Feng, Xiaodong; Qian, Yue; Shen, Wanfang MC-Nonlocal-PINNs: handling Nonlocal operators in PINNs via Monte Carlo sampling. (English) Zbl 07814753 Numer. Math., Theory Methods Appl. 16, No. 3, 769-791 (2023). MSC: 65C05 65D30 65R20 PDFBibTeX XMLCite \textit{X. Feng} et al., Numer. Math., Theory Methods Appl. 16, No. 3, 769--791 (2023; Zbl 07814753) Full Text: DOI arXiv
Du, Qiang; Tian, Xiaochuan; Zhou, Zhi Nonlocal diffusion models with consistent local and fractional limits. (English) Zbl 07814301 Mengesha, Tadele (ed.) et al., A\(^3\) N\(^2\) M: approximation, applications, and analysis of nonlocal, nonlinear models. Proceedings of the 50th John H. Barrett memorial lectures, Knoxville, TN, USA, virtual, May 2021. Cham: Springer. IMA Vol. Math. Appl. 165, 175-213 (2023). MSC: 65N30 35R11 47G10 46E35 PDFBibTeX XMLCite \textit{Q. Du} et al., IMA Vol. Math. Appl. 165, 175--213 (2023; Zbl 07814301) Full Text: DOI arXiv
D’Elia, Marta; Littlewood, David J.; Trageser, Jeremy; Perego, Mauro; Bochev, Pavel B. An optimization-based strategy for peridynamic-FEM coupling and for the prescription of nonlocal boundary conditions. (English) Zbl 07814300 Mengesha, Tadele (ed.) et al., A\(^3\) N\(^2\) M: approximation, applications, and analysis of nonlocal, nonlinear models. Proceedings of the 50th John H. Barrett memorial lectures, Knoxville, TN, USA, virtual, May 2021. Cham: Springer. IMA Vol. Math. Appl. 165, 151-174 (2023). MSC: 74S05 35Q74 35R11 65M60 74A45 PDFBibTeX XMLCite \textit{M. D'Elia} et al., IMA Vol. Math. Appl. 165, 151--174 (2023; Zbl 07814300) Full Text: DOI arXiv
Han, Zhaolong; Tian, Xiaochuan Nonlocal half-ball vector operators on bounded domains: Poincaré inequality and its applications. (English) Zbl 07778941 Math. Models Methods Appl. Sci. 33, No. 12, 2507-2556 (2023). MSC: 47B92 46E35 PDFBibTeX XMLCite \textit{Z. Han} and \textit{X. Tian}, Math. Models Methods Appl. Sci. 33, No. 12, 2507--2556 (2023; Zbl 07778941) Full Text: DOI arXiv
Glusa, Christian; D’Elia, Marta; Capodaglio, Giacomo; Gunzburger, Max; Bochev, Pavel B. An asymptotically compatible coupling formulation for nonlocal interface problems with jumps. (English) Zbl 07704386 SIAM J. Sci. Comput. 45, No. 3, A1359-A1384 (2023). MSC: 65-XX 35R11 65R20 PDFBibTeX XMLCite \textit{C. Glusa} et al., SIAM J. Sci. Comput. 45, No. 3, A1359--A1384 (2023; Zbl 07704386) Full Text: DOI arXiv
Capanna, Monia; Rossi, Julio D. Mixing local and nonlocal evolution equations. (English) Zbl 1509.35026 Mediterr. J. Math. 20, No. 2, Paper No. 59, 36 p. (2023). MSC: 35B27 45K05 60J60 35K15 PDFBibTeX XMLCite \textit{M. Capanna} and \textit{J. D. Rossi}, Mediterr. J. Math. 20, No. 2, Paper No. 59, 36 p. (2023; Zbl 1509.35026) Full Text: DOI arXiv
Barros de Moraes, Eduardo A.; D’Elia, Marta; Zayernouri, Mohsen Machine learning of nonlocal micro-structural defect evolutions in crystalline materials. (English) Zbl 07644208 Comput. Methods Appl. Mech. Eng. 403, Part B, Article ID 115743, 20 p. (2023). MSC: 74-XX 82-XX PDFBibTeX XMLCite \textit{E. A. Barros de Moraes} et al., Comput. Methods Appl. Mech. Eng. 403, Part B, Article ID 115743, 20 p. (2023; Zbl 07644208) Full Text: DOI arXiv
