Fourier multipliers for nonlocal Laplace operators

References

• Du Q, Gunzburger M, Lehoucq RB, et al. A nonlocal vector calculus, nonlocal volume-constrained problems, and nonlocal balance laws. Math Models Methods Appl Sci. 2013;23(3):493–540. Available from: http://www.worldscientific.com/doi/abs/10.1142/S0218202512500546
   Web of Science ®Google Scholar
• Silling SA. Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids. 2000;48:175–209. doi: 10.1016/S0022-5096(99)00029-0
   Web of Science ®Google Scholar
• Silling SA. Linearized theory of peridynamic states. J Elast. 2010;99(1):85–111. doi: 10.1007/s10659-009-9234-0
   Web of Science ®Google Scholar
• Bobaru F, Foster JT, Geubelle PH, et al. Handbook of peridynamic modeling. CRC Press; 2016.
   Google Scholar
• Du Q, Gunzburger M, Lehoucq R, et al. Analysis of the volume-constrained peridynamic Navier equation of linear elasticity. J Elast. 2013;113(2):193–217. doi: 10.1007/s10659-012-9418-x
   Web of Science ®Google Scholar
• Emmrich E, Weckner O, On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity. Commun Math Sci. 2007;5(4):851–864. doi: 10.4310/CMS.2007.v5.n4.a6
   Web of Science ®Google Scholar
• Alali B, Lipton R. Multiscale dynamics of heterogeneous media in the peridynamic formulation. J Elast. 2012;106(1):71–103. doi: 10.1007/s10659-010-9291-4
   Web of Science ®Google Scholar
• Mengesha T, Du Q. Nonlocal constrained value problems for a linear peridynamic Navier equation. J Elast. 2014;116(1):27–51. doi: 10.1007/s10659-013-9456-z
   Web of Science ®Google Scholar
• Alali B, Gunzburger M. Peridynamics and material interfaces. J Elast. 2015;120(2):225–248. doi: 10.1007/s10659-014-9512-3
   Web of Science ®Google Scholar
• Madenci E, Oterkus E. Peridynamic theory and its applications. Vol. 17. Springer; 2014.
   Google Scholar
• Bobaru F, Duangpanya M. The peridynamic formulation for transient heat conduction. Int J Heat Mass Transf. 2010;53(19–20):4047–4059. doi: 10.1016/j.ijheatmasstransfer.2010.05.024
   Web of Science ®Google Scholar
• Burch N, Lehoucq R. Classical, nonlocal, and fractional diffusion equations on bounded domains. Int J Multiscale Comput Eng. 2011;9(6). doi: 10.1615/IntJMultCompEng.2011002402
   Web of Science ®Google Scholar
• Lehoucq RB, Reu PL, Turner DZ. A novel class of strain measures for digital image correlation. Strain. 2015;51(4):265–275. doi: 10.1111/str.12138
   Web of Science ®Google Scholar
• Seleson P, Gunzburger M, Parks ML. Interface problems in nonlocal diffusion and sharp transitions between local and nonlocal domains. Comput Methods Appl Mech Eng. 2013;266:185–204. doi: 10.1016/j.cma.2013.05.018
   Web of Science ®Google Scholar
• Radu P, Toundykov D, Trageser J. A nonlocal biharmonic operator and its connection with the classical analogue. Arch Ration Mech Anal. 2017;223(2):845–880. doi: 10.1007/s00205-016-1047-2
   Web of Science ®Google Scholar
• Du Q, Gunzburger M, Lehoucq RB, et al. Analysis and approximation of nonlocal diffusion problems with volume constraints. SIAM Rev. 2012;54(4):667–696. doi: 10.1137/110833294
   Web of Science ®Google Scholar
• Aksoylu B, Parks ML. Variational theory and domain decomposition for nonlocal problems. Appl Math Comput. 2011;217(14):6498–6515.
   Web of Science ®Google Scholar
• Du Q, Yang J. Asymptotically compatible Fourier spectral approximations of nonlocal Allen–Cahn equations. SIAM J Numer Anal. 2016;54(3):1899–1919. doi: 10.1137/15M1039857
   Web of Science ®Google Scholar
• Du Q, Yang J. Fast and accurate implementation of Fourier spectral approximations of nonlocal diffusion operators and its applications. J Comput Phys. 2017;332:118–134. doi: 10.1016/j.jcp.2016.11.028
   Web of Science ®Google Scholar
• NIST digital library of mathematical functions. Release 1.0.17 of 2017-12-22. Olver FWJ, Olde Daalhuis AB, Lozier DW, Schneider BI, Boisvert RF, Clark CW, Miller BR, Saunders BV, editors. Available from: http://dlmf.nist.gov/
   Google Scholar
• Abramowitz M, Stegun IA. Handbook of mathematical functions: with formulas, graphs, and mathematical tables. Vol. 55. Courier Corporation; 1972.
   Google Scholar
• Johansson F. mpmath: a Python library for arbitrary-precision floating-point arithmetic (version 0.18); 2013. Available from: http://mpmath.org/
   Google Scholar