Free Access
Issue |
ESAIM: M2AN
Volume 55, 2021
Regular articles published in advance of the transition of the journal to Subscribe to Open (S2O). Free supplement sponsored by the Fonds National pour la Science Ouverte
|
|
---|---|---|
Page(s) | S65 - S102 | |
DOI | https://doi.org/10.1051/m2an/2020030 | |
Published online | 26 February 2021 |
- X. Antoine, C. Geuzaine and K. Ramdani, Computational methods for multiple scattering at high frequency with applications to periodic structure calculations. Wave Propag. Periodic Media Prog. Comput. Phys. 1 (2010) 73–107. [Google Scholar]
- K. Atkinson, A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind. Society for Industrial and Applied Mathematics, Philadelphia, PA (1976). [Google Scholar]
- K. Atkinson and W. Han, Numerical solution of Fredholm integral equations of the second kind. In: Theoretical Numerical Analysis: A Functional Analysis Framework. Springer, New York (2005) 447–522. [CrossRef] [Google Scholar]
- K. Barros, D. Sinkovits and E. Luijten, Efficient and accurate simulation of dynamic dielectric objects. J. Chem. Phys. 140 (2014) 064903. [Google Scholar]
- H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations. Springer-Verlag, New York (2011). [Google Scholar]
- M. Brunner, J. Dobnikar, H.-H. von Grünberg and C. Bechinger, Direct measurement of three-body interactions amongst charged colloids. Phys. Rev. Lett. 92 (2004) 078301. [CrossRef] [PubMed] [Google Scholar]
- X. Claeys, A single trace integral formulation of the second kind for acoustic scattering. In: ETH, Seminar of Applied Mathematics Research (2011). [Google Scholar]
- X. Claeys and R. Hiptmair, Multi-trace boundary integral formulation for acoustic scattering by composite structures. Commun. Pure Appl. Math. 66 (2013) 1163–1201. [Google Scholar]
- X. Claeys, R. Hiptmair, C. Jerez-Hanckes and S. Pintarelli, Novel multi-trace boundary integral equations for transmission boundary value problems. In: Unified Transform for Boundary Value Problems, chapter 7, edited by A. Fokas and B. Pelloni. (2014) 227–258. [Google Scholar]
- X. Claeys, R. Hiptmair and E. Spindler, A second-kind Galerkin boundary element method for scattering at composite objects. BIT Numer. Math. 55 (2015) 33–57. [Google Scholar]
- X. Claeys, R. Hiptmair and E. Spindler, Second kind boundary integral equation for multi-subdomain diffusion problems. Adv. Comput. Math. 43 (2017) 1075–1101. [Google Scholar]
- H. Clercx and G. Bossis, Many-body electrostatic interactions in electrorheological fluids. Phys. Rev. E 48 (1993) 2721. [Google Scholar]
- M. Costabel, Some historical remarks on the positivity of boundary integral operators. In: Boundary Element Analysis. Springer (2007) 1–27. [Google Scholar]
- M. Costabel and E. Stephan, A direct boundary integral equation method for transmission problems. J. Math. Anal. App. 106 (1985) 367–413. [CrossRef] [MathSciNet] [Google Scholar]
- E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [CrossRef] [MathSciNet] [Google Scholar]
- J. Elschner, The double layer potential operator over polyhedral domains I: Solvability in weighted Sobolev spaces. Appl. Anal. 45 (1992) 117–134. [Google Scholar]
- J. Elschner, The double-layer potential operator over polyhedral domains II: Spline Galerkin methods. Math. Methods Appl. Sci. 15 (1992) 23–37. [Google Scholar]
- E. Fabes, M. Jodeit and N. Rivière, Potential techniques for boundary value problems on C1-domains. Acta Math. 141 (1978) 165–186. [CrossRef] [Google Scholar]
- G. Folland, Introduction to Partial Differential Equations. Princeton University Press (1995). [Google Scholar]
- K. Freed, Perturbative many-body expansion for electrostatic energy and field for system of polarizable charged spherical ions in a dielectric medium. J. Chem. Phys. 141 (2014) 034115. [Google Scholar]
- M. Ganesh and S. Hawkins, A high-order algorithm for multiple electromagnetic scattering in three dimensions. Numer. Algorithms 50 (2009) 469. [Google Scholar]
- M. Ganesh and S. Hawkins, An efficient algorithm for simulating scattering by a large number of two dimensional particles. ANZIAM J. 52 (2011) 139–155. [CrossRef] [Google Scholar]
- L. Greengard, The rapid evaluation of potential fields in particle systems. Ph.D. thesis, Yale University, New Haven, CT, USA (1987). [Google Scholar]
- L. Greengard and V. Rokhlin, A fast algorithm for particle simulations. J. Comput. Phys. 73 (1987) 325–348. [Google Scholar]
- B. Grzybowski, A. Winkleman, J. Wiles, Y. Brumer and G. Whitesides, Electrostatic self-assembly of macroscopic crystals using contact electrification. Nat. Mater. 2 (2003) 241–245. [CrossRef] [PubMed] [Google Scholar]
- W. Haibing and L. Jijun, On decomposition method for acoustic wave scattering by multiple obstacles. Acta Math. Sci. 33 (2013) 1–22. [Google Scholar]
