Publications

In preparation

on heterogeneous dam problems; on restricted additive methods; on higher-order finite volume methods; on high-contrast asymptotic expansions; on random elliptic equations; on high-contrast problems for topology optimization; on kernel methods and reproducing kernel spaces; on exponential integrators for high-contrast problems; on  PAI,  Green's and Poisson kernels, ....

Submitted (Jan 2024)

1. Generalized multiscale finite element method for a nonlinear elastic strain-limiting Cosserat model, Dmitry Ammosova, Tina Maib, J. Galvis

2. A second-order exponential integration constraint energy minimizing generalized multiscale method for parabolic problems, LA Poveda, J Galvis, E Chung

3. Robust domain decomposition methods for high-contrast multiscale problems on irregular domains with virtual element discretizations, JG Calvo, J Galvis, arXiv preprint arXiv:2306.15424

4. Multicontinuum homogenization. General theory and applications, E Chung, Y Efendiev, J Galvis, WT Leung, arXiv preprint arXiv:2309.08128

5. On L2-solutions for a neural field equation, Cordero, Saldaña, Aldana, Cuervo, g..

6. A note on averaging prediction accuracy, Green's functions and other kernels, J. Galvis, Freddy Hernández, Francisco Gómez

Accepted (Jan 2024)

1. A compact video descriptor from a geometric mean representation of symmetric positive definite matrices,  Juan Olmos,  Juan Galvis, Fabio Martínez, RCM.

Published (Jan 2024)

1. Higher order derivatives of the adjugate matrix and the Jordan form, JI Rubiano-Murcia, J Galvis, Linear Algebra and its Applications 680, 137-155

2. Modelling and simulation of brinicle formation. Royal Society Open Science 10.10 (2023): 230268. Gómez-Lozada, F., Del Valle, C. A., Jiménez-Paz, J. D., Lazarov, B. S., & Galvis, J. (2023). 

3. Towards a Modeling of the Impacts of Road Verge Management on the Pollination Service Using System Dynamics: A Case Study in France, Juan Pablo Ortega; Diana Daza-Gacha; Mauricio Camargo Pardo; Clémence Chaudron; Frédérique Mayer; Juan Galvis. Applied Mathematics 14 (5), 349-385

4. Parkinsonian gait patterns quantification from principal geodesic analysis, S Niño, JA Olmos, JC Galvis, F Martínez, Pattern Analysis and Applications 26 (2), 679-689

5. A foot and mouth disease ranking of risk using cattle transportation, F Moreno, J Galvis, F Gómez, Plos one 18 (4), e0284180 

6. An exponential integration generalized multiscale finite element method for parabolic problems, LF Contreras, D Pardo, E Abreu, J Muñoz-Matute, C Diaz, J Galvis, Journal of Computational Physics, 112014, 

7.  Finite difference and finite element methods for partial differential equations on fractals, Juan Galvis, Luis F. Contreras. Revista Integración.

8. Olmos, Juan, Juan Galvis, and Fabio Martínez. "Gait Patterns Coded as Riemannian Mean Covariances to Support Parkinson’s Disease Diagnosis." Advances in Artificial Intelligence–IBERAMIA 2022: 17th Ibero-American Conference on AI, Cartagena de Indias, Colombia, November 23–25, 2022, Proceedings. Cham: Springer International Publishing, 2023.

9.  Parkinsonian gait patterns quantification from principal geodesic analysis, S Niño, JA Olmos, JC Galvis, F Martínez. Pattern Analysis and Applications, 1-11,2022

10. A phase‐field porous media fracture model based on homogenization theory, J Galvis, HM Versieux, ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 2022

11. Mathematical modelling of proton migration in Earth mantle, Vadim Bobrovskiy, Juan Galvis, Alexey Kaplin, Alexander Sinitsyn, Marco Tognoli, Paolo Trucco,  Mathematical Modelling of Natural Phenomena., 2022

12. Natural Factor Based Solvers,  O. Andrés Cuervo, Juan Galvis, Marcus Sarkis, proceeedings of the 26th International Domain Decomposition Conference, DD XXVI, to be published by Springer, 2021

13. Fast multiscale contrast independent preconditioners for linear elastic topology optimization problems, Miguel Zambrano, Sintya Serrano, Boyan  S. Lazarov, Juan Galvis,   Journal of Computational and Applied Mathematics, Volume 389, June 2021, 113366.

