Castro Díaz, Manuel J.

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After completing the degree on Mathematics at the University of Malaga (1987-92), I moved to Paris, where I obtained the D.E.A. of Numerical Analysis at the P. and M. Curie University (Paris VI). I did my PhD thesis at INRIA (Rocquencourt) under the direction of F. Hetch and Carlos Parés on mesh generation/adaptation and a posteriori FEM error estimations for some elliptic problems. Since 1996, I have held various teaching positions at the University of Malaga, obtaining the position of full professor in the year 2020. I’m a member of EDANYA group (Differential Equations Numerical Analysis and Applications), which is currently a reference group on Numerical Analysis.  I have published more than 100 works, most of them in top rated journals on Numerical Analysis, Computer Science and Geophysical applications.  I’ve been PI of several Spanish projects and researcher Several international projects funded by EU. I have been plenary/invited lecturer in several top rated Spanish and international Numerical Analysis conferences: XI EHF 2004, XXI CEDYA 2009, XXIV CEDYA 2015, NUMHYP 2013, ECMI 2014, HYP 2016. Finally,  I have been invited as lecturer of sections 15 (Numerical Analysis and Scientific Computing) and 18 (Mathematics in Science and Technology) of the last ICM 2018. I have also been invited as a lecturer to numerous workshops or courses. Finally, in 2008 I was awarded with the J.Lions Lions Award to Young Scientists in Computational Mathematics, awarded by ECCOMAS, and recently, our group EDANYA has been awarded with the Nvidia Global Impact Award 2018, for our contributions in tsunami modeling, and in particular for the numerical development of Tsunami-HySEA model, that has been incorporated in the core of  several national tsunami early warning systems.
I focus my research on the numerical analysis of non-conservative hyperbolic systems and the modeling of geophysical flows. Specifically, I have been working on the development and analysis of numerical schemes for those systems in the framework of ‘path-conservative’ methods introduced by C. Parés, with applications to the simulation of coastal currents, floods, avalanches, sediment transport, turbidity currents, generation and propagation of tsunamis, biphasic flows, magnetohydrodynamics, etc … I have also been interested in the efficient implementation of the numerical models using multicore and multiGPU architectures and, more recently, on uncertainty quantification and data assimilation.

Awards

  • L. Lions ECCOMAS Award to Young Scientists in Computational Mathematics (2008)
  • Nvidia Global Impact Award 2018 to EDANYA team, for our the contributions in tsunami modeling (2018

Main research results

  • I have made fundamental contributions on the field of numerical analysis of nonlinear hyperbolic systems. In particular, I have contributed to stablish the framework of path-conservative numerical schemes and to develop well-balanced numerical schemes. Those results have contributed to better understand the numerical approximation of different nonlinear PDEs that appear on the modeling of geophysical flows, multiphase fluids, magneto-hydrodynamics, Relativistic fluids, etc … Those results have been published in a series por articles, some of them with more than 100 citations. A review of the main results have been published as a chapter of the prestigious series Handbook of Numerical Analysis. (Well-Balanced Schemes and Path-Conservative Numerical Methods. Castro, M.J, Morales de Luna, T., Parés, C. In Handbook of Numerical Analysis, 2017, 18, pp. 131–175, Elsevier. 17 citations (Scopus))
  • In the last two years I have published a series of papers about the numerical approximation of non-hydrostatic shallow flows. In those papers we propose different numerical models and schemes that allow to consider non-hydrostatic effects in shallow flows. HPC techniques are also developed to improve the efficiency of the numerical schemes. See for example: C. Escalante, E.D. Fernández-Nieto,T. Morales de Luna, M.J. Castro. “An efficient two-layer non-hydrostatic approach for dispersive water waves”. Journal of Scientific Computing 79 (1), 273-320, 2019. Citations: 9 (Scopus),  8 (journal web page).
  • I also have contributed to the derivation of Arbitrary-Lagrangian-Eulerian and Lagrange-Projection finite volume schemes with enhanced properties like the exact preservation of a relevant set of stationary solutions (well-balanced properties), as well as their extension to high order. See for example: Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity”. Monthly Notices of the Royal Astronomical Society 477 (2), 2251-2275, 2018. Citations: 19 (Scopus)
  • I have collaborated in multi-disciplinary works with scientists of other disciplines, in particular in problems related with tsunami modelling and their risk mitigation. See for example: I. Molinari et al. “Fast evaluation of tsunami scenarios: uncertainty assessment for a Mediterranean Sea database”. Natural Hazards and Earth System Sciences 16 (12), 2593-2602, 2016. Citations:  11 (Scopus), 11 (Journal web page).
  • I have contributed to the design of efficient implementation of sophisticated numerical methods using innovative HPC techniques. See for example: M. de la Asunción, M.J. Castro, J.M. Mantas, S. Ortega. “Numerical simulation of tsunamis generated by landslides on multiple GPUs”. Advances in Engineering Software 99, 59-72, 2016. Citations: 17 (Scopus), 18 (journal web page).

Research highlights

  • PI and coordinator of 3 MINECO projects, the last one corresponding to “Convocatorias 2018 Proyectos de I+D de GENERACIÓN DE CONOCIMIENTO y Proyectos de I+D+i RETOS INVESTIGACIÓN” and two regional (Junta de Andalucía and FEDER projects).
  • I have been advisor or co-advisor of 8 PhD tesis, two of them selected by SEMA for ECCOMAS PhD awards.
  • PI of 5 art. 83 projects (transfer of knowledge) with NOAA (National Oceanic and Atmospheric Administration, USA) related with tsunami modelling.
  • I have been member of a multidisciplinary team that has elaborated 4 patents, two of them related with water purification and cleaning.