A Poisson-Boltzmann solver on irregular domains with Neumann or Robin boundary conditions on non-graded adaptive grid

Journal of Computational Physics

Volumn 230, Issue 10, 2011, Pages 3830-3848

  Helgadóttir, Ásdís ^a   Gibou, Frédéric ^a  

^a University of California   (United States)

Author keywords

Adaptive grid; Finite Difference method; Irregular domain; Level set; Neumann boundary condition; Octree; Poisson Boltzmann solver; Robin boundary condition

Indexed keywords

BOLTZMANN EQUATION; BOUNDARY CONDITIONS; FINITE DIFFERENCE METHOD; GEOMETRY; MATRIX ALGEBRA; NUMERICAL METHODS; POISSON EQUATION;

ADAPTIVE GRIDS; FINITE-DIFFERENCE METHODS; IRREGULAR DOMAINS; LEVEL SET; NEUMANN BOUNDARY CONDITION; OCTREES; POISSON-BOLTZMANN; POISSON-BOLTZMANN SOLV; ROBIN BOUNDARY CONDITIONS; SPATIAL DIMENSION;

LINEAR SYSTEMS;

EID: 79952900041     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2011.02.010     Document Type: Article

References (48)

1. M.J. Aftosmis, M.J. Berger, J.E. Melton, Adaptive cartesian mesh generation, in: CRC Handbook of Mesh Generation (Contributed Chapter), 1998.
2. Baker N., Holst M., Wang F. Adaptive multilevel finite element solution of the Poisson-Boltzmann equation; II: Refinement at solvent accessible surfaces in biomolecular systems. J. Comput. Chem. 2000, 21:1343-1352.
3. Baker N., Sept D., Holst M., McCammon J.A. The adaptive multilevel finite element solution of the Poisson-Boltzmann equation on massively parallel computers. IBM J. Res. Dev. 2001, 45(3/4):427.
4. Bashford D. An object-oriented programming suite for electrostatic effects in biological molecules. Lect. Notes Comput. Sci. 1997, 1343:233-240.
5. Bowen W.R., Williams P.M. Finite difference solution of the 2-dimensional Poisson-Boltzmann equation for spheres in confined geometries. Colloids Surfaces A: Physicochem. Eng. Aspects 2002, 204:103-115.
6. Chen H., Min C., Gibou F. A supra-convergent finite difference scheme for the Poisson and heat equations on irregular domains and non-graded adaptive cartesian grids. J. Sci. Comput. 2007, 31:19-60.
7. Chen H., Min C., Gibou F. A numerical scheme for the Stefan problem on adaptive Cartesian grids with supralinear convergence rate. J. Comput. Phys. 2009, 228.
8. Chen L., Holst M.J., Xu J. The finite element approximation of the nonlinear Poisson-Boltzmann equation. SIAM J. Numer. Anal. 2007, 45(6):2298-2320.
9. Chern I.L., Liu J.C., Wang W.C. Accurate evaluation of electrostatics for macromolecules in solution. Methods Appl. Anal. 2003, 10:309-328.
10. Cortis C.M., Friesner R.A. Numerical solution of the Poisson-Boltzmann equation using tetrahedral finite-element meshes. J. Comput. Chem. 1997, 18(13):1591-1608.
11. Dyshlovenko P. Adaptive mesh enrichment for the Poisson-Boltzmann equation. J. Comput. Phys. 2001, 172:198-208.
12. Dyshlovenko P. Adaptive mesh enrichment for the Poisson-Boltzmann equation and its application. Comput. Phys. Commun. 2002, 147:335-338.
13. Geng W., Yu S., Wei G.W. Treatment of charge singularities in implicit solvent models. J. Chem. Phys. 2007, 127(11):114106.
14. Gibou F., Fedkiw R. A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains, with applications to the Stefan problem. J. Comput. Phys. 2005, 202:577-601.
15. Gibou F., Fedkiw R., Caflisch R., Osher S. A level set approach for the numerical simulation of dendritic growth. J. Sci. Comput. 2003, 19:183-199.
16. Gibou F., Fedkiw R., Cheng L.-T., Kang M. A second-order-accurate symmetric discretization of the Poisson equation on irregular domains. J. Comput. Phys. 2002, 176:205-227.
17. G. Guyomarch, C.-O. Lee, A discontinuous Galerkin method for elliptic interface problems with applications to eletroporation, Tech. Rep., Korea Advanced Institute of Science and Technology, 2004.
18. M. Holst, Multilevel methods for the Poisson-Boltzmann equation, Ph.D. Thesis, Numerical Computing Group, University of Illinois at Urbana-Champaign, June 1993.
19. Holst M. Adaptive numerical treatment of elliptic systems on manifolds. Adv. Comput. 2001, 15(1-4):139-191.
20. Holst M., Baker N., Wang F. Adaptive multilevel finite element solution of the Poisson-Boltzmann equation; I: algorithms and examples. J. Comput. Chem. 2000, 21:1319-1342.