Yu, Xiaoxuan; Xu, Yan; Du, Qiang Asymptotically compatible approximations of linear nonlocal conservation laws with variable horizon. (English) Zbl 07779686 Numer. Methods Partial Differ. Equations 38, No. 6, 1948-1966 (2022). MSC: 65M60 65M06 65N30 65M12 41A58 PDFBibTeX XMLCite \textit{X. Yu} et al., Numer. Methods Partial Differ. Equations 38, No. 6, 1948--1966 (2022; Zbl 07779686) Full Text: DOI
D’Elia, Marta; Gulian, Mamikon; Mengesha, Tadele; Scott, James M. Connections between nonlocal operators: from vector calculus identities to a fractional Helmholtz decomposition. (English) Zbl 1503.26006 Fract. Calc. Appl. Anal. 25, No. 6, 2488-2531 (2022). MSC: 26A33 26B12 PDFBibTeX XMLCite \textit{M. D'Elia} et al., Fract. Calc. Appl. Anal. 25, No. 6, 2488--2531 (2022; Zbl 1503.26006) Full Text: DOI arXiv
dos Santos, Bruna C.; Oliva, Sergio M.; Rossi, Julio D. Coupled local/nonlocal models in thin domains. (English) Zbl 1500.35276 Asymptotic Anal. 129, No. 3-4, 545-575 (2022). MSC: 35Q79 35K05 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{B. C. dos Santos} et al., Asymptotic Anal. 129, No. 3--4, 545--575 (2022; Zbl 1500.35276) Full Text: DOI arXiv
D’Elia, Marta; Yu, Yue On the prescription of boundary conditions for nonlocal Poisson’s and peridynamics models. (English) Zbl 1501.74068 Español, Malena I. (ed.) et al., Research in mathematics of materials science. Cham: Springer. Assoc. Women Math. Ser. 31, 185-207 (2022). MSC: 74S99 74A70 PDFBibTeX XMLCite \textit{M. D'Elia} and \textit{Y. Yu}, Assoc. Women Math. Ser. 31, 185--207 (2022; Zbl 1501.74068) Full Text: DOI arXiv
dos Santos, Bruna C.; Oliva, Sergio M.; Rossi, Julio D. A local/nonlocal diffusion model. (English) Zbl 1497.35046 Appl. Anal. 101, No. 15, 5213-5246 (2022). MSC: 35B40 35B51 35K20 35K55 35R09 PDFBibTeX XMLCite \textit{B. C. dos Santos} et al., Appl. Anal. 101, No. 15, 5213--5246 (2022; Zbl 1497.35046) Full Text: DOI arXiv
Du, Qiang; Xie, Hehu; Yin, Xiaobo On the convergence to local limit of nonlocal models with approximated interaction neighborhoods. (English) Zbl 1497.45015 SIAM J. Numer. Anal. 60, No. 4, 2046-2068 (2022). Reviewer: Eduardo Cuesta (Valladolid) MSC: 45L05 45P05 46N20 65R20 PDFBibTeX XMLCite \textit{Q. Du} et al., SIAM J. Numer. Anal. 60, No. 4, 2046--2068 (2022; Zbl 1497.45015) Full Text: DOI arXiv
Yu, Xiaoxuan; Xu, Yan; Du, Qiang Numerical simulation of singularity propagation modeled by linear convection equations with spatially heterogeneous nonlocal interactions. (English) Zbl 07568379 J. Sci. Comput. 92, No. 2, Paper No. 59, 24 p. (2022). MSC: 65-XX 35Lxx 45Kxx 74Axx PDFBibTeX XMLCite \textit{X. Yu} et al., J. Sci. Comput. 92, No. 2, Paper No. 59, 24 p. (2022; Zbl 07568379) Full Text: DOI arXiv
Pasetto, Marco; Shen, Zhaoxiang; D’Elia, Marta; Tian, Xiaochuan; Trask, Nathaniel; Kamensky, David Efficient optimization-based quadrature for variational discretization of nonlocal problems. (English) Zbl 1507.74502 Comput. Methods Appl. Mech. Eng. 396, Article ID 115104, 37 p. (2022). MSC: 74S05 65N30 65D32 65K10 74A70 PDFBibTeX XMLCite \textit{M. Pasetto} et al., Comput. Methods Appl. Mech. Eng. 396, Article ID 115104, 37 p. (2022; Zbl 1507.74502) Full Text: DOI arXiv
Leng, Yu; Tian, Xiaochuan; Demkowicz, Leszek; Gomez, Hector; Foster, John T. A Petrov-Galerkin method for nonlocal convection-dominated diffusion problems. (English) Zbl 07517745 J. Comput. Phys. 452, Article ID 110919, 24 p. (2022). MSC: 65Nxx 65Mxx 76Mxx PDFBibTeX XMLCite \textit{Y. Leng} et al., J. Comput. Phys. 452, Article ID 110919, 24 p. (2022; Zbl 07517745) Full Text: DOI arXiv
