Year: 2021
Type: article
Abstract: Time-spectral methods may feature substantial advantages over time-stepping solvers for solution of initial-value ODEs and PDEs, but their efficiency depends on the smoothness of the solution. We present two methods to overcome this problem. The first involves transforming the differential equation to an equation for a new variable, related to the time-integrated solution, before applying the solution algorithm. In the second method, a procedure for transformation to exact differential equations of a running average is outlined. Examples of solution of stiff problems and problems with multiple time scales are presented, employing the time-spectral Generalized Weighted Residual Method (GWRM). It is found that the smoothing algorithms have a significant positive effect on convergence.
Source: Computer Physics Communications
Authors: Jan Scheffel, Kristoffer Lindvall
Institution: KTH Royal Institute of Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,250
Awards: Implementation of activities described in the Roadmap to Fusion during Horizon 2020 through a Joint programme of the members of the EUROfusion consortium, G2731829129, G2808143221, Implementation of activities described in the Roadmap to Fusion during Horizon 2020 through a Joint programme of the members of the EUROfusion consortium, G6341029978, G829439530, G858011915
OpenAlex ID: W3202687206