TY - JOUR
T1 - Nonlinear multigrid implementation for the two-dimensional cahn-hilliard equation
AU - Lee, Chaeyoung
AU - Jeong, Darae
AU - Yang, Junxiang
AU - Kim, Junseok
N1 - Funding Information:
Funding: The first author (C. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education(NRF-2019R1A6A3A13094308). D. Jeong was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). J. Yang is supported by China Scholarship Council (201908260060). The corresponding author (J.S. Kim) expresses thanks for the support from the BK21 PLUS program.
PY - 2020/1/1
Y1 - 2020/1/1
N2 - We present a nonlinear multigrid implementation for the two-dimensional Cahn-Hilliard (CH) equation and conduct detailed numerical tests to explore the performance of the multigrid method for the CH equation. The CH equation was originally developed by Cahn and Hilliard to model phase separation phenomena. The CH equation has been used to model many interface-related problems, such as the spinodal decomposition of a binary alloy mixture, inpainting of binary images, microphase separation of diblock copolymers, microstructures with elastic inhomogeneity, two-phase binary fluids, in silico tumor growth simulation and structural topology optimization. The CH equation is discretized by using Eyre's unconditionally gradient stable scheme. The system of discrete equations is solved using an iterative method such as a nonlinear multigrid approach, which is one of the most efficient iterative methods for solving partial differential equations. Characteristic numerical experiments are conducted to demonstrate the efficiency and accuracy of the multigrid method for the CH equation. In the Appendix, we provide C code for implementing the nonlinear multigrid method for the two-dimensional CH equation.
AB - We present a nonlinear multigrid implementation for the two-dimensional Cahn-Hilliard (CH) equation and conduct detailed numerical tests to explore the performance of the multigrid method for the CH equation. The CH equation was originally developed by Cahn and Hilliard to model phase separation phenomena. The CH equation has been used to model many interface-related problems, such as the spinodal decomposition of a binary alloy mixture, inpainting of binary images, microphase separation of diblock copolymers, microstructures with elastic inhomogeneity, two-phase binary fluids, in silico tumor growth simulation and structural topology optimization. The CH equation is discretized by using Eyre's unconditionally gradient stable scheme. The system of discrete equations is solved using an iterative method such as a nonlinear multigrid approach, which is one of the most efficient iterative methods for solving partial differential equations. Characteristic numerical experiments are conducted to demonstrate the efficiency and accuracy of the multigrid method for the CH equation. In the Appendix, we provide C code for implementing the nonlinear multigrid method for the two-dimensional CH equation.
KW - Cahn-Hilliard equation
KW - multigrid method
KW - unconditionally gradient stable scheme
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U2 - 10.3390/math8010097
DO - 10.3390/math8010097
M3 - Article
AN - SCOPUS:85080123466
SN - 2227-7390
VL - 8
JO - Mathematics
JF - Mathematics
IS - 1
M1 - 97
ER -