Abstract
<p style='text-indent:20px;'>In this paper, a new Cartesian grid finite difference method is introduced to solve two-dimensional parabolic interface problems with second order accuracy achieved in both temporal and spatial discretization. Corrected central difference and the Matched Interface and Boundary (MIB) method are adopted to restore second order spatial accuracy across the interface, while the standard Crank-Nicolson scheme is employed for the implicit time stepping. In the proposed augmented MIB (AMIB) method, an augmented system is formulated with auxiliary variables introduced so that the central difference discretization of the Laplacian could be disassociated with the interface corrections. A simple geometric multigrid method is constructed to efficiently invert the discrete Laplacian in the Schur complement solution of the augmented system. This leads a significant improvement in computational efficiency in comparing with the original MIB method. Being free of a stability constraint, the implicit AMIB method could be asymptotically faster than explicit schemes. Extensive numerical results are carried out to validate the accuracy, efficiency, and stability of the proposed AMIB method.</p>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference42 articles.
1. L. Adams, T. P. Chartier.New geometric immersed interface multigrid solvers, SIAM J. Sci. Comput., 25 (2004), 1516-1533.
2. L. Adams, Z. Li.The immersed interface/multigrid methods for interface problems, SIAM J. Sci. Comput., 24 (2002), 463-479.
3. C. Attanayake, D. Senaratne.Convergence of an immersed finite element method for semilinear parabolic interface problems, Appl. Math. Sci. (Ruse), 5 (2011), 135-147.
4. P. A. Berthelsen.A decomposed immersed interface method for variable coefficient elliptic equations with non-smooth and discontinuous solutions, J. Comput. Phys., 197 (2004), 364-386.
5. F. Bouchon and G. H. Peichl, An immersed interface technique for the numerical solution of the heat equation on a moving domain, Numerical Mathematics and Advanced Applications 2009, Springer Berlin Heidelberg, (2010), 181–189.
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献