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- W2509943553 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." @default.
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- W2509943553 date "2017-01-01" @default.
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- W2509943553 title "A multigrid solution for the Cahn–Hilliard equation on nonuniform grids" @default.
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- W2509943553 doi "https://doi.org/10.1016/j.amc.2016.08.026" @default.
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