14. On condition numbers of symmetric and nonsymmetric domain decomposition methods, Galvis,  Linear Algebra and its Applications Volume 610, 1 February 2021, Pages 293-320

15. On the conservation properties in multiple scale coupling and simulation for Darcy flow with hyperbolic-transport in complex flows,  Eduardo Abreu, Ciro Diaz, Jonh Perez, J. Galvis, Multiscale Model. Simul., 18(4), 1375–1408. 2020.

16. Galvis, Juan, Luis F. Contreras, and Carlos Vázquez. "Numerical upscaling of the free boundary dam problem in multiscale high-contrast media." Journal of Computational and Applied Mathematics 367 (2020): 112437.

17. Abreu, Eduardo, Ciro Diaz, and Juan Galvis. "A convergence analysis of Generalized Multiscale Finite Element Methods." Journal of Computational Physics 396 (2019): 303-324. 

18. F. Gómez, J. Prieto, J. Galvis, F. Moreno and J. Vargas, "Identification of Super-Spreaders of Foot-and-Mouth Disease in the cattle transportation network: The 2018 outbreak case in Cesar (Colombia)," 2019 4th World Conference on Complex Systems (WCCS), Ouarzazate, Morocco, 2019, pp. 1-6, doi: 10.1109/ICoCS.2019.8930765.

19. Preserving data moments in density estimation via diffusion using the finite element method, K. Patarroyo, F. Gomez, J. Galvis, Bol. Mat., Volumen 25, Número 2, p. 101-121, 2018. ISSN electrónico 2357-6529. ISSN impreso 0120-0380. 

20. On polar actions invariant solutions of semilinear equations on manifolds, E. Becerra, N Martinez, J Galvis, Elsevier Journal of Mathematical Analysis and Applications, Volume 475, Issue 1, 1 July 2019, Pages 769-781

21. On the equivalence of Gaussian Sobolev norms and some weighted Wiener-Chaos norms , J. Galvis, Bol. Mat., Volumen 25, Número 1, p. 49-63, 2018. ISSN electrónico 2357-6529. ISSN impreso 0120-0380. 

22. A Monte Carlo approach to computing stiffness matrices arising in polynomial chaos approximations,J Galvis, OA Cuervo. Mathematics and Computers in Simulation Volume 160, June 2019, Pages 72-81. 

23. On Overlapping Domain Decomposition Methods for High-Contrast Multiscale Problems, Juan Galvis, Eric T. Chung, Yalchin Efendiev, Wing Tat Leung, Pages 45-57, Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XXIV.  2018 

24.  On High-Order Approximation and Stability with Conservative Properties, Juan Galvis, Eduardo Abreu, Ciro Díaz, Marcus Sarkis, Pages 253-260, Lecture Notes in Computational Science and Engineering, Domain Decomposition Methods in Science and Engineering XXIV.  2018 

25.  Solución numérica de la ecuación de onda con coeficiente estocástico, O. Cuervo, J. Galvis, páginas 565-574, Métodos Numéricos y sus aplicaciones, Memorias del XI Congreso Colombiano de Métodos Numéricos 2017, primera edición, 2018.

26. On high-order conservative finite element methods, E Abreu, C Diaz, J Galvis, M Sarkis, Computers and Mathematics with Applications, Volume 75, Issue 6, 15 March 2018, Pages 1852-1867. 

27. V.M. Calo, L. Poveda, J. Galvis and S. Huepo. Elliptic Equations with High-Contrast Coefficients and an Application to Multi-Scale Finite Element Methods. Computational and Applied Mathematics, May 2018, Volume 37, Issue 2, pp 1986–2000.

