FRANCISCO JOSÉ GASPAR

Associate Professor

University of Zaragoza

 

RESEARCH TOPICS:

1.    Deformable porous media.

2.    Stable finite element methods for poroelasticity ----> LINK

3.    Fluid and porous media coupling ---> LINK

4.    Local Fourier analysis for the convergence study of multigrid methods

5.    Multigrid methods for semi-structured grids.

6.    Stability and convergence of finite difference schemes for poroelasticity.

7.    Fast solvers for isogeometric analisys ----> LINK

8.    Fast solvers for the time fractional heat equation ----> LINK

9.     Fast solvers for fractured porous media.

10.Multilevel Monte Carlo methods for uncertainty quantification for porous media flows. ----> LINK

11.Space-Time multigrid solvers.

 

DOCTORAL STUDENTS:

1.    Rodrigo Cardiel, Carmen. Geometric Multigrid Methods on Semi-Structured Triangular Grids. December 2010. PhD with distinction. Awarded with the SEMA Antonio Valle prize to young researchers 2015. (Currently assistant professor Zaragoza University).

2.    Pablo Salinas Cortés. Semi-Structured multigrid methods on Voronoi meshes to the resolution of the Darcy-Oberbeck-Boussinesq model. September 2013. (Currently researcher at Imperial College).

3.    Sebastiao Romero. Métodos Multigrid espaco-tempo para resolver as equacoes do calor e da poroelasticidade. (2017).

LAST PROJECTS:

·     European Projects

1.    “Numerical simulation in deformable porous media. Application to carbon dioxide storage.” NILS Science and Sustainability. Coordinated Mobility of Researchers. 011-ABEL-CM-2013

2.    “Flow in deformable porous media”. NILS Science and Sustainability. Coordinated Mobility of Researchers. 007-2BBRR.

3.    “Efficient numerical methods in deformable porous media. Application to carbon dioxide storage.” H2020-MSCA-IF-2015. EU Horizon 2020 Projects. Marie Sklodowska-Curie Individual fellowships. From 01/09/2016-31/08/2018.

·     National Projects

1.    Modelización y simulación numérica en medios porosos. Aplicación al desarrollo de materiales autorreparables y al almacenamiento de dióxido de carbono. Mineco. Ministerio de Economía y Competitividad. MTM2016-75139-R (2017-2019).

2.    “Diseño de métodos numéricos muy eficientes para problemas de interés en geofísica. Aplicación al almacenamiento de CO2 y a la prospección sísmica. Mineco. Ministerio de Economía y Competitividad. MTM2013-40842-P. (2014-2016)

3.    “Estabilización y convergencia de métodos numéricos para algunos problemas con capa límite. Diseño e implementación de métodos multimalla sobre mallas semi-estructuradas”. Mineco. Ministerio de Economía y Competitividad. MTM2010-16917. (2011-2013)

 

     PLENARY AND INVITED TALKS:

1.    Plenary talk: “ Stabilized finite element discretizations for poroelasticity”. Ninth International Conference on Numerical Methods and Applications (NM\&A'18), Borovets, Bulgaria 2018.

2.    Plenary talk: “Numerical Simulation of Flow in Deformable Porous Media”. Sixth Conference on Numerical Analysis and Applications (NAA'16) Lozenetz, Bulgaria 2016.

3.    Plenary talk: “Poroelasticity. Numerical difficulties and efficient multigrid solution”. 19th International Conference Mathematical Modeling and Analysis. Druskininkai. Lithuania 2014.

4.    Plenary talk: “Development of efficient multigrid finite element methods on semi-structured triangular grids”. 14th International Conference Mathematical Modeling and Analysis. Daugavpils. Latvia 2009.

5.    Invited talk: “Multigrid waveform relaxation. Application to the time-fractional heat equation.”Valencia Numérica 2017, Valencia, Spain, 2017.

6.    Invited talk: “A segregated Uzawa smoother in multigrid for poroelastic problems. “International Conference on Domain Decomposition Methods (DD XXIV), Svalbard, Longyearbyen, Norway, 2017

7.    Invited talk: “About the Uzawa smoother for poroelastic problems.” SIAM Conference on Computational Science and Engineering, Atlanta, Georgia, USA, 2017.

