Abstract
The aim of this paper is to display numerical results that show the interest of some multilevel methods for problems of parabolic type. These schemes are based on multilevel spatial splittings and the use of dierent time steps for the various spatial components. The spatial discretization we investigate is of spectral Fourier type, so the approximate solution naturally splits into the sum of a low frequency compo- nent and a high frequency one. The time discretization is of implicit/explicit Euler type for each spatial component. Based on a posteriori estimates, we introduce adaptive one-level and mul- tilevel algorithms. Two problems are considered: the heat equation and a nonlinear problem. Numerical experiments are conducted for both problems using the one-level and the multilevel algorithms. The multilevel method is up to 70% faster than the one-level method.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
