TY - JOUR
T1 - A linear, high-order, and unconditionally energy stable scheme for the epitaxial thin film growth model without slope selection
AU - Shin, Jaemin
AU - Lee, Hyun Geun
N1 - Publisher Copyright:
© 2021 IMACS
PY - 2021/5
Y1 - 2021/5
N2 - The epitaxial thin film growth model without slope selection is the L2-gradient flow of energy with a logarithmic potential in terms of the gradient of a height function. A challenge to numerically solving the model is how to treat the nonlinear term to preserve energy stability without compromising accuracy and efficiency. To resolve this problem, we present a high-order energy stable scheme by placing the linear and nonlinear terms in the convex and concave parts, respectively, and employing the specially designed implicit–explicit Runge–Kutta method. As a result, our scheme is linear, high-order accurate in time, and unconditionally energy stable. We show analytically that the scheme is unconditionally uniquely solvable and energy stable. Numerical experiments are presented to demonstrate the accuracy, efficiency, and energy stability of the proposed scheme.
AB - The epitaxial thin film growth model without slope selection is the L2-gradient flow of energy with a logarithmic potential in terms of the gradient of a height function. A challenge to numerically solving the model is how to treat the nonlinear term to preserve energy stability without compromising accuracy and efficiency. To resolve this problem, we present a high-order energy stable scheme by placing the linear and nonlinear terms in the convex and concave parts, respectively, and employing the specially designed implicit–explicit Runge–Kutta method. As a result, our scheme is linear, high-order accurate in time, and unconditionally energy stable. We show analytically that the scheme is unconditionally uniquely solvable and energy stable. Numerical experiments are presented to demonstrate the accuracy, efficiency, and energy stability of the proposed scheme.
KW - Epitaxial thin film growth
KW - High-order time accuracy
KW - Implicit–explicit Runge–Kutta
KW - Linear convex splitting
KW - Unconditional energy stability
KW - Unconditional unique solvability
UR - http://www.scopus.com/inward/record.url?scp=85100155570&partnerID=8YFLogxK
U2 - 10.1016/j.apnum.2020.12.024
DO - 10.1016/j.apnum.2020.12.024
M3 - Article
AN - SCOPUS:85100155570
SN - 0168-9274
VL - 163
SP - 30
EP - 42
JO - Applied Numerical Mathematics
JF - Applied Numerical Mathematics
ER -