28. Hotspot mapping for perception of security, F Gómez, A Torres, J Galvis, J Camargo, O Martínez, Smart Cities Conference (ISC2), 2016 IEEE International, 1-6

29. RIEMANN PROBLEM FOR A 2X2 BALANCE NONSYMMETRIC SYSTEM OF KEYFITZ-KRANZER, Memorias grandes Maestros de la Matem.atica en Colombia: YU TAKEUCHI, pag 319-325, 2016.

30. M. Dryja, J. Galvis and M. Sarkis, A deluxe FETI-DP preconditioner for full DG discretization of elliptic problems,Domain Decomposition Methods in Science and Engineering XXII pp 157-165, 2016

31. Richard De la cruz, Juan Galvis, Juan Carlos Juajibioy and Leonardo Rendón, Delta shock wave for a 3 × 3 hyperbolic system of conservation laws. Bulletin of the Brazilian Mathematical Society, New Series, March 2016, Volume 47, Issue 1, pp 277-290.

32. Victor M. Calo, Yalchin Efendiev, Juan Galvis, Guanglian. Randomized Oversampling for Generalized Multiscale Finite Element Methods, Multiscale Model. Simul., 14(1), 482–501 (preprint). 2016

33. M. Presho, J. Galvis, A mass conservative generalized multiscale finite element method applied to two-phase flow in heterogeneous porous media. Journal of Computational and Applied Mathematics 296 (2016) 376–388.

34. V.M. Calo, L. Poveda, J. Galvis and S. Huepo. Asymptotic Expansions for High-Contrast Linear Elasticity, Journal of Computational and Applied Mathematics, Volume 295, 15 March 2016, Pages 25–34, VIII Pan-American Workshop in Applied and Computational Mathematics

35. Juan Galvis, Edixon M. Rojas, Alexander V. Sinitsyn. Electron. J. Diff. Equ., Vol. 2015 (2015), No. 236, pp. 1-7. Existence of positive solutions of a nonlinear second-order boundary-value problem with integral boundary conditions. 

36. M. Dryja, J. Galvis and M. Sarkis, A deluxe FETI-DP preconditioner for a composite finite element and DG method Computational Methods in Applied Mathematics. Volume 15, Issue 4, Pages 465–482, ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, DOI: 10.1515/cmam-2015-0025, September 2015

37. M. Dryja, J. Galvis and M. Sarkis, The analysis of FETI-DP preconditioner for full DG discretization of elliptic problem, Numerische Mathematik

38. M. Alotaibi, V. M. Calo, Y. Efendiev, J. Galvis., M. Ghommem. Global-Local Nonlinear Model Reduction for Flows in Heterogeneous Porous Media, Computer Methods in Applied Mechanics and Engineering, Volume 292, 1 August 2015, Pages 122–137 (preprint)

39. G. Li., J. Galvis, K. Shi, A Generalized Multiscale Finite Element Method for the Brinkman Equation. Journal of Computational and Applied Mathematics, Volume 280, 15 May 2015, Pages 294–309.

40. J. Galvis and H. Versieux, An iterative domaindecomposition method for free boundary problems with nonlinear fluxjump constraint. Computational and Applied Mathematics Volume 34, Issue 3(2015),Page 1199-1217 (preprint, num.example)

41. J.M. Mantilla, F. Ponce, J. Galvis. Some numericall studies of oscillating chemicalreactions using discontinuous finite elements, Revista de la Facultad de Ciencias de la Universidad Nacional de Colombia, Sede Medellín. V 3, N° 2, julio-diciembre 2014,Paginas, 81-93.

42. Y. Efendiev, J. Galvis, G. Li, M. Presho. Generalized Multiscale Finite Element Methods. Oversampling strategies, International Journal for Multiscale Computational Engineering, Volume 12, 2014 Issue 6, Pages 465-485. (arxiv preprint)

43. V. M. Calo, Y. Efendiev, J. Galvis, M. Ghommem, Multiscale Empirical Interpolation for Solving Nonlinear PDEs (using Generalized Multiscale Finite Element Methods), Journal of Computational Physics, Volume 278, 1 December 2014, Pages 204–220

44. Y. Efendiev, S. Weißer, R. Lazarov, Mixed FEM for second order elliptic problems on polygonal meshes with BEM-based spaces, proceedings of the Ninth International Conference on "Large Scale Scientific Computations", Large-Scale Scientific Computing Lecture Notes in Computer Science 2014, pp 331-338.