8.    Invited talk: “Multigrid Treatment of Poroelasticity System.” 11th International Conference on Large-Scale Scientific Computations, Sozopol, Bulgaria, 2017.

9.    Invited talk: “A new stabilized discretization for poroelasticity.” SIAM Conference on Mathematical and Computational Issues in the Geosciences (SIAM GS 2017), Erlangen, Germany, 2017.

10.Invited talk: “A  new  iterative  algorithm  based on the fixed-stress split scheme for solving the Biot's problem.” 7th International Conference on Advanced Computational Methods in Engineering (ACOMEN2017), Ghent, Belgium, 2017.

11.Invited talk: “Stable discretizations and fast solvers based on multigrid methods on semi-structured grids. “ International Workshop on Flow in Deformable Porous Media: Numerics and Benchmarks, Hamburg, Germany, 2017.

12.Invited talk: “Multigrid methods on semi-structured grids.” Finse workshop on efficient solvers for fractured porous media, Finse, Norway, 2018.

13.Invited talk: “Stabilization  techniques  for  finite element discretizations in poroelasticity.” 8th International Conference Computational Methods in Applied Mathematics (CMAM-8), Minsk, Belarus, 2018.

14.Invited talk: “Introduction to the poroelasticity problem”. Lectures on Numerical Mathematics and Applications, Wurzburg, Germany, 2014.

15.Invited talk: “Flow in deformable porous media”. 10th International conference on large-scale scientific computations. Sozopol, Bulgaria, 2015.

16.Invited talk: “Designing efficient geometric multigrid methods on triangular grids. International Conference Supercomputer technologies in Mathematical Modeling. Yakutsk, Russia 2011.

17.Invited talk: “About an analysis of the full-multigrid method and its practical utility”. Workshop Fast Solvers for Simulation, Inversion, and Control of Wave Propagation Problems. Wurzburg, Germany, 2011.

PUBLICATIONS:

1.    Peiyao Luo, Carmen Rodrigo, Francisco J. Gaspar, Cornelis W. Oosterlee,  “Uzawa Smoother in Multigrid for the Coupled Porous Medium and Stokes Flow System”, SIAM Journal on Scientific Computing, S633-S661 (2017).

2.    Francisco J. Gaspar, Carmen Rodrigo  “Multigrid Waveform Relaxation for the Time-Fractional Heat Equation”. SIAM Journal on Scientific Computing 39, A1201-A1224 (2017).

3.    Francisco J. Gaspar, Carmen Rodrigo. “On the fixed-stress split scheme as smoother in multigrid methods for coupling flow and geomechanics” Computer Methods in Applied Mechanics and Engineering 326, 526-540 (2017).

4.     P. Luo, C. Rodrigo, F.J. Gaspar, C.W. Oosterlee. “Monolithic multigrid method for the coupled Stokes flow and deformable porous medium system “Journal of Computational Physics 353, 148-168, (2018).

5.    Prashant Kumar, Peiyao Luo, Francisco J. Gaspar, Cornelis W. Oosterlee. “A multigrid multilevel Monte Carlo method for transport in the Darcy–Stokes system”. Journal of Computational Physics 371, 382-408 (2018).

6.    Kumar, Prashant; Rodrigo, Carmen; Gaspar, Francisco J.; Oosterlee, Cornelis W.  “On cell-centered multigrid methods and Local Fourier Analysis for PDEs with random coefficients”. Submitted. ArXiv: http://arxiv.org/abs/1803.08864.

7.    Hu, Xiaozhe; Rodrigo, Carmen; Gaspar, Francisco J.  “Using hierarchical matrices in the solution of the time-fractional heat equation by multigrid waveform relaxation”. Submitted. ArXiv: http://arxiv.org/abs/1706.07632.

