TY - JOUR
T1 - Exploring oversampling in RBF least-squares collocation method of lines for surface diffusion
AU - Chen, Meng
AU - Ling, Leevan
N1 - Funding information:
This work was supported by the General Research Fund (GRF no. 12301419, 112301520, 12301021, 12300922) of Hong Kong Research Grant Council, Natural Science Foundation of Jiangxi Province (Grant No. 20212BAB211020), National Natural Science Foundation of China (grant no. 12001261, 12361086), and National Key R&D Program of China (grant no. 2022YFB4501703).
Publisher Copyright:
© 2024, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2024/11
Y1 - 2024/11
N2 - This paper investigates the numerical behavior of the radial basis functions least-squares collocation (RBF-LSC) method of lines (MoL) for solving surface diffusion problems, building upon the theoretical analysis presented in [Chen et al. SIAM J. Numer. Anal. 61(3), 1386–1404 (2023)]. Specifically, we examine the impact of the oversampling ratio, defined as the number of collocation points used over the number of RBF centers for quasi-uniform sets, on the stability of the eigenvalues, time-stepping sizes taken by Runge–Kutta methods, and overall accuracy of the method. By providing numerical evidence and insights, we demonstrate the importance of the oversampling ratio for achieving accurate and efficient solutions with the RBF-LSC-MoL method. Our results reveal that the oversampling ratio plays a critical role in determining the stability of the eigenvalues, and we provide guidelines for selecting an optimal oversampling ratio that balances accuracy and computational efficiency.
AB - This paper investigates the numerical behavior of the radial basis functions least-squares collocation (RBF-LSC) method of lines (MoL) for solving surface diffusion problems, building upon the theoretical analysis presented in [Chen et al. SIAM J. Numer. Anal. 61(3), 1386–1404 (2023)]. Specifically, we examine the impact of the oversampling ratio, defined as the number of collocation points used over the number of RBF centers for quasi-uniform sets, on the stability of the eigenvalues, time-stepping sizes taken by Runge–Kutta methods, and overall accuracy of the method. By providing numerical evidence and insights, we demonstrate the importance of the oversampling ratio for achieving accurate and efficient solutions with the RBF-LSC-MoL method. Our results reveal that the oversampling ratio plays a critical role in determining the stability of the eigenvalues, and we provide guidelines for selecting an optimal oversampling ratio that balances accuracy and computational efficiency.
KW - Eigenvalue stability
KW - Kernel-based least-squares collocation methods
KW - Method of lines
KW - Partial differential equations on manifolds
KW - Surface diffusion
UR - http://www.scopus.com/inward/record.url?scp=85181724701&partnerID=8YFLogxK
U2 - 10.1007/s11075-023-01741-4
DO - 10.1007/s11075-023-01741-4
M3 - Journal article
AN - SCOPUS:85181724701
SN - 1017-1398
VL - 97
SP - 1067
EP - 1087
JO - Numerical Algorithms
JF - Numerical Algorithms
IS - 3
ER -