Personal webpage

Tlf: (34) 91 06 74 412

E-mail: carlos.castro@upm.es

Teaching (2020/21)

Teoría de campos (Graduado en Ingeniería Civil y Territorial de la UPM),

Matemáticas I (Graduado en Ingeniería de Materiales)

Office: 6th floor, Monday and Tuesday 9:30-12:30

Previous courses: 

• Informática  

• Cálculo 

• Ecuaciones Diferenciales (Graduado en Ingeniería Civil y Territorial de la UPM),

  • Análisis de Series Temporales y Análisis Espectral y Procesamiento Digital de Imágenes (Máster en Ingeniería Geodésica y Cartografía de la UPM)

Links: MateWiki (wiki for students), Wavecontrol (Matlab program to approximate control problems)

Research areas

• 1. Distributed control of PDE

  2. Optimal design problems

  3. Numerical approximation of control problems

  4. Homogenization in PDE

  5. Control and Optimization in conservation laws 

  6. Inverse problems and scattering

Publications 

Uniform boundary observability for the spectral collocation of the linear elasticity system,  preprint (2023), S. Boumimez and C. Castro, pdf-arxiv

Numerical approximation of the boundary control for the wave equation with a spectral collocation method,   to appear in Comp. and Appl. Math, S. Boumimez and C. Castro. pdf-arxiv

The Born approximation in the three-dimensional Calderon problem II: Numerical reconstruction in the radial case, to appear in Inverse Problems and Imaging, J.A. Barceló, C. Castro, F. Macià and C. Meroño,  pdf-arxiv

Live load matrix recovery from scattering data in linear elasticity, to appear in Advances in Computational Mathematics, J.A. Barceló, C. Castro, M.C. Vilela, pdf-arxiv

The Born approximation in the three-dimensional Calderon problem,  J. Funt. Anal., vol 283 (12) 2022, J.A. Barceló, C. Castro, F. Macià y C. Meroño, pdf

Achieving energy permutation of modes in the Schrödinger equation with moving Dirac potentials,  Math Cont. Relat. Fields, early access: https://www.aimsciences.org/article/doi/10.3934/mcrf.2022060 (2023), C. Castro and A. Duca, pdf-arxiv 

Numerical approximation of the scattering amplitude in elasticity,  SeMA J. 79, 549-570, 2022, J.A. Barceló and C. Castro, pdf (Best paper SEMA J. Award in 2022)

Numerical approximation of the averaged controllability for the wave equation with unknown velocity of propagation,  ESAIM COCV, 27 (61) 2021, M. Abdelli and C. Castro pdf

Singular asymptotic expansion of the exact control for the wave equation perturbed by a fourth order term,  Asymptotic Analysis, vol. 122, no. 1-2, pp. 1-33, 2021. C. Castro and A. Munch, pdf

Unicity for the fixed angle inverse scattering problem,  J. Inverse and Ill-posed Problems, 28(4) 2020, 465-470. J.A. Barceló, C. Castro, T. Luque, C. Meroño, A. Ruiz y M.C. Vilela, pdf

Numerical approximation of the best decay rate for some dissipative systems,  SIAM J Num. Anal. 57(2), 681—701, 2019. K. Ammari and C. Castro, pdf

Corrigendum: A new method to recover the potential in the inverse scattering problem,  SIAM J. Appl. Math. 79(6), 2688–2691, 2018. J.A. Barceló, C. Castro, T. Luque y M.C. Vilela, pdf

A new method to recover the potential in the inverse scattering problem,  SIAM J. Appl. Math. 78(5), 2714–2736, 2018. J.A. Barceló, C.Castro, T. Luque y M.C. Vilela, pdf

A null controllability result for the linear system of thermoelastic plates with one single control,  in Evolution Equations long time behavior and control, London Mathematical Society Lecture Notes Series 439, 77-89, 2018, C. Castro y L. de Teresa. pdf

Numerical approximation of the potential in the two dimensional inverse scattering problem,  Inverse Problems 32(1) 1-19, 2016. J.A. Barceló, C. Castro y J.M. Reyes, pdf

Optimal design in elasticity: a systematic adjoint approach to boundary cost functionals.  Optim. And Engineering 16(4), 811-829, 2015, J. Palacios, C. Castro y A. Samartin. link

Null controllability of the linear system of thermoelastic plates.  J. Math. Anal. Appl. 428(2), 772-793, 2015. C. Castro y L. de Teresa.  pdf

Controllability of the linear 1D wave equation with inner moving forces,  SIAM J. Cont. Optim. 52 (6) 4027-4056 2014. C. Castro, N. Cindea y A. Munch, pdf

Gradient Calculus for a Class of Optimal Design Problems in Engineering,  in Advances in Numerical Simulation in Physics and Engineering, SEMA-SIMAI Springer Series, Vol. 3, 2014, C. Castro. pdf

Exact controllability of the 1-d wave equation from a moving interior point,  ESAIM COCV, 19, 301-316, (2013), C. Castro pdf

Continuous adjoint approach for the Spalart-Allmaras model in aerodynamic optimization,  AIAA Journal, Vol. 50, No. 3, March 2012, A. Bueno-Orovio, C. Castro, F. Palacios y E. Zuazua.

