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We present a finite difference method for solving the Ohta--Kawasaki model, representing a model of mesoscopic phase separation for the block copolymer. The numerical methods for solving the Ohta--Kawasaki model need to inherit the mass conservation and energy dissipation properties. We prove these characteristic properties and solvability and unconditionally gradient stability of the scheme by using Hessian matrices of a discrete functional. We present numerical results that validate the mass conservation, and energy dissipation, and unconditional stability of the method.
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참고문헌 (26)
참고문헌 신청
A. Brandt / 1977 / Multi-level adaptive solutions to boundary-value problems / Math. Comp 31 (138) : 333 ~ 390
D. Furihata / 2001 / A stable and conservative finite difference scheme for the Cahn?Hilliard Equation / Numer. Math 87 (4) : 675 ~ 699
D. J. Eyre / / An unconditionally stable one-step scheme for gradient systems
D. J. Eyre / 1998 / Unconditionally gradient stable time marching the Cahn?Hilliard equation, Computational and mathematical models of microstructural evolution / Mater. Res. Soc.
F. Drolet / 1999 / Combinatorial screening of complex block copolymer assembly with self-consistent field theory / Phys. Rev. Lett 83 : 4317 ~ 4320
D. Furihata / 2001 / A stable and conservative finite difference scheme for the Cahn?Hilliard Equation / Numer. Math 87 (4) : 675 ~ 699
D. J. Eyre / / An unconditionally stable one-step scheme for gradient systems
D. J. Eyre / 1998 / Unconditionally gradient stable time marching the Cahn?Hilliard equation, Computational and mathematical models of microstructural evolution / Mater. Res. Soc.
F. Drolet / 1999 / Combinatorial screening of complex block copolymer assembly with self-consistent field theory / Phys. Rev. Lett 83 : 4317 ~ 4320
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