45. Richard De la cruz, Juan Galvis, Juan Carlos Juajibioy, and Leonardo Rendón. Delta Shock Wave for the Suliciu Relaxation System, Advances in Mathematical Physics Volume 2014 (2014), 11 pages (previous title: On the Riemann problem for the simplified Bouchut-Boyaval system (preprint)).

46. Y.Efendiev, J. Galvis, M. P. Presho and J. Zhou, A Multiscale Enrichment Procedure for Nonlinear Monotone Operators, Special issue- Multiscale problems and techniques, ESAIM: Mathematical Modelling and Numerical Analysis (M2AN), / Volume 48 / Issue 02 / March 2014, pp 475-491.

47. Y. Efendiev, J. Galvis, G. Li, M. Presho. Generalized Multiscale Finite Element Methods. Nonlinear Elliptic Equations. Commun. Comput. Phys., 15 (2014), pp. 733-755. (arxiv preprint).

48. V. Calo, Y. Efendiev and J. Galvis, Asymptotic expansions for high-contrast elliptic equations (illustration), Math. Models Methods Appl. Sci. 24, 465 (2014).

49. J. Galvis and S.K. Kang, Spectral Multiscale Finite Element for nonlinear flows in highly heterogeneous media: a Reduced Basis approach. Journal of Computational and Applied Mathematics Volume 260, April 2014, Pages 494–508.

50. J. Galvis and J. Wei, Ensemble Level Multiscale Finite Element and Preconditioner for Channelized Systems and Applications, Journal of Computational and Applied Mathematics, Volume 255, 1 January 2014, Pages 456-467.

51. Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Multiscale domain decomposition preconditioners for anisotropichigh-contrast problems, Domain Decomposition Methods in Science and Engineering XX, Editors: Randolph Bank, Michael Holst, Olof Widlund, Jinchao Xu, Volume 91 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2013.

52. Y. Efendiev, J. Galvis, M. Moon, R. Lazarov and M. Sarkis, Generalized Multiscale Finite Element Method. Symmetric Interior Penalty Coupling, Journal of Computational Physics. Volume 255, 15 December 2013, Pages 1–15.

53. Y. Efendiev, J.Galvis and T. Hou, Generalized Multiscale Finite Element Methods (GMsFEM) (arxiv preprint), Journal of Computational Physics, Volume 251, 15 October 2013, Pages 116-135.

54. Y. Efendiev, J.Galvis and M.S. Pauletti, Multiscale finite element methods for flows on rough surfaces. Commun. Comput. Phys.Vol. 14, No. 4, pp. 979-1000, October 2013. ISC preprint.

55. Maksymilian Dryja, Juan Galvis, and Marcus Sarkis, A FETI-DP Preconditioner for a Composite Finite Element and Discontinuous Galerkin Method, SIAM Journal on Numerical Analysis 2013, Vol. 51, No. 1, pp. 400-422, Posted online on 12 Feb 2013.

56. Y. Efendiev, J. Galvis and F. Thomines, A systematic coarse-scale model reduction technique for parameter-dependent flows in highly heterogeneous media and itsapplications (RB-MsFEM), Multiscale Model. Simul., 2012, 10(4), 1317–1343.

57. Y. Efendiev, J. Galvis, R. Lazarov, S. Margenov and J. Ren, Robust two-level domain decomposition preconditioners for high-contrast anisotropic flows in multiscale media. Computational Methods in Applied Mathematics Vol. 12 (2012), No. 4, pp. 1–22.

58. J. Galvis and M. Sarkis, Regularity results for the ordinary product stochastic pressure equation. SIAM J. Math. Anal., Vol. 44, Issue 4, 2637–2665, July 2012. (IMPA preprint .pdf-version_1).

59. Y. Efendiev, J. Galvis and E. Gildin, Local-global multiscale model reduction for flows in highly heterogeneous media, Journal of Computational Physics Volume 231, Issue 24, 15 October 2012, Pages 8100–8113.