Numerical approximation of a one-dimensional elliptic optimal design problem,  SIAM Multiscale Modeling and Simulation, 2011, Vol. 9, No. 3, pp. 1181-1216, J. Casado Díaz, C. Castro, M. Luna Laynez y E. Zuazua, pdf

Flux identification for 1-d scalar conservation laws in the presence of shocks,  Math. of Comp., 80, (2011) 2025-2070, C. Castro y E. Zuazua, pdf

Optimal control and vanishing viscosity for the Burgers equation,  en Integral Methods in Science and Engineering, Vol. 2 Computational Methods, C. Constanda and M.E. Pérez Ed.,  Birkauser Boston, 2010, pp. 65-90, C. Castro, F. Palacios y E. Zuazua, pdf

2D Euler shape design on non-regular flows using adjoint Rankine-Hugoniot relations,   AIAA Journal, 47 (2009) 552-562, T. Baeza, C. Castro, F. Palacios y E. Zuazua,  pdf

Optimal boundary geometry in an elasticity problem: a systematic adjoint approach, Proceedings IASS, Symposium 2009, Evolution and Trends in Design, Analysis and Construction of Shell and Spatial Structures, A. Domingo and C. Lazaro Ed., 509-524.,  J. García-Palacios, C. Castro and A. Samartín. pdf

A systematic formulation of the continuous adjoint method applied to viscous aerodynamics design, Revista de Investigación Operacional 30 (1), (2009) 3-10. C. Castro, C. Lozano, F. Palacios y E. Zuazua, ref.

An alternating descent method for the optimal control of the inviscid Burgers equation in the presence of shocks,  Mathematical Models and Methods in Applied Sciences 18 (3), (2008) 369–416. C. Castro, F. Palacios y E. Zuazua,  pdf

Numerical approximation of the boundary control of the wave equation in a square with a mixed finite element method,  IMA J. Numerical Analysis 28 (3), (2008) 186–214. C. Castro, S. Micu y A. Munch, pdf

Systematic Continuous Adjoint Approach to Viscous Aerodynamics Design on Unstructured Grids,  AIAA Journal 45 (9), (2007) 2125-2139. C. Castro, C. Lozano, F. Palacios y E. Zuazua, pdf 

Addendum to Concentration and lack of observability of waves in highly heterogeneous media,  Arch. Rat. Mech. Anal. 185 (3),  (2007) 365-377. C. Castro y E. Zuazua, pdf

Boundary controllability of a linear semi-discrete 1-D wave equation derived from a mixed finite element method,  Numerische Mathematik, 102 (3),  (2006) 413-462, C. Castro y S. Micu, pdf

Unique continuation and control for the heat equation from a lower dimensional manifold,  SIAM J. Cont. Optim, 42 (4), 1400-1434. C. Castro y E. Zuazua, pdf

Some topics on the control and homogenization of parabolic partial differential equations,  in Homogenization 2001, L. Carbone and R. De Arcangelis Ed., Gakuto Internat. Ser. Math. Sci. Appl. 18, Gakuto Tokio, 2003, pp. 49-93, C. Castro y E. Zuazua pdf

Concentration and lack of observability of waves in highly heterogeneous media,  Arch. Rat. Mech. Anal. 164 (1),  (2002) 39-72, C. Castro y E. Zuazua, pdf

Optimization of nuclear fuel reloading by the homogenization method,  Structural and Multidisciplinary Optimization, 24 (1), 11-22.  G. Allaire y C. Castro,  pdf

Achieving arbitrarily large decay in the damped wave equation,  SIAM J. Cont. Optim., 39 (6),  (2001) 1748-1755, C. Castro y S. Cox, pdf

A new approach to the optimal distribution of assemblies in a Nuclear Reactor,  Numerische Mathematik, 89 (1), (2001)  1-29, G. Allaire y C. Castro, pdf

High frequency asymptotic analysis of a string with rapidly oscillating density,  European J. Appl. Math., 11 595-622, (2000). C. Castro y E. Zuazua, pdf

Low frequency asymptotic analysis of a string with rapidly oscillating density,  SIAM J. Appl. Math., 60,  (2000) 1205-1233, C. Castro y E. Zuazua, pdf

Exact boundary controllability of two Euler-Benouilli beams connected by a point mass,  Math.& Comp. Modelling 32 (9), (2000) 955-969 C. Castro y E. Zuazua, pdf

Boundary controllability of the one-dimensional wave equation with rapidly oscillating density.  Asymptotic Analysis, 20 (3-4),  (1999), 317-350, C. Castro, pdf

Boundary controllability of a hybrid system consisting in two flexible beams connected by a point mass,  SIAM J. Cont. Optim. 36 (1998) 1576-1595, C. Castro y E. Zuazua. pdf

Asymptotic analysis and control of a hybrid system composed by two vibrating strings connected by a point mass,  ESAIM Cont. Optim. and Calculus of Variations, 2 (1997) 231-280, C. Castro, pdf

A hybrid system consisting of two flexible beams connected by a point mass: spectral analysis and well-posedness  in asymmetric Spaces,  in Élasticité, Viscoélasticité et Controle Optimal, ESAIM Proceedings, Vol. 2, 1997, pp. 17-53, C. Castro y E. Zuazua. pdf

Une remarque sur l'analyse asymptotique spectrale en homogénéisation,  C. R. Acad. Sci. Paris, 322 (1996) Serie I Mathematiques, 1043-1047, C. Castro y E. Zuazua. pdf

Une remarque sur les séries de Fourier non-harmoniques et son application à la contrôlabilité des cordes avec densité singulière, C. R. Acad. Sci. Paris, 323 (1996) Serie I Mathematiques, 365-370, C. Castro y E. Zuazua. pdf