Numerical approximation and simulation of the stochastic wave equation on the sphere
Journal article, 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
Author
David Cohen
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Annika Lang
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Calcolo
0008-0624 (ISSN) 1126-5434 (eISSN)
Vol. 59 3 32Numerical analysis and simulation of PDEs with random dispersion
Swedish Research Council (VR) (2018-04443), 2019-01-01 -- 2022-12-31.
Efficient approximation methods for random fields on manifolds
Swedish Research Council (VR) (2020-04170), 2021-01-01 -- 2024-12-31.
Subject Categories
Computational Mathematics
Fluid Mechanics and Acoustics
Mathematical Analysis
DOI
10.1007/s10092-022-00472-7