60. Y. Efendiev, J. Galvis, S. Ki Kang and R. Lazarov, Robust multiscale domain decomposition method for nonlinear flows in highly heterogeneous media. Numer. Math. Theor. Meth. Appl. Vol. 5, No. 3, pp. 359-383, August 2012. doi: 10.4208/nmtma.2012.m1112. (Isc preprint).

61. Y. Efendiev, J. Galvis, R. Lazarov and J. Willems, Robust Solvers for Symmetric Positive Definite Operators and WeightedPoincare´ Inequalities. LSSC, Lecture Notes in Computer Science, 2012, Volume 7116/2012, 43-51, DOI: 10.1007/978-3-642-29843-1_4. (Large-Scale Scientific Computing: 8th International Conference, 2011,Sozopol, Bulgaria, preprint. from J. Willems site) .

62. M. Dryja, J. Galvis and M. Sarkis, Neumann-Neumann methods for a DG discretization of elliptic problems with discontinuous coefficients on geometrically nonconforming substructures. Numerical Methods for Partial Differential Equations July 2012 Volume 28, Issue 4, pp. 1194-1226. (published online: 28 APR 2011).

63. Y. Efendiev, J. Galvis, R. Lazarov and J. Willems, Robust domain decomposition preconditioners for abstract symmetric positive definite bilinear forms, ESAIM: Mathematical Modelling and Numerical Analysis September 2012, 46 : pp 1175-1199. (Ricam Report .pdf).

64. Y. Efendiev and J. Galvis, Coarse-Grid Multiscale Model Reduction Techniques for Flows in Heterogeneous Media and Applications. Chapter of Numerical Analysis of Multiscale Problems, Lecture Notes in Computational Science and Engineering, 2012, Volume 83, 97-125.

65. V. Calo, Y. Efendiev and J. Galvis, A note on variational multiscale methods for high-contrast heterogeneous flows with rough source terms. Advances in Water Resources, 34 (9), September 2011, pp. 1177-1185.

66. Y. Efendiev, J. Galvis, and X.-H. Wu, Multiscale finite element methods for high-contrast problems using local spectral basis functions. Journal of Computational Physics. Volume 230, Issue 4, 20 February 2011, Pages 937-955.

67. Efendiev, J. Galvis, and P. Vassielvski, Spectral Element Agglomerate Algebraic Multigrid Methods for Elliptic Problems with High-Contrast Coefficients, in Domain Decomposition Methods in Science and Engineering XIX, Huang, Y.; Kornhuber, R.; Widlund, O.; Xu, J. (Eds.), Volume 78 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2011, Part 3 , pp. 407-414.

68. Y. Efendiev and J. Galvis, A Domain Decomposition Preconditioner for Multiscale High-Contrast Problems, in Domain Decomposition Methods in Science and Engineering XIX, Huang, Y.; Kornhuber, R.; Widlund, O.; Xu, J. (Eds.), Volume 78 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2011, Part 2, pp. 189-196.

69. J. Galvis and M. Sarkis, FETI-DP for Stokes-Mortar-Darcy Systems, in Domain Decomposition Methods in Science and Engineering XIX, Huang, Y.; Kornhuber, R.; Widlund, O.; Xu, J. (Eds.), Volume 78 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2011, Part 2, pp. 221-228.

70. M. Dryja, J. Galvis and M. Sarkis, N-N Solvers for a DG Discretization for Geometrically Nonconforming Substructures and Discontinuous Coefficients, in Domain Decomposition Methods in Science and Engineering XIX, Huang, Y.; Kornhuber, R.; Widlund, O.; Xu, J. (Eds.), Volume 78 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2011, Part 1, pp.27-38.

71. J. Galvis and Y. Efendiev, Domaindecomposition preconditioners for multiscale flows in high contrastmedia. Reduced dimension coarse spaces. Multiscale Model. Simul. Volume 8, Issue 5, pp. 1621-1644 (2010). Listed Top 20 Most Downloaded Articles Multiscale Model. Simul. Sep-2010, Oct-2010, Nov-2010, Dic-2010, Jan-2011, Feb-2011, Apr-2012.

