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ספרים

1. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, Navier-Stokes Equations in Planar Domains, Imperial College Press, 316 pages (2013). ISBN: 978-1-84816-275-4.
2. D. Fishelov, E. Farkhi and S. Mayberg, Introduction to Numerical Analysis, Bak Publications, Haifa, 268 pages (2010).
3. D. Fishelov and E. Farkhi, Ordinary Differential Equations: Theory and Exercises, 2nd edition, Bak Publications, Haifa, 197 pages (2010).

מאמרים, פרקים בספרים ופרסומים בכנסים

1. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “A Compact Scheme for the Munk Boundary-Layer Equation in One Dimension”, Journal of Computational and Applied Mathematics.
2. M. Ben-Artzi, Y. Eidelman and D. Fishelov, “Numerical solution of the boundary value problems for the biharmonic equations via quasiseparable representations”, Numerical Algorithms (2024).
3. D. Fishelov and J.-P. Croisille, “Optimal convergence for time-dependent Linearized Kuramoto-Sivashinsky type problems: A new Approach”, Journal of Computational and Applied Mathematics, 429, 115229 (2023).
4. I. Ben-Shaul, L. Bar, D. Fishelov and N. Sochen, “Deep Learning Solution of the Eigenvalue Problem for Differential Operators”, Neural Computation (2023).
5. N. Rabin, A. Fernandez and D. Fishelov, “Multiscale Extensions for Enhancing Coarse Grid Computations”, Journal of Computational and Applied Mathematics, 427, 115116 (2023).
6. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “Convergence of finite difference schemes: matrix versus kernel analysis”, in Spectral and High Order Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering, Springer (2022).
7. D. Fishelov and J.-P. Croisille, “Optimal Convergence for Time-Dependent Stokes Equation: A New Approach”, Journal of Scientific Computing, 89, Article 66 (2021).
8. J.-P. Croisille and D. Fishelov, “Time-Dependent Two-Dimensional Fourth-Order Problems: Optimal Convergence”, in Numerical Mathematics and Advanced Applications – ENUMATH 2019, Lecture Notes in Computational Science and Engineering, 139, 429–438, Springer (2021).
9. A. Fernandez, N. Rabin, D. Fishelov and J. R. Dorronsoro, “Auto-adaptive multi-scale Laplacian Pyramids for modeling non-uniform data”, Engineering Applications of Artificial Intelligence, 93, 103682 (2020).
10. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “A Cartesian Compact Scheme for the Navier-Stokes Equations in Streamfunction Formulation in Irregular Domains”, Journal of Scientific Computing, 81, 1386–1408 (2019).
11. N. Rabin and D. Fishelov, “Two Directional Laplacian Pyramids with Application to Data Imputation”, Advances in Computational Mathematics (2019).
12. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “Time evolution of discrete fourth-order elliptic operators”, Numerical Methods for Partial Differential Equations, 35, 1429–1457 (2019).
13. N. Rabin and D. Fishelov, “A multi-scale approach for data imputation”, 2018 IEEE International Conference on the Science of Electrical Engineering in Israel (ICSEE), Eilat, Israel, 1–5 (2018).
14. M. Ben-Artzi, J.-P. Croisille, D. Fishelov and R. Katzir, “Discrete Fourth-order Sturm-Liouville problems”, IMA Journal of Numerical Analysis, 38, 1475–1522 (2018).
15. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “An embedded compact scheme for biharmonic problems in irregular domains”, in Advanced Computing in Industrial Mathematics, Studies in Computational Intelligence, K. Georgiev, M. Todorov and I. Georgiev (eds.), 11–23, Springer (2018).
16. N. Rabin and D. Fishelov, “Multi-scale kernels for Nyström based extension schemes”, Applied Mathematics and Computation, 319, 165–177 (2018).
17. N. Rabin and D. Fishelov, “Missing data completion using diffusion maps and Laplacian Pyramids”, in Computational Science and Its Applications – ICCSA 2017, Lecture Notes in Computer Science, O. Gervasi et al. (eds.), 284–297, Springer (2017).
18. D. Fishelov, “A New Fourth-Order Compact Scheme for the Navier-Stokes Equations in Irregular Domains”, Computers and Mathematics with Applications, 74, 6–25 (2017).
19. D. Fishelov, “A Fourth-Order Compact Scheme for the Navier-Stokes Equations in Irregular Domains”, Proceedings of the 20th Conference on Scientific Computing, A. Handlovičová and D. Ševčovič (eds.), Publishing House of Slovak University of Technology in Bratislava (2016).
20. A. Fernandez, N. Rabin, D. Fishelov and J. Dorronsoro, “Auto-adaptive Laplacian Pyramids”, ESANN 2016 Proceedings: European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, 201–206 (2016).
21. D. Fishelov, “Semi-discrete time-dependent fourth-order problems on an interval: error estimate”, in Numerical Mathematics and Advanced Applications – ENUMATH 2013, A. Abdulle, S. Deparis, D. Kressner, F. Nobile and M. Picasso (eds.), 103, 133–142, Springer (2015).