8.    C. Rodrigo, X. Hu, P. Ohm, J.H. Adler, F.J. Gaspar, L.T. Zikatanov.  “New stabilized discretizations for poroelasticity and the Stokes’ equations”. Computer Methods in Applied Mechanics and Engineering 341.  467-484 (2018)

9.    Borregales, Manuel; Kumar, Kundan; Radu, Florin Adrian; Rodrigo, Carmen; Gaspar, Francisco José.  “A parallel-in-time fixed-stress splitting method for Biot's consolidation model”. Computers & Mathematics with Applications.  Accepted (2018).ArXiv: http://arxiv.org/abs/1802.00949.

10.P. Luo, C. Rodrigo, F. J. Gaspar, C. W. Oosterlee.  “On an Uzawa smoother in multigrid for poroelasticity equations”. Numerical Linear Algebra with Applications 24 (2017).

11.Carmen Rodrigo, Francisco J. Gaspar, Ludmil T. Zikatanov.  “On The Validity of the Local Fourier Analysis”. Journal of Computational Mathematics 37, 340-348 (2018).

12.Pé de la Riva, Alvaro, Rodrigo, Carmen, Gaspar, Francisco.  “An efficient multigrid solver for isogeometric analysis”. Submitted. https://arxiv.org/abs/1806.05848.

13.P. Matus, F. J. Gaspar, V.T.K. Tuyen.  “Monotone difference schemes for weakly coupled elliptic and parabolic systems”. Computational Methods in Applied Mathematics 15, 287-298 (2017).

14.A. Arrarás, F.J. Gaspar, L. Portero, C. Rodrigo.  “Geometric multigrid methods for Darcy-Forchheimer flow in fractured porous media”. Submiited.

15.A. Arrarás, F.J. Gaspar, L. Portero, C. Rodrigo.  “Mixed-dimensional multi-grid methods for fractured porous media”. Submiited.

16.Rodrigo C., Gaspar F.J., Hu X., Zikatanov L., Stability and monotonicity for some discretizations of the Biot’s consolidation model. Computer Methods in Applied Mechanics and Engineering 298. 183-204 (2016)

17.Gaspar F.J., Lisbona F.J., Matus, P., Tuyen, V.T.K., Numerical methods for a one-dimensional non-linear Biot’s model. Journal of Computational and Applied Mathematics, 293. 62-72 (2016)

18.Rodrigo C., Gaspar F.J., Hu X., Zikatanov L, A finite element framework for some mimetic finite difference discretizations. Computers & Mathematics with Applications, 70. 2661-2673 (2015)

19.Arraras, A., Gaspar F.J., Portero L., Rodrigo C., Domain decomposition multigrid methods for nonlinear reaction–diffusion problems, Communications in Nonlinear Science and Numerical Simulation, 20, 699-710. (2015).

20.Rodrigo C., Sanz F., Gaspar F.J., Lisbona F.J., Local Fourier Analysis for Edge-Based Discretizations on Triangular Grids, Numerical Mathematics: Theory, Methods and Applications 8, 78-96 (2015).

21.Gaspar F.J, Notay Y., Oosterlee C. W. , Rodrigo C. , A simple and efficient segregated smoother for the discrete Stokes equations, SIAM J. Sci.. Comput.  36, 1187-1206 (2014).

22.Rodrigo C., Salinas P., Gaspar F.J. ,  Lisbona F.J., Local Fourier analysis for cell-centered multigrid methods on triangular grids, Journal of Computational and Applied Mathematics 259, 35-47 (2014).

23.Gaspar F.J., Rodrigo C., Heidenreich E.,  Geometric multigrid method on structured triangular grids for incompressible Navier-Stokes equations at low Reynolds numbers International Journal of Numerical Analysis & Modeling 11, 400-411 (2014).

24.Gaspar F.J., Grigoriev A., Vabishchevich P.N., Explicit-Implicit splitting scheme for some systems of evolutionary equations, International Journal of Numerical Analysis & Modeling 11, 346-357  (2014).

25.Gaspar F.J., Rodrigo C., Ciegis R., Mirinavicius A., Comparison of solvers for 2D Schrodinger problems, International Journal of Numerical Analysis & Modeling 11, 131-147 (2014).

