Open Access
Volume 57, Number 5, September-October 2023
Page(s) 3029 - 3059
Published online 06 October 2023
  1. X. Antoine and E. Lorin, Towards perfectly matched layers for time-dependent space fractional PDEs. J. Comput. Phys. 391 (2019) 59–90. [CrossRef] [MathSciNet] [Google Scholar]
  2. X. Antoine, A. Arnold, C. Besse, M. Ehrhardt and A. Schädle, A review of transparent and artificial boundary conditions techniques for linear and nonlinear Schrödinger equations. Commun. Comput. Phys. 4 (2008) 729–796. [MathSciNet] [Google Scholar]
  3. X. Antoine, E. Lorin and Q. Tang, A friendly review of absorbing boundary conditions and perfectly matched layers for classical and relativistic quantum waves equations. Mol. Phys. 115 (2017) 1861–1879. [CrossRef] [Google Scholar]
  4. X. Antoine, E. Lorin and Y. Zhang, Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers. Numer. Algorithms 87 (2021) 409–444. [CrossRef] [MathSciNet] [Google Scholar]
  5. B. Baeumer, M. Kovcs, M.M. Meerschaert and H. Sankaranarayanan, Boundary conditions for fractional diffusion. J. Comput. Appl. Math. 336 (2018) 408–424. [CrossRef] [MathSciNet] [Google Scholar]
  6. A. Bayliss and E. Turkel, Radiation boundary conditions for wavelike equations. Commun. Pure Appl. Math. 33 (1981) 707–725. [Google Scholar]
  7. C. Bekar and E. Madenci, Peridynamics enabled learning partial differential equations. J. Comput. Phys. 434 (2021) 110193. [CrossRef] [Google Scholar]
  8. J. Chandra, On a generalization of the Gronwall-Bellman lemma in partially ordered Banach spaces. J. Math. Anal. App. 31 (1970) 668–681. [CrossRef] [Google Scholar]
  9. M. D’Elia, Q. Du, C. Glusz, M. Gunzburger, X. Tian and Z. Zhou, Numerical methods for nonlocal and fractional models. Acta Numer. 29 (2020) 1–124. [CrossRef] [MathSciNet] [Google Scholar]
  10. Q. Du, Nonlocal Modelling, Analysis and Computation. CBMS-NSF Regional Conference Series in Applied Mathematics. Vol. 94. SIAM, Philadelphia, PA (2019). [Google Scholar]
  11. Q. Du, H. Han, J. Zhang and C. Zheng, Numerical solution of a two-dimensional nonlocal wave equation on unbounded domains. SIAM J. Sci. Comput. 40 (2018) 1430–1445. [Google Scholar]
  12. Q. Du, J. Zhang and C. Zheng, Nonlocal wave propagation in unbounded multiscale media. Commun. Comput. Phys. 24 (2018) 1049–1072. [MathSciNet] [Google Scholar]
  13. Q. Du, Y. Tao and X. Tian, Asymptotically compatible discretization of multidimensional nonlocal diffusion models and approximation of nonlocal Green’s functions. IMA J. Numer. Anal. 39 (2019) 607–625. [CrossRef] [MathSciNet] [Google Scholar]
  14. B. Engquist and A. Majda, Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31 (1977) 629–651. [Google Scholar]
  15. B. Engquist and A. Majda, Radiation boundary conditions for acoustic and elastic calculations. Commun. Pure Appl. Math. 32 (1979) 313–357. [CrossRef] [Google Scholar]
  16. W. Gerstle, N. Sau and S. Silling, Peridynamic modeling of concrete structures. Nucl. Eng. Design 237 (2007) 1250–1258. [CrossRef] [Google Scholar]
  17. D. Givoli, High-order local non-reflecting boundary conditions: a review. Wave Motion 39 (2004) 319–326. [CrossRef] [MathSciNet] [Google Scholar]
  18. T. Hagstrom, Radiation boundary conditions for the numerical simulation of waves. Acta Numer. 8 (1999) 47–106. [CrossRef] [Google Scholar]
  19. H. Han and X. Wu, Artificial Boundary Method. Spring-Verlag and Tsinghua University Press (2013). [CrossRef] [Google Scholar]
  20. S. Ji, Y. Yang, G. Pang and X. Antoine, Accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations on rectangular domains. Comput. Phys. Commun. 222 (2018) 84–93. [CrossRef] [MathSciNet] [Google Scholar]
  21. J.F. Kelly, H. Sankaranarayanan and M.M. Meerschaert, Boundary conditions for two-sided fractional diffusion. J. Comput. Phys. 376 (2019) 1089–1107. [Google Scholar]
  22. B. Kilic, A. Agwai and E. Madenci, Peridynamic theory for progressive damage prediction in center-cracked composite laminates. Comp. Struct. 90 (2009) 141–151. [CrossRef] [Google Scholar]
