Journal
ADVANCES IN COMPUTATIONAL MATHEMATICS
Volume 45, Issue 3, Pages 1551-1580Publisher
SPRINGER
DOI: 10.1007/s10444-019-09678-w
Keywords
Modified phase field crystal equation; Unconditionally energy stable; Pseudo energy; Invariant energy quadratization
Categories
Funding
- China Scholarship Council (CSC) [201806280137]
- NSFC [11371289, 11601416]
- NSF [DMS-1720212]
- USC ASPIRE I Track-III/IV Fund
Ask authors/readers for more resources
We consider numerical approximations for the modified phase field crystal equation in this paper. The model is a nonlinear damped wave equation that includes both diffusive dynamics and elastic interactions. To develop easy-to-implement time-stepping schemes with unconditional energy stabilities, we adopt the Invariant Energy Quadratization approach. By using the first-order backward Euler, the second-order Crank-Nicolson, and the second-order BDF2 formulas, we obtain three linear and symmetric positive definite schemes. We rigorously prove their unconditional energy stabilities and implement a number of 2D and 3D numerical experiments to demonstrate the accuracy, stability, and efficiency.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available