TY - JOUR
T1 - A localized extrinsic collocation method for Turing pattern formations on surfaces
AU - Tang, Zhuochao
AU - Fu, Zhuojia
AU - Chen, Meng
AU - Ling, Leevan
N1 - Funding Information:
The work described in this paper was supported by the National Science Funds of China (Grant No. 11772119, No. 12001261 ), the Fundamental Research Funds for the Central Universities, China (Grant No. B200203122 ), the Six Talent Peaks Project in Jiangsu Province of China (Grant No. 2019-KTHY-009 ), the Postgraduate Research and Practice Innovation Program of Jiangsu Province, China (Grant No. KYCX20_0427 ), and a Hong Kong Research Grant Council GRF, China Grant.
Publisher Copyright:
© 2021 Elsevier Ltd
PY - 2021/12
Y1 - 2021/12
N2 - In this paper, we give our first attempt to implement a localized collocation method, namely Generalized Finite Difference Method (GFDM), for the Turing patterns formation problems on smooth, closed, connected surfaces of codimension one embedded in R3. Based on projections from surface differential operators to Euclidean differential operators, the surface PDEs in extrinsic form are given explicitly and could be solved directly by GFDM only using a set of collocation points distributed on surfaces. A sparse system formed from localization scheme makes it efficient for solving long time evolution Turing patterns formation problems. Numerical demonstrations including convergence test, Turing spot and stripe problems are provided to illustrate its potentiality.
AB - In this paper, we give our first attempt to implement a localized collocation method, namely Generalized Finite Difference Method (GFDM), for the Turing patterns formation problems on smooth, closed, connected surfaces of codimension one embedded in R3. Based on projections from surface differential operators to Euclidean differential operators, the surface PDEs in extrinsic form are given explicitly and could be solved directly by GFDM only using a set of collocation points distributed on surfaces. A sparse system formed from localization scheme makes it efficient for solving long time evolution Turing patterns formation problems. Numerical demonstrations including convergence test, Turing spot and stripe problems are provided to illustrate its potentiality.
KW - Generalized Finite Difference Method
KW - Localized meshless method
KW - PDEs on surfaces
KW - Semi-implicit backward differentiation method
UR - http://www.scopus.com/inward/record.url?scp=85111280889&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2021.107534
DO - 10.1016/j.aml.2021.107534
M3 - Journal article
AN - SCOPUS:85111280889
SN - 0893-9659
VL - 122
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 107534
ER -