Laplace's equation and the Dirichlet-Neumann map: A new mode for Mikhlin's method

Journal of Computational Physics

Volumn 202, Issue 2, 2005, Pages 391-410

  Helsing, Johan ^a   Wadbro, Eddie ^a,b  

^a LUND UNIVERSITY   (Sweden)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

Dirichlet Neumann map; Exterior problem; Fast solvers; Integral equations; Multiply connected domains

Indexed keywords

LAPLACE TRANSFORMS;

CLOSED CONTOURS; DIRICHLET-NEUMANN MAPS; EXTERIOR PROBLEM; FAST SOLVERS; HIGHLY ACCURATE; MULTIPLY CONNECTED DOMAIN; SIMPLE++;

INTEGRAL EQUATIONS;

EID: 10244259131     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jcp.2004.06.024     Document Type: Article

References (28)

1. N. Akaiwa D.I. Meiron Two-dimensional late-stage coarsening for nucleation and growth at high-area fractions Phys. Rev. E 54 1 1996 R13-R16
2. N. Akaiwa K. Thornton P.W. Voorhees Large-scale simulations of microstructural evolution in elastically stressed solids J. Comput. Phys. 173 1 2001 61-86
3. G. Biros L. Ying D. Zorin A fast solver for the Stokes equation with distributed forces in complex geometries J. Comput. Phys. 193 1 2003 317-348
4. J. Carrier L. Greengard V. Rokhlin A fast adaptive multipole algorithm for particle simulations SIAM J. Sci. Stat. Comp. 9 4 1988 669-686
5. A. Greenbaum L. Greengard G.B. McFadden Laplace's equation and the Dirichlet Neumann map in multiply connected domains J. Comput. Phys. 105 2 1993 267-278
6. L. Greengard M.C. Kropinski Integral equation methods for Stokes flow in doubly-periodic domains J. Eng. Math. 48 2 2004 157-170
7. L. Greengard M.C. Kropinski A. Mayo Integral equation methods for Stokes flow and isotropic elasticity in the plane J. Comput. Phys. 125 2 1996 403-414
8. L. Greengard V. Rokhlin A fast algorithm for particle simulations J. Comput. Phys. 73 2 1987 325-348
9. J. Helsing Thin bridges in isotropic electrostatics J. Comput. Phys. 127 1 1996 142-151
10. J. Helsing On the interior stress problem for elastic bodies J. Appl. Mech. T. ASME 67 4 2000 658-662
11. J. Helsing A. Jonsson Stress calculations on multiply connected domains J. Comput. Phys. 176 2 2002 456-482
12. H.V. Henderson S.R. Searle On deriving the inverse of a sum of matrices SIAM Rev. 23 1 1981 53-60
13. T.Y. Hou J.S. Lowengrub M.J. Shelley Boundary integral methods for multicomponent fluids and multiphase materials J. Comput. Phys. 169 2 2001 302-362
14. S.D. Jiang V. Rokhlin Second kind integral equations for the classical potential theory on open surfaces I: Analytical apparatus J. Comput. Phys. 191 1 2003 40-74
15. S.D. Jiang V. Rokhlin Second kind integral equations for the classical potential theory on open surfaces II J. Comput. Phys. 195 1 2004 1-16
16. H.-J. Jou P.H. Leo J.S. Lowengrub Microstructural evolution in inhomogeneous elastic media J. Comput. Phys. 131 1 1997 109-148
17. MadMax Optics Inc., User's Manual FMM Toolbox (2D) for MATLAB ®, Version 1.1, 2002
18. G.B. McFadden P.W. Voorhees R.F. Boiswert D.I. Meiron A boundary integral method for the simulation of two-dimensional particle coarsening J. Sci. Comp. 1 2 1986 117-144
19. S.G. Mikhlin Integral Equations and their Applications to Certain Problems in Mechanics, Mathematical Physics and Technology second ed. 1964 Pergamon Press London
20. N.I. Muskhelishvili Some Basic Problems of the Mathematical Theory of Elasticity 1953 P. Noordhoff Ltd. Groningen
21. K. Nabors F.T. Korsmeyer F.T. Leighton J. White Preconditioned, adaptive, multipole-accelerated iterative methods for three-dimensional first-kind integral equations of potential theory SIAM J. Sci. Comput. 15 3 1994 713-735
22. H. Power The completed double layer boundary integral equation method for two-dimensional Stokes flow IMA J. Appl. Math. 51 2 1993 123-145
23. V. Rokhlin Rapid solution of integral equations of classical potential theory J. Comput. Phys. 60 2 1985 187-207
24. D. Russell Z.J. Wang A cartesian grid method for modeling multiple moving objects in 2D incompressible viscous flow J. Comput. Phys. 191 1 2003 177-205
25. Y. Saad M.H. Schultz GMRES: A generalized minimum residual algorithm for solving nonsymmetric linear systems SIAM J. Sci. Stat. Comp. 7 3 1986 856-869
26. J. Tausch J. White Second-kind integral formulations of the capacitance problem Adv. Comput. Math. 9 (1 2) 1998 217-232
27. K. Thornton J. Ågren P.W. Voorhees Modelling the evolution of phase boundaries in solids at the meso- and nano-scales Acta Mater. 51 19 2003 5675-5710
28. K. Thornton N. Akaiwa P.W. Voorhees Large-scale simulations of Ostwald ripening in elastically stressed solids: I. Development of microstructure Acta Mater. 52 5 2004 1353-1364