there is a lack of tools to visualize and post-treat the solutions given by these metho

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9ca0e27326651887f2108e334c0250eb
https://hal.archives-ouvertes.fr/hal-01743380/document

Accurate, Automatic and Compressed Visualization of Radiated Helmholtz Fields from Boundary Element Solutions

Autor: Christophe Besse, Vincent Mouysset, Sébastien Pernet, Matthieu Maunoury

Publikováno v: Lecture Notes in Computer Science ISBN: 9783319936970
ICCS (1)

We propose a methodology to generate an accurate and efficient reconstruction of radiated fields based on high order interpolation. As the solution is obtained with the convolution by a smooth but potentially high frequency oscillatory kernel, our ba

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::3fa946faf20b091b6ca105a56c0aa712
https://doi.org/10.1007/978-3-319-93698-7_54