22. D. Fishelov, M. Ben-Artzi and J.-P. Croisille, “Fourth-order convergence of a compact scheme for the one-dimensional biharmonic equation”, AIP Conference Proceedings, 1479, 1101–1104 (2012).
23. D. Fishelov, M. Ben-Artzi and J.-P. Croisille, “Recent advances in the study of a fourth-order compact scheme for the one-dimensional biharmonic equation”, Journal of Scientific Computing, 53(1), 55–79 (2012).
24. D. Fishelov, M. Ben-Artzi and J.-P. Croisille, “Recent Developments in the Pure Streamfunction Formulation of the Navier-Stokes System”, Journal of Scientific Computing, 45, 238–258.
25. “Highly Accurate Discretization of the Navier-Stokes Equations in Streamfunction Formulation”, in Spectral and High Order Methods for Partial Differential Equations, Lecture Notes in Computational Science and Engineering, 76, 189–197 (2010).
26. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “A high order compact scheme for the pure-streamfunction formulation of the Navier-Stokes Equations”, Journal of Scientific Computing, 42(2), 216–250 (2010).
27. M. Ben-Artzi, I. Chorev, J.-P. Croisille and D. Fishelov, “A compact difference scheme for the biharmonic equation in planar irregular domains”, SIAM Journal on Numerical Analysis, 47(4), 3087–3108 (2009).
28. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “A fast direct solver for the biharmonic problem in a rectangular grid”, SIAM Journal on Scientific Computing, 31(1), 303–333.
29. D. Fishelov and N. Sochen, “Image Impainting via fluid equation”, 4th IEEE International Conference on Information Technology, 23–25 (2006).
30. M. Ben-Artzi, J.-P. Croisille and D. Fishelov, “Convergence of a compact scheme for the pure streamfunction formulation of the unsteady Navier-Stokes system”, SIAM Journal on Numerical Analysis, 44(5), 1997–2024 (2006).
31. M. Ben-Artzi, J.-P. Croisille, D. Fishelov and S. Trachtenberg, “A pure-compact scheme for the streamfunction formulation of Navier-Stokes equations”, Journal of Computational Physics, 205(2), 640–664 (2005).
32. S. Trachtenberg, D. Fishelov and M. Ben-Artzi, “Bacterial flagellar microhydrodynamics: laminar flow over complex flagellar filaments, analog archimedean screws and cylinders, and its perturbations”, Biophysical Journal, 85(3), 1345–1357 (2003).
33. D. Fishelov, M. Ben-Artzi and J.-P. Croisille, “A compact scheme for the streamfunction formulation of Navier-Stokes equations”, International Conference on Computational Science and Its Applications, 809–817 (2003).
34. M. Ben-Artzi, D. Fishelov and S. Trachtenberg, “Vorticity dynamics and numerical resolution of Navier-Stokes equations”, ESAIM: Mathematical Modelling and Numerical Analysis, 35(2), 313–330 (2001).
35. D. Fishelov, “Simulation of three-dimensional turbulent flow in non-cartesian geometry”, Journal of Computational Physics, 115(2), 249–266 (1994).
36. D. Fishelov, “Simulation of three-dimensional turbulent flow”, Proceedings of the 24th Israel Conference on Mechanical Engineering (1992).
37. D. Fishelov, “Vortex Schemes for Viscous Flow”, Vortex Dynamics and Vortex Methods, 28, 153–164 (1990).
38. D. Fishelov, “Vortex methods for slightly viscous three-dimensional flow”, SIAM Journal on Scientific and Statistical Computing, 11(3), 399–424 (1990).
39. D. Fishelov, “A new vortex scheme for viscous flows”, Journal of Computational Physics, 86(1), 211–224 (1990).
40. D. Fishelov, “Vortex methods for slightly viscous three-dimensional flow”, 11th International Conference on Numerical Methods in Fluid Dynamics, 256–261 (1989).
41. D. Fishelov, “Spectral methods for the small disturbance equation of transonic flows”, SIAM Journal on Scientific and Statistical Computing, 9(2), 232–251 (1988).
42. D. Fishelov, “The spectrum and the stability of the Chebyshev collocation operator for transonic flow”, Mathematics of Computation, 51(184), 559–579 (1988).
43. B. Schiff, D. Fishelov and J. R. Whiteman, “Determination of a stress intensity factor using local mesh refinement”, The Mathematics of Finite Elements and Applications III, 55–64 (1979).
44. J. A. Gregory, D. Fishelov, B. Schiff and J. R. Whiteman, “Local mesh refinement with finite elements for elliptic problems”, Journal of Computational Physics, 29(1), 133–140 (1978).

דוחות מחקר ופרסומים מוקדמים

1. Á. Fernández, N. Rabin, D. Fishelov and J. R. Dorronsoro, “Auto-adaptative Laplacian Pyramids for High-dimensional Data Analysis”. arXiv:1311.6594.
2. D. Fishelov, “A convergent particle scheme for convection-diffusion equations”, Preprint No. 2, The Edmund Landau Research Center for Research in Mathematical Analysis (1992).
3. D. Fishelov, “A fixed grid for vortex methods”, Lawrence Berkeley Laboratory, Report 27489 (1990).
4. D. Fishelov, “Vortex methods for slightly viscous three dimensional flow”, Lawrence Berkeley Laboratory, Report 25176 (1988).

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