  23. E. Madenci, A. Barut and M. Futch, Peridynamic differential operator and its applications. Comput. Methods Appl. Mech. Eng. 304 (2016) 408–451. [CrossRef] [Google Scholar]
  24. E. Madenci, A. Barut, M. Dorduncu and M. Futch, Numerical solution of linear and nonlinear partial differential equations by using the peridynamic differential operator. Numer. Methods Part. Differ. Equ. 33 (2017) 1726–1753. [CrossRef] [Google Scholar]
  25. E. Madenci, A. Barut and M. Dorduncu, Peridynamic Differential Operators for Numerical Analysis. Springer, Boston, MA (2019). [CrossRef] [Google Scholar]
  26. Y. Mikata, Analytical solutions of peristatic and peridynamic problems for a 1D infinite rod. Int. J. Solids Struct. 49 (2012) 2887–2897. [CrossRef] [Google Scholar]
  27. E. Oterkus and E. Madenci, Peridynamic analysis of fiber-reinforced composite materials. J. Mech. Mater. Struct. 70 (2012) 45–84. [CrossRef] [Google Scholar]
  28. E. Oterkus and E. Madenci, Peridynamic theory for damage initiation and growth in composite laminate. Adv. Fract. Damage Mech. 488 (2012) 355–358. [Google Scholar]
  29. G. Pang, S. Ji, Y. Yang and S. Tang, Eliminating corner effects in square lattice simulation. Comput. Mech. 62 (2018) 111–122. [CrossRef] [MathSciNet] [Google Scholar]
  30. G. Pang, S. Ji and X. Antoine, Artificial boundary conditions for the semi-discretized one-dimensional nonlocal Schrödinger equation. J. Comput. Phys. 444 (2021) 110575. [CrossRef] [Google Scholar]
  31. G. Pang, Y. Yang, X. Antoine and S. Tang, Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain. Math. Comput. 90 (2021) 2731–2756. [CrossRef] [Google Scholar]
  32. G. Pang, S. Ji and X. Antoine, Accurate absorbing boundary conditions for two-dimensional peridynamics. J. Comput. Phys. 466 (2022) 111351. [CrossRef] [Google Scholar]
  33. S. Silling, Reformulation of elasticity theory for discontinuities and long-range forces. J. Mech. Phys. Solids 48 (2000) 175–209. [CrossRef] [MathSciNet] [Google Scholar]
  34. S. Tang, S. Zhu and D. Qian, Energy-based matching boundary conditions for non-ordinary peridynamics in one space dimension. Int. J. Multiscale Comput. Eng. 16 (2020) 611–636. [CrossRef] [Google Scholar]
  35. S.V. Tsynkov, Numerical solution of problems on unbounded domains. A review. Appl. Numer. Math. 27 (1998) 465–532. [CrossRef] [MathSciNet] [Google Scholar]
  36. J. Wang, J. Zhang and C. Zheng, Stability and error analysis for a second-order approximate of the 1D nonlocal Schrödinger equation under DtN-type boundary conditions, to appear. [Google Scholar]
  37. L. Wang, Y. Chen, J. Xu, J. Wang, Transmitting boundary conditions for 1D peridynamics, Int. J. Numer. Methods Eng. 110 (2017) 379–400. [CrossRef] [Google Scholar]
  38. O. Weckner and R. Abeyaratne, The effect of long-range forces on the dynamics of a bar. J. Mech. Phys. Solids 53 (2005) 705–728. [CrossRef] [MathSciNet] [Google Scholar]
  39. O. Weckner and E. Emmrich, Numerical simulation of the dynamics of a nonlocal, inhomogeneous, infinite bar. J. Comput. Appl. Mech. 6 (2005) 311–319. [MathSciNet] [Google Scholar]
  40. J. Xu, A. Askari, O. Weckner and S. Silling, Peridynamic analysis of impact damage in composite laminates. J. Aerospace Eng. 21 (2008) 187–194. [CrossRef] [Google Scholar]
  41. Y. Yan, J. Zhang and C. Zheng, Numerical computations of nonlocal Schrödinger equations on the real line. Commun. Appl. Math. Comput. 2 (2020) 241–260. [CrossRef] [MathSciNet] [Google Scholar]
  42. W. Zhang, J. Yang, J. Zhang and Q. Du, Absorbing boundary conditions for nonlocal heat equations on unbounded domain. Commun. Comput. Phys. 21 (2017) 16–39. [CrossRef] [MathSciNet] [Google Scholar]
  43. C. Zheng, J. Hu, Q. Du and J. Zhang, Numerical solution of the nonlocal diffusion equation on the real line. SIAM J. Sci. Comput. 39 (2017) 1951–1968. [Google Scholar]

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