Yao, Changhui; Fan, Huijun; Zhao, Yanmin; Shi, Yanhua; Wang, Fenling Fast algorithm for nonlocal Allen-Cahn equation with scalar auxiliary variable approach. (English) Zbl 1524.65431 Appl. Math. Lett. 126, Article ID 107805, 9 p. (2022). MSC: 65M06 65M12 35R11 65M15 26A33 65N06 PDFBibTeX XMLCite \textit{C. Yao} et al., Appl. Math. Lett. 126, Article ID 107805, 9 p. (2022; Zbl 1524.65431) Full Text: DOI
dos Santos, Bruna C.; Oliva, Sergio M.; Rossi, Julio D. Splitting methods and numerical approximations for a coupled local/nonlocal diffusion model. (English) Zbl 1499.35092 Comput. Appl. Math. 41, No. 1, Paper No. 6, 38 p. (2022). MSC: 35B40 65M06 65M20 PDFBibTeX XMLCite \textit{B. C. dos Santos} et al., Comput. Appl. Math. 41, No. 1, Paper No. 6, 38 p. (2022; Zbl 1499.35092) Full Text: DOI
Petit, Julien; Lambiotte, Renaud; Carletti, Timoteo Random walks on dense graphs and graphons. (English) Zbl 1477.05175 SIAM J. Appl. Math. 81, No. 6, 2323-2345 (2021). MSC: 05C81 05C42 05C22 34G10 45K05 47D06 PDFBibTeX XMLCite \textit{J. Petit} et al., SIAM J. Appl. Math. 81, No. 6, 2323--2345 (2021; Zbl 1477.05175) Full Text: DOI arXiv
D’Elia, Marta; Gunzburger, Max; Vollmann, Christian A cookbook for approximating Euclidean balls and for quadrature rules in finite element methods for nonlocal problems. (English) Zbl 1473.65188 Math. Models Methods Appl. Sci. 31, No. 8, 1505-1567 (2021). MSC: 65M60 45A99 45P05 65D30 65M15 65R99 PDFBibTeX XMLCite \textit{M. D'Elia} et al., Math. Models Methods Appl. Sci. 31, No. 8, 1505--1567 (2021; Zbl 1473.65188) Full Text: DOI
D’Elia, M.; De Los Reyes, J. C.; Miniguano-Trujillo, A. Bilevel parameter learning for nonlocal image denoising models. (English) Zbl 1515.94014 J. Math. Imaging Vis. 63, No. 6, 753-775 (2021). MSC: 94A08 PDFBibTeX XMLCite \textit{M. D'Elia} et al., J. Math. Imaging Vis. 63, No. 6, 753--775 (2021; Zbl 1515.94014) Full Text: DOI arXiv
Capanna, Monia; Nakasato, Jean C.; Pereira, Marcone C.; Rossi, Julio D. Homogenization for nonlocal problems with smooth kernels. (English) Zbl 1466.45001 Discrete Contin. Dyn. Syst. 41, No. 6, 2777-2808 (2021). MSC: 45A05 45C05 45M05 45H05 PDFBibTeX XMLCite \textit{M. Capanna} et al., Discrete Contin. Dyn. Syst. 41, No. 6, 2777--2808 (2021; Zbl 1466.45001) Full Text: DOI arXiv
Ding, Ming-Hui; Zheng, Guang-Hui Determination of the reaction coefficient in a time dependent nonlocal diffusion process. (English) Zbl 1456.65092 Inverse Probl. 37, No. 2, Article ID 025005, 28 p. (2021). MSC: 65M32 65M30 65M06 35B65 35A02 44A10 76M30 76M21 35Q35 62F15 PDFBibTeX XMLCite \textit{M.-H. Ding} and \textit{G.-H. Zheng}, Inverse Probl. 37, No. 2, Article ID 025005, 28 p. (2021; Zbl 1456.65092) Full Text: DOI
D’Elia, Marta; Du, Qiang; Glusa, Christian; Gunzburger, Max; Tian, Xiaochuan; Zhou, Zhi Numerical methods for nonlocal and fractional models. (English) Zbl 07674560 Acta Numerica 29, 1-124 (2020). MSC: 65-XX 76-XX PDFBibTeX XMLCite \textit{M. D'Elia} et al., Acta Numerica 29, 1--124 (2020; Zbl 07674560) Full Text: DOI arXiv
