A Matlab-based finite-difference solver for the Poisson problem with mixed Dirichlet-Neumann boundary conditions. (English) Zbl 1302.35005

Comput. Phys. Commun. 184, No. 3, 783-798 (2013); corrigendum ibid. 209, 200-201 (2016).
Summary: A Matlab-based finite-difference numerical solver for the Poisson equation for a rectangle and a disk in two dimensions, and a spherical domain in three dimensions, is presented. The solver is optimized for handling an arbitrary combination of Dirichlet and Neumann boundary conditions, and allows for full user control of mesh refinement. The solver routines utilize effective and parallelized sparse vector and matrix operations. Computations exhibit high speeds, numerical stability with respect to mesh size and mesh refinement, and acceptable error values even on desktop computers.


35-04 Software, source code, etc. for problems pertaining to partial differential equations
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations


Matlab; FDMRP
Full Text: DOI


[1] Moon, P.; Spencer, D. E., Field theory handbook, (1971), Springer-Verlag · Zbl 0097.39403
[2] P. Moon, D.E. Spencer, Field Theory for Engineers, D. Van Nostrand Company, 1961.
[3] Lukoshkov, V. S., Some electrostatic properties of grid electrodes, Izv. Akad. Nauk SSSR Ser. Fiz., 8, 243-247, (1944), (in Russian)
[4] Moizhes, B. Ya., Averaged electrostatic boundary conditions for metallic meshes, Zh. Tekh. Fiz., 25, 167-176, (1955), (in Russian)
[5] Schuss, Z.; Singer, A.; Holcman, D., The narrow escape problem for diffusion in cellular microdomains, PNAS, 104, 41, 16098-16103, (2007)
[6] Bénichou, O.; Voituriez, R., Narrow escape time problem:time needed for a particle to exit a confining domain through a small window, Phys. Rev. Lett., 100, 168105, (2008)
[7] Holcman, D.; Schuss, Z., Escape through a small opening: receptor trafficking in a synaptic membrane, J. Stat. Phys., 117, 5-6, 975-1014, (2004) · Zbl 1087.82018
[8] Cheviakov, A. F.; Ward, M. J.; Straube, R., An asymptotic analysis of the mean first passage time for narrow escape problems: part ii: the sphere, Multiscale Model. Simul., 8, 3, 836-870, (2010) · Zbl 1204.35030
[9] Pillay, S.; Ward, M. J.; Peirce, A.; Kolokolnikov, T., An asymptotic analysis of the mean first passage time for narrow escape problems: part i: two-dimensional domains, Multiscale Model. Simul., 8, 3, 803-835, (2010) · Zbl 1203.35023
[10] Liniger, W.; Odeh, F., On the numerical treatment of singularities in solutions of laplace’s equation, Numer. Funct. Anal. Optim., 16, 3-4, 379-393, (1995) · Zbl 0830.65098
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