Numerical approximation and simulation of the stochastic wave equation on the sphere
Artikel i vetenskaplig tidskrift, 2022
Solutions to the stochastic wave equation on the unit sphere are approximated by spectral methods. Strong, weak, and almost sure convergence rates for the proposed numerical schemes are provided and shown to depend only on the smoothness of the driving noise and the initial conditions. Numerical experiments confirm the theoretical rates. The developed numerical method is extended to stochastic wave equations on higher-dimensional spheres and to the free stochastic Schrödinger equation on the unit sphere.
Gaussian random fields
Strong and weak convergence rates
Spectral Galerkin methods
Stochastic Schrödinger equation
Sphere
Stochastic wave equation
Karhunen–Loève expansion
Stochastic partial differential equations
Almost sure convergence
Spherical harmonic functions
Författare
David Cohen
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Annika Lang
Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik
Calcolo
0008-0624 (ISSN) 1126-5434 (eISSN)
Vol. 59 3 32Numerisk analys och simulering av PDE med slumpmässig dispersion
Vetenskapsrådet (VR) (2018-04443), 2019-01-01 -- 2022-12-31.
Efficienta approximeringsmetoder för stokastiska fält på mångfalder
Vetenskapsrådet (VR) (2020-04170), 2021-01-01 -- 2024-12-31.
Ämneskategorier
Beräkningsmatematik
Strömningsmekanik och akustik
Matematisk analys
DOI
10.1007/s10092-022-00472-7