A jump condition capturing finite difference scheme for elliptic interface problems

SIAM Journal on Scientific Computing

Volumn 25, Issue 5, 2004, Pages 1479-1496

  Wang, Wei Cheng ^a  

^a NATIONAL TSING HUA UNIVERSITY   (Taiwan)

Author keywords

Curvilinear coordinate system; Discontinuous coefficient; Finite difference scheme; Interface problem; Poisson equation

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; POISSON EQUATION; PROBLEM SOLVING; SEMICONDUCTOR DEVICE MANUFACTURE; STIFFNESS;

CURVILINEAR COORDINATE SYSTEMS; DISCONTINUOUS COEFFICIENTS; INTERFACE PROBLEMS;

FINITE DIFFERENCE METHOD;

EID: 6344243481     PISSN: 10648275     EISSN: None     Source Type: Journal    
DOI: 10.1137/S1064827502405987     Document Type: Article

References (15)

1. J. BRAMBLE AND J. KING, A finite element method for interface problems in domains with smooth boundaries and interfaces, Adv. Comput. Math., 6 (1996), pp. 109-138.
2. Z. CHEN AND J. ZOU, Finite element methods and their convergence for elliptic and parabolic interface problems, Numer. Math., 79 (1998), pp. 175-202.
3. R. EWING, Z. LI, T. LIN, AND Y. LIN, The immersed finite volume element methods for the elliptic interface problems, Math. Comput. Simulation, 50 (1999), pp. 63-76.
4. T. Y. HOU, Z. LI, S. OSHER, AND H. ZHAO, A hybrid method for moving interface problems with application to the Hele-Shaw flow, J. Comput. Phys., 134 (1997), pp. 236-252.
5. J. HUANG AND J. ZOU, A mortar element method for elliptic problems with discontinuous coefficients, IMA J. Numer. Anal., 22 (2002), pp. 549-576.
6. T.-M. HUANG, W.-W. LIN, J.-L. LIU, AND W.-C. WANG, Numerical computation of cubic eigenvalue problems for a semiconductor quantum dot model, J. Comput. Phys., to appear.
7. T.-M. HUANG, W.-W. LIN, W.-C. WANG, AND W.-C. WANG, Numerical simulation of three dimensional pyramid quantum dot, J. Comput. Phys., to appear.
8. Y.-L. HUANG AND W.-C. WANG, A Monotone Jump Condition Capturing Scheme for Elliptic Interface Problems on Arbitrary Domains, preprint.
9. M.-C. LAI AND W.-C. WANG, Fast direct solvers for Poisson equation on 2D polar and spherical geometries, Numer. Methods Partial Differential Equations, 18 (2002), pp. 56-68.
10. R. J. LEVEQUE AND Z. LI, Immersed interface methods for Stokes flow with elastic boundaries or surface tension, SIAM J. Sci. Comput., 18 (1997), pp. 709-735.
11. Z. LI, A fast iterative algorithm for elliptic interface problems, SIAM J. Numer. Anal., 35 (1998), pp. 230-254.
12. Z. LI, W.-C. WANG, I.-L. CHERN, AND M.-C. LAI, New formulations for interface problems in polar coordinates, SIAM J. Sci. Comput., 25 (2003), pp. 224-245.
13. X.-D. LIU, R. P. FEDKIW, AND M. KANG, A boundary condition capturing method for Poisson's equation on irregular domains, J. Comput. Phys., 160 (2000), pp. 151-178.
14. S. OSHER AND R. P. FEDKIW, Level set methods: An overview and some recent results, J. Comput. Phys., 169 (2001), pp. 463-502.
15. M. KANG, R. P. FEDKIW, AND X.-D. LIU, A boundary condition capturing method for multiphase incompressible flow, J. Sci. Comput., 15 (2000), pp. 323-360.