26.Boal N., Gaspar F.J., Lisbona F.J., Vabishchevich P.N., Stabilized Finite Difference Methods for the Fully Dynamic Biot's Problem, Mathematical Modelling and Analysis 18, 463-479 (2013).

27.Salinas P., Rodrigo C., Gaspar F.J. ,  Lisbona F.J., Multigrid methods for cell-centered discretizations on triangular meshes. Numerical Linear Algebra with Applications 20, 626-644 (2013).

28.Gmeiner B., Gradl T., Gaspar F.J.; Ruede U., Optimization of the multigrid convergence rate on semi-structured meshes by local Fourier analysis. Computers & Mathematics with Applications 65, 694-711 (2013).

29.Garamendi J., Gaspar F.J., Malpica N., Schiavi E. Box Relaxation Schemes in Staggered Discretizations for the Dual Formulation of Total Variation Minimization.  IEEE Transactions on Image Processing, 22, 2030-2043 (2013).

30.Rodrigo C., Salinas P., Gaspar F.J., Lisbona F.J. Local Fourier analysis for cell-centered multigrid methods on triangular grids. Journal of Computational and Applied Mathematics, (2013).

31.Salinas P., Rodrigo C., Gaspar F.J., Lisbona F.J. An efficient cell-centered multigrid method for problems with discontinuous coefficients on semi-structured triangular grids. Computers & Mathematics with Applications 65, 1978-1989 (2013).

32.Rodrigo C., Gaspar F.J., Lisbona F.J. Multigrid Methods on Semi-Structured Grids. Archives of Computational Methods in Engineering 19, 499-538 (2012).

33.Rodrigo C., Gaspar F.J.; Lisbona F.J., Multigrid Fourier analysis of the multigrid method for quadratic FEM discretizations. Applied Mathematics and Computations 218, 11182-11195 (2012).

34.Boal N., Gaspar F.J., Lisbona F.J. and Vabishchevich P.N., Finite Difference Analysis for the linear thermoporoelasticity problems and its numerical resolution by multigrid methods. Mathematical modelling and analysis 17, 227-244 (2012)

35.Boal N., Gaspar F.J., Lisbona F.J. and Vabishchevich P.N., Finite Difference Analysis of a double porosity consolidation model. Numer. Methods Partial Differential Equations, 28 138-154 (2012)

36.Salinas P., Rodrigo C., Gaspar F.J., Lisbona F.J. Multigrid Methods for cell-centered discretizations on triangular grids. Numerical Linear Algebra, (2012), doi: 10.1002/nla.1864

37.Boal N., Gaspar F.J., Lisbona F.J. and Vabishchevich P.N., Finite Difference Analysis of fully dynamic problems for saturated porous media. J. Comput. Appl. Math. 236, 1090-1102 (2011)

38.Rodrigo C, Gaspar, F.J., Oosterlee, C.W., Yavneh I. Accuracy measures and Fourier analysis for the full multigrid algorithms. SIAM J. Sci. Comput. 32 3108 (2010)

39.Gaspar F.J.; Lisbona F.J.; Rodrigo C. Multigrid finite element method on semi-structured grids for the poro-elasticity problem. To appear in Lectures Notes in Comput. Sci.

40.Heidenreich, E.A.; Gaspar, F.J.; Ferrero, J.F.; Rodriguez, J.F. Compact schemes for anisotropic reaction-diffusion equations with adaptive time step.  Int. J. Numer. Meth. Eng. 82, 1022-1043 (2010).

41.Gaspar F.J.; Lisbona F.J.; Rodrigo C. Multigrid Fourier analysis on semi-structured anisotropic meshes for vector problems. Math. Modelling and analysis. 15, 39-54 (2010).

42.F.J. Gaspar, J.L. Gracia, F. Lisbona and C. Rodrigo. Efficient geometric multigrid implementation for triangular grids.  J. Comput. Appl. Math, 234, 1027-1035 (2010).