21. Im W., Beglov D., Roux B. Continuum solvation model: computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation. Comput. Phys. Commun. 1998, 111:59-75.
22. Klapper I., Hagstrom R., Fine R., Sharp K., Honig B. Focusing of electric fields in the active site of Cu-Zn superoxide dismutase: effects of ionic strength and amino-acid modification. Proteins 1986, 1(1):47-59.
23. LeVeque R.J., Li Z. The immersed interface method for elliptic equations with discontinuous coefficients and singular sources. SIAM J. Numer. Anal. 1994, 31:1019.
24. Li Z., Pao C.V., Qiao Z. A finite difference method and analysis for 2D nonlinear Poisson-Boltzmann equations. J. Sci. Comput. 2007, 30(1):61-81.
25. Lu B.Z., Zhou Y.C., Holst M.J., McCammon J.A. Recent progress in numerical methods for the Poisson-Boltzmann equation in biophysical applications. Commun. Comput. Phys. 2008, 3(5):973-1009.
26. Lu Q., Lou R. The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology. J. Chem. Phys. 2003, 119:11035.
27. Madura J.D., Briggs J.M., Wade R.C., Davis M.E., Luty B.A., Ilin A., Antosiewicz J., Gilson M.K., Bagheri B., Scott L.R., McCammon J.A. Electrostatics and diffusion of molecules in solution - simulations with the University of Houston Brownian dynamics program. Comput. Phys. Commun. 1995, 91(1-3):57-95.
28. Min C. Local level set method in high dimension and codimension. J. Comput. Phys. 2004, 200:368-382.
29. Min C., Gibou F. A second order accurate projection method for the incompressible Navier-Stokes equation on non-graded adaptive grids. J. Comput. Phys. 2006, 219:912-929.
30. Min C., Gibou F. Geometric integration over irregular domains with application to level set methods. J. Comput. Phys. 2007, 226:1432-1443.
31. Min C., Gibou F. A second order accurate level set method on non-graded adaptive Cartesian grids. J. Comput. Phys. 2007, 225:300-321.
32. Min C., Gibou F., Ceniceros H. A supra-convergent finite difference scheme for the variable coefficient Poisson equation on non-graded grids. J. Comput. Phys. 2006, 218:123-140.
33. Ng Y-T., Min C., Gibou F. An efficient fluid-solid coupling algorithm for single-phase flows. J. Comput. Phys. 2009, 228:8807-8829.
34. Nicholls A., Bharadwaj R., Honig B. Grasp - graphical representation and analysis of surface-properties. Biophys. J. 1993, 64(2):A166.
35. Nicholls A., Honig B. A rapid finite difference algorithm, utilizing successive over-relaxation to solve the Poisson-Boltzmann equation. J. Comput. Chem. 1991, 12:435.
36. Osher S., Sethian J. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 1988, 79:12-49.
37. Papac J., Gibou F., Ratsch C. Efficient symmetric discretization for the Poisson, heat and Stefan-type problems with Robin boundary conditions. J. Comput. Phys. 2010, 229:875-889.
38. Peskin C.S. Numerical analysis of blood flow in the heart. J. Comput. Phys. 1977, 25:220.
39. Prabhu N.V., Zhu P., Sharp K.A. The Poisson-Boltzmann equation for biomolecular electrostatics: a tool for structural biology. J. Comput. Chem. 2004, 25(16):2049-2064.
40. Qiao Z., Li Z., Tang T. A finite difference scheme for solving the nonlinear Poisson-Boltzmann equation modeling charged spheres. J. Comput. Math. 2006, 24:252-264.
41. Samet H. The Design and Analysis of Spatial Data Structures 1989, Addison-Wesley, New York.
42. Samet H. Applications of Spatial Data Structures: Computer Graphics, Image Processing and GIS 1990, Addison-Wesley, New York.
43. Shestakov A.I., Milovich J.L., Noy A. Solution of the nonlinear Poisson-Boltzmann equation using pseudo-transient continuation and the finite element method. J. Colloid Interf. Sci. 2002, 247(1):62-79.
44. Wang W-C. A jump condition capturing finite difference scheme for elliptic interface problems. SIAM J. Sci. Comput. 2004, 25:1479.
45. Xie D., Zhou S. A new minimization protocol for solving nonlinear Poisson-Boltzmann mortar finite element equation. BIT 2007, 47:853-871.
46. Yang C., Li D., Maliyah J.H. Modeling forced liquid convection in rectangular microchannels with electrokinetic effects. Int. J. Heat Mass Transfer 1998, 41(24):4229-4249.
47. Zheng Z., Hansford D.J., Vonlisk A.T. Effect of multivalent ions on electroosmotic flow in micro- and nanochannels. Electrophoresis 2003, 24.
48. Zhou Y.C., Feig M., Wei G.W. Highly accurate biomolecular electrostatics in continuum dielectric environments. J. Comput. Chem. 2007, 29:87-97.