A Cartesian Grid Embedded Boundary Method for Poisson's Equation on Irregular Domains

Journal of Computational Physics

Volumn 147, Issue 1, 1998, Pages 60-85

  Johansen, Hans ^a   Colella, Phillip ^a,b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b LAWRENCE BERKELEY NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; CELLS; CYTOLOGY; FINITE VOLUME METHOD; NUMERICAL METHODS;

CARTESIAN GRID; CELL VOLUME; DIRICHLET BOUNDARY CONDITION; DOMAIN BOUNDARY; EMBEDDED BOUNDARY METHODS; FINITE VOLUME DISCRETIZATIONS; IRREGULAR DOMAINS; SECOND ORDERS; TWO-DIMENSIONAL; VARIABLE COEFFICIENTS;

POISSON EQUATION;

EID: 0001827481     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1006/jcph.1998.5965     Document Type: Article

References (36)

1. L. Adams, A multigrid algorithm for immersed interface problems, Proceedings, 7th Copper Mountain Multigrid Conference, Copper Mountain, CO, April 2-7, 1995. http://na.cs.yale.edu/mgnet/www/mgnet-ccmm95.html.
2. M. J. Aftosmis, J. E. Melton, M. J. Berger, Adaptation and surface modelling for Cartesian mesh methods, AIAA 12th Computational Fluid Dynamics Conference, San Diego, CA, June 19-22, 1995.
3. Almgren A. S., Bell J. B., Colella P., Howell L. H., Welcome M. L. A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. J. Comput. Phys. 142:1998;1.
4. A. S. Almgren, J. B. Bell, P. Colella, L. H. Howell, An adaptive projection method for the incompressible Euler equations, Proceedings, AIAA 11th Computational Fluid Dynamics Conference, Orlando, FL, July 6-9, 1993.
5. Almgren A., Bell J. B., Colella P., Marthaler T. A Cartesian grid projection method for the incompressible Euler equations in complex geometries. SIAM J. Sci. Comput. 18:1998;1289.
6. Babuska I. Modeling, Mesh Generation, and Adaptive Numerical Methods for Partial Differential Equations. 1995.
7. J. B. Bell, P. Colella, M. Welcome, Conservative front-tracking for inviscid compressible flow, Proceedings, AIAA 10th Computational Fluid Dynamics Conference, Honolulu, Hawaii, June 24-27, 1991, 814.
8. Berger M. J., Colella P. Local adaptive mesh refinement for shock hydrodynamics. J. Comput. Phys. 82:1989;64.
9. Berger M. J., Oliger J. Adaptive mesh refinement for hyperbolic partial differential equations. J. Comput. Phys. 53:1984;484.
10. Bramble J. H., Ewing R. E., Pasciak J. E., Shen J. The analysis of multigrid algorithms for cell-centered finite difference methods. Adv. Comput. Math. 5:1996;15.
11. Briggs W. A Multigrid Tutorial. 1987.
12. Chan T. F., Mathew T. P. Domian decomposition algorithms. Acta Numer. 1994;41.
13. Chern I., Colella P. A Convervative Front Tracking Method for Hyperbolic Conservation Laws. July 1987.
14. Colella P., Henderson L. F. The von Neumann paradox for the diffraction of weak shock waves. J. Fluid Mech. 213:1990;71.
15. Crutchfield W. Y., Welcome M. L. Object-oriented implementations of adaptive mesh refinement algorithms. Sci. Programming. 2:1993;145.
16. Demkowicz L., Oden J. T., Rachowicz W., Hardy O. Toward a universal h-p adaptive finite element strategy. Comput. Methods Appl. Mech. Eng. 77:1989;79.
17. Greengard L., Lee J. A direct Poisson solver of arbitrary order accuracy. J. Comput. Phys. 125:1996;415.
18. Chesshire G., Henshaw W. D. Composite overlapping meshes for the solution of partial differential equations. J. Comput. Phys. 90:1990;1.
19. Gilbarg N., Trudinger N. S. Elliptic Partial Differential Equations of Second Order. 1977.
20. Howell L. H., Bell J. B. An adaptive-mesh projection method for viscous incompressible flow. SIAM J. Sci. Comp. 18:1997;996.
21. Johnson C. Numerical Solution of Partial Differential Equations by the Finite Element Method. 1987.
22. LeVeque R. J., Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 31:1994;1019.
23. M. S. Day, P. Colella, M. Lijewski, C. A. Rendleman, D. L. Marcus, Embedded boundary algorithms for solving elliptic PDEs on complex domains, J. Comput. Phys.
24. Puckett E. G., Almgren A. S., Bell J. B., Marcus D. L., Rider W. J. A high-order projection method for tracking fluid interfaces in variable density incompressible flows. J. Comput. Phys. 130:1997;269.
25. Johansen H. Cartesian Grid Embedded Boundary Finite Difference Methods for Elliptic and Parabolic Differential Equations on Irregular Domains, 1997.
26. Li Z. The Immersed Interface Method - A Numerical Approach for Partial Differential Equations with Interfaces, 1994.
27. Li Z. A fast iterative method for elliptic interface problems. SIAM J. Numer. Anal. 35:1998;230.
28. Martin D. F., Cartwright K. L. Solving Poisson's Equation Using Adaptive Mesh Refinement. October 1996.
29. Mayo A. The rapid evaluation of volume integrals of potential theory on general regions. J. Comput. Phys. 100:1992;236.
30. McKenney A., Greengard L., Mayo A. A fast Poisson solver for complex geometries. J. Comput. Phys. 118:1995;348.
31. Minion M. A projection method for locally refined grids. J. Comput. Phys. 127:1996;158.
32. Pember R. B., Bell J. B., Colella P., Crutchfield W. Y., Welcome M. An adaptive Cartesian grid method for unsteady compressible flow in irregular regions. J. Comput. Phys. 120:1995;278.
33. Peskin C. S., Printz B. F. Improved volume conservation in the computation of flows with immersed elastic boundaries. J. Comput. Phys. 105:1993;33.
34. C. Rendleman, BoxLib tutorial, http://www.nersc.gov/research/CCSE/software/boxlib.tutorial/boxlib.html.
35. Schmidt A. Computation of three dimensional dendrites with finite elements. J. Comput. Phys. 125:1996;293.
36. Young D. P., Melvin R. G., Bieterman M. B., Johnson F. T., Samant S. S., Bussoletti J. E. A locally refined rectangular grid finite element method: Application to computational fluid dynamics and computational physics. J. Comput. Phys. 62:1991;1.