Pang, G.; D’Elia, M.; Parks, M.; Karniadakis, G. E. nPINNs: nonlocal physics-informed neural networks for a parametrized nonlocal universal Laplacian operator. Algorithms and applications. (English) Zbl 07508384 J. Comput. Phys. 422, Article ID 109760, 26 p. (2020). MSC: 35-XX 86-XX PDFBibTeX XMLCite \textit{G. Pang} et al., J. Comput. Phys. 422, Article ID 109760, 26 p. (2020; Zbl 07508384) Full Text: DOI arXiv
Gárriz, Alejandro; Quirós, Fernando; Rossi, Julio D. Coupling local and nonlocal evolution equations. (English) Zbl 1443.35069 Calc. Var. Partial Differ. Equ. 59, No. 4, Paper No. 112, 24 p. (2020). MSC: 35K55 35B40 35R09 58D25 PDFBibTeX XMLCite \textit{A. Gárriz} et al., Calc. Var. Partial Differ. Equ. 59, No. 4, Paper No. 112, 24 p. (2020; Zbl 1443.35069) Full Text: DOI arXiv
Capodaglio, Giacomo; D’Elia, Marta; Bochev, Pavel; Gunzburger, Max An energy-based coupling approach to nonlocal interface problems. (English) Zbl 1521.76117 Comput. Fluids 207, Article ID 104593, 11 p. (2020). MSC: 76D27 74F10 PDFBibTeX XMLCite \textit{G. Capodaglio} et al., Comput. Fluids 207, Article ID 104593, 11 p. (2020; Zbl 1521.76117) Full Text: DOI arXiv
Tian, Hao; Zhang, Jing; Ju, Lili A spectral collocation method for nonlocal diffusion equations with volume constrained boundary conditions. (English) Zbl 1433.65321 Appl. Math. Comput. 370, Article ID 124930, 15 p. (2020). MSC: 65N35 35K57 PDFBibTeX XMLCite \textit{H. Tian} et al., Appl. Math. Comput. 370, Article ID 124930, 15 p. (2020; Zbl 1433.65321) Full Text: DOI
Heydari, Mohammad Hossein; Avazzadeh, Zakieh; Yang, Yin A computational method for solving variable-order fractional nonlinear diffusion-wave equation. (English) Zbl 1429.65240 Appl. Math. Comput. 352, 235-248 (2019). MSC: 65M70 35R11 PDFBibTeX XMLCite \textit{M. H. Heydari} et al., Appl. Math. Comput. 352, 235--248 (2019; Zbl 1429.65240) Full Text: DOI
D’Elia, Marta; Glusa, Christian; Otárola, Enrique A priori error estimates for the optimal control of the integral fractional Laplacian. (English) Zbl 1473.35625 SIAM J. Control Optim. 57, No. 4, 2775-2798 (2019). MSC: 35R11 35Q93 49J20 49M25 65K10 65N15 65N30 PDFBibTeX XMLCite \textit{M. D'Elia} et al., SIAM J. Control Optim. 57, No. 4, 2775--2798 (2019; Zbl 1473.35625) Full Text: DOI arXiv
Burkovska, O.; Gunzburger, M. Regularity analyses and approximation of nonlocal variational equality and inequality problems. (English) Zbl 1421.49009 J. Math. Anal. Appl. 478, No. 2, 1027-1048 (2019). MSC: 49J40 35R11 65N30 35B65 PDFBibTeX XMLCite \textit{O. Burkovska} and \textit{M. Gunzburger}, J. Math. Anal. Appl. 478, No. 2, 1027--1048 (2019; Zbl 1421.49009) Full Text: DOI arXiv
Zhao, Wei; Hon, Yiu-chung; Stoll, Martin Localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for nonlocal diffusion problems. (English) Zbl 1409.65081 Comput. Math. Appl. 75, No. 5, 1685-1704 (2018). MSC: 65M70 35R09 PDFBibTeX XMLCite \textit{W. Zhao} et al., Comput. Math. Appl. 75, No. 5, 1685--1704 (2018; Zbl 1409.65081) Full Text: DOI
Jin, Bangti (ed.); Lazarov, Raytcho (ed.); Vabishchevich, Petr (ed.) Preface: Numerical analysis of fractional differential equations. (English) Zbl 1431.00030 Comput. Methods Appl. Math. 17, No. 4, 643-646 (2017). MSC: 00B15 65-06 34A08 35R11 PDFBibTeX XMLCite \textit{B. Jin} (ed.) et al., Comput. Methods Appl. Math. 17, No. 4, 643--646 (2017; Zbl 1431.00030) Full Text: DOI Link