- M. Hassan and B. Stamm, An integral equation formulation of the N-body dielectric spheres problem. Part II: complexity analysis. Preprint arXiv:1911.07258 (2019). [Google Scholar]
- R. Hockney and J. Eastwood, Computer Simulation Using Particles. CRC Press (1988). [CrossRef] [Google Scholar]
- P. Houston and E. Süli, hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems. SIAM J. Sci. Comput. 23 (2001) 1226–1252. [Google Scholar]
- P. Houston, C. Schwab and E. Süli, Stabilized hp-finite element methods for first-order hyperbolic problems. SIAM J. Numer. Anal. 37 (2000) 1618–1643. [Google Scholar]
- P. Houston, C. Schwab and E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002) 2133–2163. [Google Scholar]
- G. Hsiao and W. Wendland, Boundary Integral Equations. Springer-Verlag, Berlin Heidelberg (2008). [CrossRef] [Google Scholar]
- V. Lee, S. Waitukaitis, M. Miskin and H. Jaeger, Direct observation of particle interactions and clustering in charged granular streams. Nat. Phys. 11 (2015) 733. [Google Scholar]
- E. Lindgren, A. Stace, E. Polack, Y. Maday, B. Stamm and E. Besley, An integral equation approach to calculate electrostatic interactions in many-body dielectric systems. J. Comput. Phys. 371 (2018) 712–731. [Google Scholar]
- E. Lindgren, B. Stamm, Y. Maday, E. Besley and A. Stace, Dynamic simulations of many-body electrostatic self-assembly. Philos. Trans. R. Soc. A: Math. Phys. Eng. Sci. 376 (2018) 20170143. [CrossRef] [Google Scholar]
- P. Linse, Electrostatics in the presence of spherical dielectric discontinuities. J. Chem. Phys. 128 (2008) 214505. [Google Scholar]
- J. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Springer-Verlag, Berlin Heidelberg 1 (2012). [Google Scholar]
- I. Lotan and T. Head-Gordon, An analytical electrostatic model for salt screened interactions between multiple proteins. J. Chem. Theory Comput. 2 (2006) 541–555. [PubMed] [Google Scholar]
- V. Maz’ya, Boundary integral equations. In: Analysis IV: Linear and Boundary Integral Equations. Springer Berlin Heidelberg, Berlin, Heidelberg (1991) 127–222. [Google Scholar]
- L. McCarty, A. Winkleman and G. Whitesides, Electrostatic self-assembly of polystyrene microspheres by using chemically directed contact electrification. Angew. Chem. Int. Ed. 46 (2007) 206–209. [Google Scholar]
- W. McLean, Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press (2000). [Google Scholar]
- R. Messina, Image charges in spherical geometry: Application to colloidal systems. J. Chem. Phys. 117 (2002) 11062–11074. [Google Scholar]
- C. Müller, Foundations of the Mathematical Theory of Electromagnetic Waves. Springer-Verlag, Berlin Heidelberg (1969). [Google Scholar]
- I. Newton, Philosophiæ Naturalis Principia Mathematica (1687). [Google Scholar]
- H. Poincaré, Sur le problème des trois corps et les équations de la dynamique. Acta Math. 13 (1890) A3–A270. [Google Scholar]
- J. Qin, J. Li, V. Lee, H. Jaeger, J. de Pablo and K. Freed, A theory of interactions between polarizable dielectric spheres. J. Colloid Interface Sci. 469 (2016) 237–241. [Google Scholar]
- W. Qiu-Dong, The global solution of the N-body problem. Celestial Mech. Dyn. Astron. 50 (1990) 73–88. [Google Scholar]
- V. Rokhlin, Solution of acoustic scattering problems by means of second kind integral equations. Wave Motion 5 (1983) 257–272. [Google Scholar]
- S. Sauter and C. Schwab, Boundary Element Methods. Springer-Verlag, Berlin Heidelberg (2011). [Google Scholar]
- E. Shevchenko, D. Talapin, N. Kotov, S. O’Brien and C. Murray, Structural diversity in binary nanoparticle superlattices. Nature 439 (2006) 55–59. [CrossRef] [PubMed] [Google Scholar]
- S. Soh, H. Liu, R. Cademartiri, H.J. Yoon and G. Whitesides, Charging of multiple interacting particles by contact electrification. J. Am. Chem. Soc. 136 (2014) 13348–13354. [Google Scholar]
- O. Steinbach, W. Wendland and C. On, Neumann’s method for second-order elliptic systems in domains with non-smooth boundaries. J. Math. Anal. App. 262 (2001) 733–748. [Google Scholar]
- K. Sundman, Mémoire sur le problème des trois corps. Acta Math. 36 (1913) 105–179. [Google Scholar]
- G. Verchota, Layer potentials and regularity for the Dirichlet problem for Laplace’s equation in Lipschitz domains. J. Funct. Anal. 59 (1984) 572–611. [Google Scholar]
- T. Von Petersdorff, Boundary integral equations for mixed Dirichlet, Neumann and transmission problems. Math. Methods Appl. Sci. 11 (1989) 185–213. [Google Scholar]
- Z. Xu, Electrostatic interaction in the presence of dielectric interfaces and polarization-induced like-charge attraction. Phys. Rev. E 87 (2013) 013307. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.