Abstract
We present a nonlinear multigrid method to solve the Cahn–Hilliard (CH) equation on nonuniform grids. The CH equation was originally proposed as a mathematical model to describe phase separation phenomena after the quenching of binary alloys. The model has the characteristics of thin diffusive interfaces. To resolve the sharp interfacial transition, we need a very fine grid, which is computationally expensive. To reduce the cost, we can use a fine grid around the interfacial transition region and a relatively coarser grid in the bulk region. The CH equation is discretized by a conservative finite difference scheme in space and an unconditionally gradient stable type scheme in time. We use a conservative restriction in the nonlinear multigrid method to conserve the total mass in the coarser grid levels. Various numerical results on one-, two-, and three-dimensional spaces are presented to demonstrate the accuracy and effectiveness of the nonuniform grids for the CH equation.
| Original language | English |
|---|---|
| Pages (from-to) | 320-333 |
| Number of pages | 14 |
| Journal | Applied Mathematics and Computation |
| Volume | 293 |
| DOIs | |
| Publication status | Published - 2017 Jan 15 |
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Keywords
- Cahn–Hilliard equation
- Finite difference method
- Multigrid method
- Nonuniform grid
ASJC Scopus subject areas
- Computational Mathematics
- Applied Mathematics
Cite this
A multigrid solution for the Cahn–Hilliard equation on nonuniform grids. / Choi, Yongho; Jeong, Darae; Kim, Junseok.
In: Applied Mathematics and Computation, Vol. 293, 15.01.2017, p. 320-333.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A multigrid solution for the Cahn–Hilliard equation on nonuniform grids
AU - Choi, Yongho
AU - Jeong, Darae
AU - Kim, Junseok
PY - 2017/1/15
Y1 - 2017/1/15
N2 - We present a nonlinear multigrid method to solve the Cahn–Hilliard (CH) equation on nonuniform grids. The CH equation was originally proposed as a mathematical model to describe phase separation phenomena after the quenching of binary alloys. The model has the characteristics of thin diffusive interfaces. To resolve the sharp interfacial transition, we need a very fine grid, which is computationally expensive. To reduce the cost, we can use a fine grid around the interfacial transition region and a relatively coarser grid in the bulk region. The CH equation is discretized by a conservative finite difference scheme in space and an unconditionally gradient stable type scheme in time. We use a conservative restriction in the nonlinear multigrid method to conserve the total mass in the coarser grid levels. Various numerical results on one-, two-, and three-dimensional spaces are presented to demonstrate the accuracy and effectiveness of the nonuniform grids for the CH equation.
AB - We present a nonlinear multigrid method to solve the Cahn–Hilliard (CH) equation on nonuniform grids. The CH equation was originally proposed as a mathematical model to describe phase separation phenomena after the quenching of binary alloys. The model has the characteristics of thin diffusive interfaces. To resolve the sharp interfacial transition, we need a very fine grid, which is computationally expensive. To reduce the cost, we can use a fine grid around the interfacial transition region and a relatively coarser grid in the bulk region. The CH equation is discretized by a conservative finite difference scheme in space and an unconditionally gradient stable type scheme in time. We use a conservative restriction in the nonlinear multigrid method to conserve the total mass in the coarser grid levels. Various numerical results on one-, two-, and three-dimensional spaces are presented to demonstrate the accuracy and effectiveness of the nonuniform grids for the CH equation.
KW - Cahn–Hilliard equation
KW - Finite difference method
KW - Multigrid method
KW - Nonuniform grid
UR - http://www.scopus.com/inward/record.url?scp=84985906573&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84985906573&partnerID=8YFLogxK
U2 - 10.1016/j.amc.2016.08.026
DO - 10.1016/j.amc.2016.08.026
M3 - Article
VL - 293
SP - 320
EP - 333
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
SN - 0096-3003
ER -