| Autor: |
Leung, Shingyu, Chau, Wai Ming, Lee, Young Kyu |
| Zdroj: |
Journal of Scientific Computing; Dec2024, Vol. 101 Issue 3, p1-28, 28p |
| Abstrakt: |
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 ≥ 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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