Hermann Mena, Ph.D.

Biografía

Hermann Mena is an Ecuadorian mathematician, with contributions to applied mathematics, numerical analysis and optimal control. He is author of two books and many scientific publications. He studied pure mathematics at Escuela Politecnica Nacional in Quito, Ecuador. Following a Ph.D. in applied Mathematics in the same university within a joint program with the Technical University of Berlin, Germany (2007) and a postdoc at Technical University of Chemnitz, Germany; he took up a position as Associate Professor at Escuela Politecnica Nacional, Ecuador. Since 2013 he worked at University of Innsbruck, Austria as Assistant Professor. In 2016 he completed his Habilitation in Mathematics at the University of Innsbruck on stochastic control. Hermann Mena has been the principal investigator of many relevant founded research projects in applied mathematics, e.g. his project “Simulation of Glyphosate Aerial Spray Drift at the Ecuador-Colombia border” attracted the attention of the international community due to the political conflict involved. He has taught courses in the undergraduate and PhD program in Croatia, Uruguay and China and he has been visiting professor at several universities in Europe and USA including the Massachusetts Institute of Technology MIT, USA.

Summary of Interests

Hermann Mena’s research interest are: applied mathematics, numerical analysis, optimal control and scientific computing. The main focus of his research are control problems governed by stochastic and deterministic partial differential equations. These problems naturally arise in science and engineering, e.g. river floods, crime modeling, mathematical finance etc. Their computational cost is very high. Therefore, he is also interested in high performance computing techniques to speed up these computations.

Current Research projects

Numerical solution of stochastic control problems.
Equations involving Mallivin calculus operators
Solution of large-scale Lyapunov differential equations

Selected Publications

  • I. Lasiecka, T. Levajkovic, H. Mena, A. Tuffaha and C. Hafizoglu. The Stochastic Linear Quadratic Control Problem with Singular Estimates. SIAM Journal on Control and Optimization, to appear (2017).
  • R. Altmann, T. Levajkovic and H. Mena. Operator Differential Algebraic Equations with Noise Arising in Fluid Dynamics. Monatshefte für Mathematik, Springer Online First, Open Access (2016). DOI: 10.1007/s00605-016-0931-z
  • T. Levajkovic, H. Mena and A. Tuffaha. A Numerical Approximation Framework for the Stochastic Linear Quadratic Regulator Problem on Hilbert Spaces. Applied Mathematics and Optimization, Springer Online First (2016). DOI: 10.1007/s00245-016-9339-3
  • T. Levajkovic, H. Mena and A. Tuffaha. The Stochastic Linear Quadratic Control Problem: A Chaos Expansion Approach. Evolution Equations and Control Theory, 5(1) (2016), pp. 105 – 134. DOI: 10.3934/eect.2016.5.105
  • P. Benner, H. Mena and R. Schneider. Modelling of the Glyphosate Aerial Spray Drift at the Ecuador-Colombia border. Applied Mathematical Modelling, 40 (2016), pp. 373-387. DOI:10.1016/j.apm.2015.04.057.
  • H. Mena, N. Lang and J. Saak. On the benefits of the LDL factorization for large-scale differential matrix equation solvers. Linear Algebra and its Applications, Vol. 480 (2015), pp. 44-71. DOI:10.1016/j.laa.2015.04.006
  • P. Benner, H. Mena and R. Schneider. Modelo para las aspersiones con glifosato: frontera Ecuador-Colombia (in Spanish). Shaker-Verlag, Aachen-Germany, 2014, 208 pages. DOI:10.2370/9783844030617

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