TY - JOUR
T1 - A linear second-order convex splitting scheme for the modified phase-field crystal equation with a strong nonlinear vacancy potential
AU - Lee, Hyun Geun
N1 - Publisher Copyright:
© 2024 Elsevier Ltd
PY - 2024/10
Y1 - 2024/10
N2 - The modified phase-field crystal (MPFC) equation was extended to the MPFC equation with a strong nonlinear vacancy potential (VMPFC) to include vacancies. In this paper, we develop a linear, second-order, and unconditionally energy stable scheme for solving the VMPFC equation by proposing a new linear convex splitting, using the Crank–Nicolson formula to the contractive part and the second-order Adams–Bashforth formula to the expansive part, and adding a second-order Douglas–Dupont regularization. The unconditional energy stability of the developed scheme is proved. By solving the VMPFC equation, vacancies which exist in real materials can be observed in numerical simulations.
AB - The modified phase-field crystal (MPFC) equation was extended to the MPFC equation with a strong nonlinear vacancy potential (VMPFC) to include vacancies. In this paper, we develop a linear, second-order, and unconditionally energy stable scheme for solving the VMPFC equation by proposing a new linear convex splitting, using the Crank–Nicolson formula to the contractive part and the second-order Adams–Bashforth formula to the expansive part, and adding a second-order Douglas–Dupont regularization. The unconditional energy stability of the developed scheme is proved. By solving the VMPFC equation, vacancies which exist in real materials can be observed in numerical simulations.
KW - Linear convex splitting
KW - Modified phase-field crystal equation
KW - Strong nonlinear vacancy potential
KW - Unconditional energy stability
UR - http://www.scopus.com/inward/record.url?scp=85193250901&partnerID=8YFLogxK
U2 - 10.1016/j.aml.2024.109145
DO - 10.1016/j.aml.2024.109145
M3 - Article
AN - SCOPUS:85193250901
SN - 0893-9659
VL - 156
JO - Applied Mathematics Letters
JF - Applied Mathematics Letters
M1 - 109145
ER -