On the study and development of high-order time integration schemes for odes applied to acoustic and electromagnetic wave propagation problems

Mamadou N'Diaye 1, 2
1 Magique 3D - Advanced 3D Numerical Modeling in Geophysics
LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau], Inria Bordeaux - Sud-Ouest
Abstract : In this thesis, we study and develop different families of time integration schemes for linear ODEs. After presenting the space discretisation methods and a review of classical Runge-Kutta schemes in the first part, we construct high-order A-stable time integration schemes for an arbitrary order with low-dissipation and low-dispersion effects in the second part. Then we develop explicit schemes with an optimal CFL number for a typical profile of spectrum. The obtained CFL number and the efficiency on the typical profile for each explicit scheme are given. Pursuing our aim, we propose a methodology to construct locally implicit methods of arbitrary order. We present the locally implicit methods obtained from the combination of the A-stable implicit schemes we have developed and explicit schemes with optimal CFL number. We use them to solve the acoustic wave equation and provide convergence curves demonstrating the performance of the obtained schemes. In addition of the different 1D and 2D validation tests performed while solving the acoustic wave equation, we present numerical simulation results for 3D acoustic wave and the Maxwell’s equations in the last part.
Complete list of metadatas

Cited literature [53 references]  Display  Hide  Download

https://hal.inria.fr/tel-01808393
Contributor : Mamadou N'Diaye <>
Submitted on : Tuesday, June 5, 2018 - 4:02:36 PM
Last modification on : Sunday, April 7, 2019 - 3:00:04 PM
Long-term archiving on : Thursday, September 6, 2018 - 7:08:36 PM

File

Thesis_MamadouNdiaye.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : tel-01808393, version 1

Citation

Mamadou N'Diaye. On the study and development of high-order time integration schemes for odes applied to acoustic and electromagnetic wave propagation problems. Mathematics [math]. Université de Pau et des pays de l'Adour, 2017. English. ⟨tel-01808393⟩

Share

Metrics

Record views

203

Files downloads

157