43.Gaspar, F.J.; Gracia, J.L.; Lisbona, F.J.; Rodrigo, C. Multigrid finite element methods on semi-structured triangular grids for planar elasticity. Numer. Linear Algebra Appl., 17, 473-493 (2010).

44.  F.J. Gaspar, J.L. Gracia and F. Lisbona. Fourier analysis for multigrid methods on triangular grids SIAM J. Sci. Comput. 31, 2081-2102 (2009).

45.  F.J. Gaspar, J.L. Gracia, F. Lisbona and C. Rodrigo. "On geometric multigrid methods for triangular grids using three-coarsening strategy” Appl. Numer. Math. 59, 1693-1708 (2009).

46.  Ciegis,R.; Gaspar F.J. and Rodrigo C, “Parallel multiblock multigrid algorithms for poroelastic models”, Parallel Scientific Computing and Optimization, Springer New York 169-180 (2009).

47.  G. Aguilar, F.J. Gaspar, F.J. Lisbona and C. Rodrigo.  Numerical stabilization of Biot’s consolidation model by a perturbation on the flow equation. Int. J. Num. Meth. Eng. 75, 1282-1300 (2008).

48.  Ciegis,R.; Gaspar F.J. and Rodrigo C, “On the parallel multiblock geometric multigrid algorithm”, Comput. Methods Appl. Math 8, 223-236 (2008).

49.  Gaspar, F.J.; Gracia, J.L.; Lisbona, F.J. and Oosterlee, C.W. "Distributive Smoothers in Multigrid for Problems with Dominating Grad-Div Operators." Numer. Linear Algebra Appl. 15, 661-683 (2008).

50.  C.W. Oosterlee and F.J. Gaspar. "An overview of multigrid relaxation methods for systems of equations of saddle point type". Appl. Num. Math. 58, 1933-1950 (2008).

51.  E. Heidenreich, J.F. Rodriquez, F.J. Gaspar and M. Doblaré. "Fourth order compact schemes for monodomain reaction diffusion equations". J. Comput. Appl. Math. 216, 39-55 (2008).

52.   F.J. Gaspar, F. Lisbona and C.W. Oosterlee. "A stabilized difference scheme for deformable porous media and its numerical resolution by multigrid methods" Comput. Vis. Sci. 11, 67-76 (2008).

53.   A. Naumovich and F.J. Gaspar. " On a multigrid solver for the three-dimensional Biot poroelasticity system in multilayered domains. Comput. Vis. Sci. 11, 77-87 (2008).

54.   F.J. Gaspar, J.L. Gracia, F.J. Lisbona and P.N. Vabishchevich. A stabilized method for a secondary consolidation Biot's model. Numer. Methods Partial Differential Equations. 24, 60-78 (2008).

55.   F.J. Gaspar, F. Lisbona, C.W. Oosterlee and P.N. Vabishchevich. "An efficient multigrid solver for a reformulated version of the poroelasticity system" Comput. Methods Appl. Mech. Engrg. 196, 1447-1457 (2007).

56.   C.W. Oosterlee and F.J. Gaspar. "Multigrid methods for the Stokes system". Computing in Science & Engineering. 8, 34-43 (2006).

57.   F.J. Gaspar, F. Lisbona and P.N. Vabishchevich. "Staggered grid discretizations for the quesi-static Biot's consolidation problem" Appl. Num. Math. 56, 888-898 (2006).

58.   A. Naumovich, O. Iliev, F.J. Gaspar, F. J. Lisbona and P.N. Vanishchevich."On numerical solution of 1-D poroelasticity equations in a multilayered domain" . Math. Model. Anal. 10, nº 3, 287-304 (2005).

59.   F.J. Gaspar, F. Lisbona, C.W. Oosterlee and R. Wienands, "Systematic comparison of coupled and distributive smoothing in multigrid for the poroelasticity problem" Numer. Linear Algebra Appl. 11, 93-113 (2004)

60.   F.J. Gaspar, F. Lisbona and P.N. Vabishchevich, "A numerical model for radial flow through porous and deformable shells" Comput. Methods Appl. Math. 4, 34-47 (2004)

61.   R. Wienands, F.J. Gaspar, F. Lisbona and C.W. Oosterlee "An efficient multigrid solver based on distributive smoothing for poroelasticity equations" Computing 73, 99-119 (2004).

