Year: 2024
Type: article
Abstract: We mimic the conventional explicit Total Variation Diminishing Runge–Kutta (TVDRK) schemes and propose a class of numerical integrators to solve differential equations on a unit sphere. Our approach utilizes the exponential map inherent to the sphere and employs spherical linear interpolation (SLERP). These modified schemes, named SLERP-TVDRK methods or STVDRK, offer improved accuracy compared to typical projective RK methods. Furthermore, they eliminate the need for any projection and provide a straightforward implementation. While we have successfully constructed STVDRK schemes only up to third-order accuracy, we explain the challenges in deriving STVDRK-r for $$r\ge 4$$ r ≥ 4 . To showcase the effectiveness of our approach, we will demonstrate its application in solving the eikonal equation on the unit sphere and simulating p-harmonic flows using our proposed method.
Source: Journal of Scientific Computing
Authors: Shingyu Leung, Wai Ming Chau, Young Kyu Lee
Institution: Hong Kong University of Science and Technology
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: G3042908541, G8768483371
OpenAlex ID: W4403786446