A finite difference method for a conservative Allen–Cahn equation on non-flat surfaces
| Autor: | Darae Jeong, Yongho Choi, Seong-Deog Yang, Junseok Kim |
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| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Physics and Astronomy (miscellaneous) Applied Mathematics Mathematical analysis Finite difference method Boundary (topology) 010103 numerical & computational mathematics 01 natural sciences Poincaré–Steklov operator Computer Science Applications 010101 applied mathematics Euler method Computational Mathematics symbols.namesake Operator (computer programming) Modeling and Simulation Lagrange multiplier symbols Boundary value problem 0101 mathematics Laplace operator Mathematics |
| Zdroj: | Journal of Computational Physics. 334:170-181 |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2016.12.060 |
| Popis: | We present an efficient numerical scheme for the conservative AllenCahn (CAC) equation on various surfaces embedded in a narrow band domain in the three-dimensional space. We apply a quasi-Neumann boundary condition on the narrow band domain boundary using the closest point method. This boundary treatment allows us to use the standard Cartesian Laplacian operator instead of the LaplaceBeltrami operator. We apply a hybrid operator splitting method for solving the CAC equation. First, we use an explicit Euler method to solve the diffusion term. Second, we solve the nonlinear term by using a closed-form solution. Third, we apply a spacetime-dependent Lagrange multiplier to conserve the total quantity. The overall scheme is explicit in time and does not need iterative steps; therefore, it is fast. A series of numerical experiments demonstrate the accuracy and efficiency of the proposed hybrid scheme. |
| Databáze: | OpenAIRE |
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