72. J. Galvis and Y. Efendiev, Domain Decomposition Preconditioners for MultiscaleFlows in High-Contrast Media, Multiscale Model. Simul. Volume 8, Issue 4, pp. 1461-1483 (2010). Listed Top 20 Most Downloaded Articles Multiscale Model. Simul. Aug-2010, Sep-2010, Oct-2010.

73. J. GALVIS, M. SARKIS, BDD and FETI Methods for Mortar Coupling of Stokes-Darcy Systems. Commun. Appl. Math. Comput. Sci. Vol. 5 (2010), No. 1, 1-30 (Preprint)

74. J. Galvis and M. Sarkis, Approximating infinity-dimensional stochastic Darcy's equations without uniformellipticity. SIAM J. Numer. Anal. Volume 47(2009), Issue 5, pp. 3624-3651 (Preprint)

75. J. GALVIS AND M. SARKIS, A Priori error estimates and FETI preconditioners for Coupling Stokes-Darcy Equations, in Memorias de la Escuela Internacional CIMPA -UNESCO-REALMA "Matemáticas para el modelamiento y la simulación, Published by the Universidad del Valle, eds. Marc Lassonde and Olga Vasilieva., 2008. 

76. M. DRYJA, J. GALVIS, M. SARKIS, Balancing domain decomposition methods for discontinuous Galerkin discretization, in Domain Decomposition Methods in Science and Engineering XVII, Ulrich Langer et al. (eds.), vol. 60 of Lecture Notes in Computational Science and Engineering, Springer-Verlag, 2008, pp 271-278.

77. M. DRYJA, J. GALVIS, M. SARKIS, BDDC Methods for discontinuous Galerkin discretization of elliptic problems, Journal of Complexity, Volume 23, Issues 4-6, August-December 2007, Pages 715-739.

78. J. GALVIS AND M. SARKIS, Non-matching mortar discretization analysis for the coupling Stokes-Darcy equations. Electron. Trans. Numer. Anal. Vol. 26 (2007), pp. 350-384.

79. J. GALVIS AND M. SARKIS, Balancing domain decomposition methods for mortar coupling Stokes-Darcy systems, in Domain Decomposition Methods in Science and Engineering XVI, D. Keyes and O. B. Widlund, eds., vol. 55 of Lecture Notes in Computational Science and Engineering, Springer, 2007, pp. 373-380.

80. J. Galvis and M. Sarkis, Inf-sup for coupling Stokes–Darcy, In: XXV Iberian Latin American Congress in Computational Methods in Engineering, 2005, Recife. Proceedings of the XXV Iberian Latin American Congress in Computational Methods in Engineering, Recife, Brazil, 2004. Published by the Universidade Federal de Pernambuco, eds. Abimael Loula et al., 2004.

Other publications

1. Y. Efendiev, J. Galvis and P. S. Vassilevski, Multiscale Spectral AMGe Solvers for High-Contrast Flow Problems (preprint)

2. J.Galvis and H. Versieux. Introdução a Aproximação Numérica de Equações Diferenciais Parciais Via o Método de Elementos Finitos. Lecture notes for a minicourse in the 28 Colóquio Brasileiro de Matemática IMPA, Rio de Janeiro, 19 a 29 de julho de 2011. Disponible aquí en las Publicações do IMPA

3. J. Galvis, Introdução aos métodos de decomposição de domínio. Lecture notes for a minicourse in the 27 Colóquio Brasileiro de Matemática IMPA, Rio de Janeiro, 27 a 31 de julho de 2009. Disponible aquí en las Publicações do IMPA 

4. J. Galvis, Domain decomposition analysis for heterogeneous Darcy's flow, PhD thesis, Instituto Nacional de Matemática Pura e Aplicada-IMPA, March 2008.

5. J. Galvis, Finite elements for well-reservoir coupling, master's thesis, Instituto Nacional de Matemática Pura e Aplicada-IMPA, April 2004.