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, and T.Hagstrom
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, and J.Toledo
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, The peridynamic formulation for transient heat conduction, Int. J. Heat Mass Transfer, 53 (2010), 4047–4059.
, A peridynamic formulation for transient heat conduction in bodies with evolving discontinuities, J. Comput. Phys., 231 (2012), 2764–2785.
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and W. H.Weedon
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and S. A.Silling
, An approach to modeling extreme loading of structures using peridynamics, J. Mech. Mater. Struct., 2:10 (2007), 1921–1945.
, Analysis and approximation of nonlocal diffusion problems with volume constraints, SIAM Rev., 54 (2012), 667–696.
, A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws, Math. Mod. Meth. Appl. Sci., 23 (2013), 493–540.
, Mathematical analysis for the peridynamic nonlocal continuum theory, ESIAM: Math. Model. Numer. Anal., 45 (2011), 217–234.
, Analysis and numerical approximation of an integro-differential equation modelling non-local effects in linear elasticity, Math. Mech. Solids, 12 (2007), 363–384.
, On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity, Commun. Math. Sci., 5 (2007), 851–864.
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, Absorbing boundary conditions for the numerical simulation of waves, Math. Comput., 31 (1977), 629–651.
, A nonlocal vector calculus with application to nonlocal boundary value problems, Multiscale Model. Simul., 8 (2010), 1581–1598.
, Studies of dynamic crack propagation and crack branching with peridynamics, Int. J. Fract., 162:1-2 (2010), 229–244.
, Exact and approximating boundary conditions for the parabolic problems on unbounded domains, Comput. Math. Appl., 44 (2002), 655–666.
, A class of artificial boundary conditions for heat equation in unbounded domains, Comput. Math. Appl., 43 (2002), 889–900.
, Artificial Boundary Method, Spring-Verlag and Tsinghua Unversity Press, Berlin Heidelberg and Beijing, 2013.
, Fast Evaluation of Nonreflecting Boundary Conditions for the Schrödinger Equation in One Dimension, Comput. Math. Appl., 47 (2004), no. 6-7, 955–966.
, Efficient representation of nonreflecting boundary conditions for the time-dependent Schrödinger equation in two dimensions, Comm. Pure Appl. Math., 61 (2008), 261–288.
, A fast time stepping method for evaluating fractional integrals, SIAM J. Sci. Comput., 31 (2010), 4696–4714.
, Finite difference/spectral approximations for the time-fractional diffusion equation, J. Comput. Phys., 225 (2007), 1533–1552.
, Peridynamics via finite element analysis, Finite Elem. Anal. Des., 43 (2007), 1169–1178.
, Analysis of a scalar peridynamic model with a sign changing kernel, Disc. Cont. Dyn. Systems B, 18 (2013), 1415–1437.
, Characterization of function spaces of vector fields via nonlocal derivatives and an application in peridynamics, Nonlinear Anal. A, 140 (2016), 82–111.
, The restaurant at the end of the random walk: Recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A, 37 (2004), R161.
and D. M.Tartakovsky
, Perspective on theories of non-Fickian transport in heterogenous media, Adv. Water Resources, 32 (2009), 670–680.
, A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct., 83:17-18 (2005), 1526–1535.
, Peridynamic theory of solid mechanics, Adv. Appl. Mech., 44 (2010), 73–166.
, Crack nucleation in a peridynamic solid, Int. J. Fracture, 162 (2010), 219–227.
, A fully discrete difference scheme for a diffusion-wave system, Appl. Numer. Math., 56 (2006), 193–209.
, Analysis and comparison of different approximations to nonlocal diffusion and linear peridynamic equations, SIAM J. Numer. Anal., 51 (2013), 3458–3482.
, Asymptotically compatible schemes and applications to robust discretization of nonlocal models, SIAM J. Numer. Anal., 52 (2014), 1641–1665.
, A perfectly matched layer for peridynamics in two dimensions, J. Mech. Mater. Struct., 7:8-9 (2012), 765–781.
, Mathematical and Numerical Analysis of Linear Peridynamic Models with Nonlocal Boundary Conditions, SIAM J. Numer. Anal., 48 (2010), 1759–1780.