Fourth order accurate evaluation of integrals in potential theory on exterior 3D regions

Alpert, 1993, Wavelets for the fast solution of second kind integral equations, SIAM J. Sci. Comp., 14, 1, 10.1137/0914010 A. Armstrong, C. Collie, J. Simpkin, C. Trowbridge, The solution of 3D magnetostatic problems using scalar potentials, Rutherford Laboratory, RL-78-078, September, 1978. T. Beale, A. Lai, On the accuracy of finite difference methods for elliptic problems with interfaces, manuscript. G. Biros, L. Ying, D. Zorin, The embedded boundary integral method for the incompressible Navier Stokes equations, in: Proceedings of the International Association for Boundary Element Methods, 2002 Symposium, CDROM, University of Texas at Austin, Austin TX, May 28–30, 2002. Biros, 2004, A fast solver for the Stokes equations with distributed fores in complex geometries, J. Comput. Phys., 194, 317, 10.1016/j.jcp.2003.08.011 Brebbia, 1978 Buneman, 1969 Buneman, 1971, Analytic inversion of the five point operator, JCP, 8, 500, 10.1016/0021-9991(71)90029-5 Burkhart, 1997, Asymptotic expansion of the free space Greens function for the discrete Poisson equation, SIAM J. Sci. Comp., 18, 1142, 10.1137/S1064827594261589 Buzbee, 1971, The direct solution of the discrete Poisson equation on irregular domains, SIAM J. Numer. Anal., 8, 722, 10.1137/0708066 Etheridge, 2001, A new fast-multipole accelerated Poisson solver in two dimensions, SIAM J. Sci. Comp., 23, 741, 10.1137/S1064827500369967 Gibou, 2001, A fourth order accurate discretization for the Laplace and heat equations on arbitrary domains with applications to the Stefan problem, J. Comput. Phys., 171, 205 Fauci, 1988, A computational model of aquatic animal locomotion, J. Comput. Phys., 17, 85, 10.1016/0021-9991(88)90158-1 Greenbaum, 1992, The rapid numerical solution of the biharmonic equation, Physica D, 60, 216, 10.1016/0167-2789(92)90238-I Greenbaum, 1998, Rapid parallel evaluation of integrals in potential theory on general three-dimensional regions, J. Comput. Phys., 145, 731, 10.1006/jcph.1998.6048 Greengard, 1996, A direct adaptive Poisson solver of arbitrary order accuracy, J. Comput. Phys., 125, 415, 10.1006/jcph.1996.0103 Greengard, 1997, A new version of the fast multipole method for the Laplace equation in three dimensions, Acta Numerica, 229, 10.1017/S0962492900002725 Greengard, 1996, Integral equation methods for Stokes flow and isotropic elasticity in the plane, J. Comput. Phys., 125, 403, 10.1006/jcph.1996.0102 Hockney, 1965, A fast direct solution of Poisson’s equation using Fourier analysis, J. Assoc. Comput. Mach., 12, 95, 10.1145/321250.321259 Hockney, 1970, vol. 9 Hockney, 1985 James, 1977, The solution of Poissons equation for for isolated source distributions, J. Comput. Phys., 25, 1534 Johansen, 1998, A Cartesian grid embedded boundary method for Poisson’s equation on irregular domains, J. Comput. Phys., 147, 60, 10.1006/jcph.1998.5965 Kellogg, 1953 Lean, 1984, Nonlinear boundary element method for two dimensional magnetostatics, J. Appl. Phys., 55, 2195, 10.1063/1.333608 Leveque, 1994, The immersed interface method for elliptic equations with discontinuous coefficients and singular sources, SIAM J. Numer. Anal., 31, 1019, 10.1137/0731054 Li, 2001, The immersed interface method for the Navier Stokes equations with singular forces, J. Comput. Phys., 171, 822, 10.1006/jcph.2001.6813 Li, 1994, ADI Methods for heat equations with discontinuities along an arbitrary interface, Proc. Symp. Appl. Math. (PSAPM), AMS, 48, 311, 10.1090/psapm/048/1314863 Lindholm, 1984, Three dimensional magnetostatic fields from point matched integral equations with linearly varying scalar sources, IEEE Trans. Magn., 20, 143, 10.1109/TMAG.1984.1063254 McKenney, 1995, A fast Poisson solver for complex geometries, J. Comput. Phys, 118, 348, 10.1006/jcph.1995.1104 Mayo, 1992, Fast parallel solution of Poisson’s and the biharmonic equations on irregular regions, SIAM J. Sci. Stat. Comput., 13, 1, 10.1137/0913006 Mayo, 1986, Rapid methods for the conformal mapping of multiconnected regions, Journal of Computational and Applied Mathematics, 14, 143, 10.1016/0377-0427(86)90135-4 Mayo, 1984, The fast solution of Poisson’s and the biharmonic equations on irregular regions, SIAM J. Numer. Anal., 21, 285, 10.1137/0721021 Mayo, 1992, The rapid evaluation of volume integrals of potential theory on general regions, J. Comput. Phys., 100, 236, 10.1016/0021-9991(92)90231-M Mayo, 2003 A. Mayo, Rapid, fourth order accurate solution of the steady Navier Stokes equations on general regions, Dyn. Contin. Discrete Impulsive Syst., to appear 2005. A. Mayo, Rapid fourth order accurate methods of the solution of the Stokes equations in the presence of an immersed boundary, IBM Research Report, RC 19603, 1994. IBM Research Report. Mikhlin, 1957 Peskin, 1989, A three dimensional computational method for blood flow in the heart i. Immersed elastic fibers in a viscous incompressible fluid, J. Comput. Phys, 81, 372, 10.1016/0021-9991(89)90213-1 Pozrikidis, 1992 Proskurowski, 1976, On the numerical solution of Helmholz’s equation by the capacitance matrix method, Math. Comput., 30, 433 Rokhlin, 1985, Rapid solution of integral equations of classical potential theory, J. Comput. Phys., 60, 187, 10.1016/0021-9991(85)90002-6 Rokhlin, 1993, Rapid solution of integral equations of scattering in two dimensions, J. Comput. Phys., 106, 355 Ruppert, 1992, On the difficulty of triangulating three dimensional nonconvex polyhedra, Discrete Comput. Geom., 7 K. Von Hagenow, K. Lackner, in: Proceedings of the 7th Conference on Numerical Simulation of Plasma, New York, 1975. Zhou, 2006, High order matched interface and boundary method for elliptic equations with discontinuous coefficients and singular sources, J. Comput. Phys., 212, 1, 10.1016/j.jcp.2005.07.022