instituto de matemáticas universidad de sevilla
Antonio de Castro Brzezicki
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Data and Model Reduction of Multidimensional Problems
Seminario IMUS
Since the beginning of this century the question of data and model reduction has given rise to a large research projects and scientific publications activities. Many new algorithms have emerged with varying degrees of success. Among these we can cite the Proper Generelizd Decomposition method to solve multidimensional  PDEs and High Order SVD, Recursive POD, ... techniques to reduce the size of data by tensorization.
During the forth last years, in collaboration with  Prof  Tomás Chacón Rebollo and his team, we have  made a number of contributions in terms of algorithms and numerical analysis.  In this talk we will present some these  results related two topics :
1) The reduction of multidimensional data by tensorization
2) The reduction of models by the PGD technique: Case of Elliptical PDEs
In both cases we will present some mathematical results accompanied by numerical illustrations
 
Some references
M. Azaiez, F. Ben Belgacem, J. Casado-D, T. Chacon and F. Murat -- A new Algorithm  of proper generalized decomposition for parametrics symmetric elliptic problems. SIAM J. M ATH . A NAL . Vol. 50, No. 5, pp. 5426–5445 (2018)
M. Azaiez, T. Chacon , E. Perracchione and J. M. Vega – Recursive POD Expansion for the Advection-Diffusion-Reaction Equation.   Commun. Comput. Phys. 24, 1556-1578, (2018)
M. Azaïez, F. Ben Belgacem, T. Chacón Rebollo, M. Gómez Mármol, I. Sánchez Muñoz. Error bounds in high-order Sobolev norms for POD expansions of parameterized transient temperatures. C. R. Acad. Sci. Paris, Ser. I Vol. 355, No. 4, pp. 432-438, (2017)
M. Azaïez, F. Ben Belgacem and T. Chacón Rebollo., Error Bounds for POD expansions of parameterized transient temperatures Comput. Methods Appl. Mech. Engrg. 305. pp 501–515 (2016)
M. Azaïez, F. Ben Belgacem and T. Chacón Rebollo., Recursive POD expansion for reaction-diffusion equation. Adv. Model. and Simul. in Eng. Sci. 3:3  (2016)
M. Azaïez, F. Ben Belgacem, Karhunen-Loève’s truncation error for bivariate functions Comp. Methods in Applied Mech. and Engineering, V. 290, 15 , Pages 57-72 June (2015)

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