62.   C.W. Oosterlee, J.C. Frisch and F.J. Gaspar "TVD, WENO and blended BDF discretizations for Asian options" Comput. Vis. Sci. 6, 131-138 (2004)

63.   F.J. Gaspar, F. Lisbona and P.N. Vabishchevich, "Finite difference scheme for filtration and consolidation problems" Lecture Notes in Computer Science 2542 454-462 (2003)

64.   F.J. Gaspar, F. Lisbona and P.N. Vabishchevich, "A finite difference analysis of Biot's consolidation model" Appl. Num. Math. 44, 487-506 (2003)

65.   C.W. Oosterlee, F.J. Gaspar and J.C. Frisch. "WENO and blended BDF discretizations for options pricing problems" Proc. ENUMATH 2001, (Ischia, Italy) Springer Verlag 419-428 (2003)

66.   R. Wienands, F.J. Gaspar, F. Lisbona and C.W. Oosterlee "Analysis of a pointwise smoother in multigrid for poroelasticity" Computational fluid and solid mechanic, 2178-2181 (2003).

67.   F.J. Gaspar, F. Lisbona and P.N. Vabishchevich, "Finite difference schemes for poro-elastic problems" Comput. Methods Appl. Math. 2, 132-142 (2002)

68.   F.J. Gaspar, C. Clavero and F. Lisbona, "Some numerical experiments with multigrid methods on Shishkin meshes" J. Comput. Appl. Math. 138, 21-35 (2002)

69.   F.J. Gaspar, F. Lisbona and C. Clavero "Multigrid methods and finite difference schemes for 2D singularly perturbed problems" Lecture Notes Comput. Sci. 1988 (L. Vulkov, J. Wasnievski, P. Yalamov, eds) 316-324 (2001)

70.   C.W. Oosterlee, R. Wienands, T. Washio and F.J. Gaspar "The acceleration of multigrid convergence by recombination techniques." Multigrid methods, VI (Gent, 1999), 34--43, Lect. Notes Comput. Sci. Eng., 14, Springer, Berlin, 2000.

71.   C.W. Oosterlee, F.J. Gaspar, T. Washio und R. Wienands, `New smoothers for higher order upwind discretizations of convection-dominated problems like the Euler equations'. In : A. Schüller (Hrsg.) `Portable Parallelization of Industrial Aerodynamic Applications (POPINDA), Results of a BMBF Project', Notes on Num. Fluid Mech. 71, Vieweg Braunschweig (1999)

72.   C.W. Oosterlee, F.J. Gaspar und T. Washio, `Parallel adaptive multigrid with nonlinear Krylov subspace acceleration for steady 3D CFD problems' In: K.D. Papailiou et al. (Hrsg.), Computational Fluid Dynamics'98, "Proceedings of the ECCOMAS conference'' Vol 2, 272-277 Wiley Chichester (1998).

73.   F.J. Gaspar und C.W. Oosterlee, `A parallel adaptive mesh refinement multigrid solution method for 3D CFD problems' In: S.K. Dey et al. (Hrsg.), "Proc. of Advances in Sci. Comput. and Modeling'', IMACS'98 Konferenz, Alicante Spanien, 38-42 (1998).

74.   C.W. Oosterlee, F.J. Gaspar, T. Washio und R. Wienands, `Fast multigrid solvers for higher order upwind discretizations of convection-dominated problems' In: W. Hackbusch, G. Wittum (Hrsg.) Multigrid Methods V, Lecture Notes in Computational Science and Engineering 3, Springer Berlin, 212-224 (1998).

75.   C.W. Oosterlee, F.J. Gaspar, T. Washio und R. Wienands. "Multigrid line smoothers for higher order upwind discretizations of convection-dominated problems" Journ. Comp. Physics 139, 274-307 (1998).