A preconditioner for the Ohta--Kawasaki equation
We propose a new preconditioner for the Ohta–Kawasaki equation, a nonlocal Cahn– Hilliard equation that describes the evolution of diblock copolymer melts. We devise a computable approximation to the inverse of the Schur complement of the coupled second-order formulation via a matching strategy. The...
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| Format: | Journal article |
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Society for Industrial and Applied Mathematics
2017
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| Summary: | We propose a new preconditioner for the Ohta–Kawasaki equation, a nonlocal Cahn– Hilliard equation that describes the evolution of diblock copolymer melts. We devise a computable approximation to the inverse of the Schur complement of the coupled second-order formulation via a matching strategy. The preconditioner achieves mesh independence: as the mesh is refined, the number of Krylov iterations required for its solution remains approximately constant. In addition, the preconditioner is robust with respect to the interfacial thickness parameter if a timestep criterion is satisfied. This enables the highly resolved finite element simulation of three-dimensional diblock copolymer melts with over one billion degrees of freedom. |
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