Explicit adaptive time stepping for the Cahn-Hilliard equation by exponential Krylov subspace and Chebyshev polynomial methods

2025/02/20 by Botchev, Mike A.
#65L04 #65L20 #65M20 #Computational Engineering #Computational Physics (physics.comp-ph) #FOS: Computer and information sciences #FOS: Mathematics #FOS: Physical sciences #Finance #Numerical Analysis (math.NA) #and Science (cs.CE)

paper · doi:10.48550/arxiv.2502.14589

Abstract

The Cahn-Hilliard equation has been widely employed within various mathematical models in physics, chemistry and engineering. Explicit stabilized time stepping methods can be attractive for time integration of the Cahn-Hilliard equation, especially on parallel and hybrid supercomputers. In this paper, we propose an exponential time integration method for the Cahn-Hilliard equation and describe its efficient Krylov subspace based implementation. We compare the method to a Chebyshev polynomial local iteration modified (LIM) time stepping scheme. Both methods are explicit (i.e., do not involve linear system solution) and tested with both constant and adaptively chosen time steps.

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