Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose an efficient finite difference scheme for solving the Cahn-Hilliard equation with a variable mobility in complex domains. Our method employs a type of unconditionally gradient stable splitting discretization.  also extend the scheme to compute the Cahn-Hilliard equation in arbitrarily shaped domains.  prove the mass conservation property of the proposed discrete scheme for complex domains. The resulting discretized equations are solved using a multigrid method. Numerical simulations are presented to demonstrate that the proposed scheme can deal with complex geometries robustly. Furthermore, the multigrid efficiency is retained even if the embedded domain is present.
['Jaemin Shin', 'Darae Jeong', 'Junseok Kim']
I am writing a research paper on a idea A conservative numerical method for the Cahn-Hilliard equation in complex domains
[{"from": "human", "value": "I am writing a research paper on a idea A conservative numerical method for the Cahn-Hilliard equation in complex domains"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose an efficient finite difference scheme for solving the Cahn-Hilliard equation with a variable mobility in complex domains. Our method employs a type of unconditionally gradient stable splitting discretization.  also extend the scheme to compute the Cahn-Hilliard equation in arbitrarily shaped domains.  prove the mass conservation property of the proposed discrete scheme for complex domains. The resulting discretized equations are solved using a multigrid method. Numerical simulations are presented to demonstrate that the proposed scheme can deal with complex geometries robustly. Furthermore, the multigrid efficiency is retained even if the embedded domain is present."}]