english

PhD in Mathematical Modelling and Numerical Simulation in Engineering and Applied Science

2026/2027

Quality assurance

The UDC International Doctoral School (EIDUDC) is subject to an Internal Quality Assurance System (IQAS) which governs all UDC PhD programmes ratified by Royal Decree-Law 99/2011, in compliance with EU Standards and Guidelines for Quality Assurance in the EHEA. For more information, see documentation relating to the UDC International Doctoral School Internal Quality Assurance System (Regulations for the implementation and administration of the International Doctoral School SGIC for UDC PhD programmes ratified under RD 99/2011; International Doctoral School IQAS Manual; International Doctoral School IQASProcedures).

Guidelines for the monitoring and supervision of the student learning process and outcomes are established in the IQAS Procedures document. The bodies and mechanisms responsible for the coordination, evaluation and continuous improvement of the programme of study are as follows:

Academic Committee for PhD Programmes (CAPD): university body responsible for the academic coordination of PhD programmes and academic decisions regarding PhD degree and degree candidates. The CAPD establishes the guidelines and procedures for the programme coordinator and all individuals involved in the degree. A UDC coordinator is appointed for all UDC PhD programmes ratified under RD 99/2011, including inter-university programmes operated by partner universities.

EIDUDC Quality Assurance Committee (CGC): body responsible for formulating and monitoring the SGIC and PhD degree programmes. The CGC also fulfils an internal communication role within the EIDUDC in relation to its objectives, plans, programmes and responsibilities. An annual monitoring report is produced by the EIDUDC Permanent Committee, acting in the name of the CGC.

Learning outcomes

The International Doctoral School IQAS sets out the standards and indicators applied by Academic Committees in relation to UDC PhD programmes for the measurement and analysis of learning outcomes and academic standards.

These indicators include the number of doctoral theses defended, ‘International Doctorate’ certifications awarded, PhDs completed within the published time scale (3-4 years), PhDs awarded and PhDs abandoned, in addition to the average timescale for completion of the degree.

Quality assurance

To ensure that the title is developed in accordance with the verification report presented the center conducts an annual monitoring report in accordance with the procedures of the center IQAS and results. This report is reviewed by the ACSUG, external evaluation agency.

The outcome of this analysis will emerge corrective actions and improvement proposals that achieve the intended objectives and the improvement of the degree.

UDC quality regulations and norms

Committees

In order to ensure proper standards and quality at UDC, a specific academic management committee of the PhD programme will be established.

Vázquez Cendón, Carlos

Arregui Álvarez, Iñigo

theses

publications

This is a sample of the scientific production of the PhD students and is intended to guide prospective students interested in this program. Under no circumstances should it be considered a full and exhaustive list of all the scientific production of the students. The information is supplied by the PhD students themselves in a relatively unstructured manner but it has been checked and approved by the academic committee.

Artículos en revistas internacionales
Articulo bajo revisión titulado: Well-balanced DG schemes for multidimensional shallow water systems with Coriolis forces: evolving fluctuations of stationarity preserving continuous finite elements 
Otras publicaciones
PIDE models for efficient control of stochastic gene regulatory circuits ( https://doi.org/10.1016/j.ifacol.2025.11.104 ). Autores: Christian Fernández Pérez, Manuel Pájaro Diéguez, Gábor Szederkényi, Irene Otero-Muras Predictive-Switching Control of Stochastic Gene Regulatory Networks: A Contractive PIDE Framework ( arXiv:2605.07614 ). Autores: Christian Fernández Pérez, Manuel Pájaro Diéguez, Gábor Szederkényi, Irene Otero-Muras
Artículos en revistas internacionales
Publicación do artigo "Davide Trevisani, José Germán López-Salas, Carlos Vázquez, José Antonio García-Rodríguez. Mathematical models and numerical methods for a capital valuation adjustment (KVA) problem, Applied Mathematics and Computation, 488 (2025) 129105". A revista "Applied Mathematics and Computation" está na categoría Q1 do JCR 2024 na categoría MATHEMATICS, APPLIED. Máis concretamente ocupa a posición 11/343, polo que está no primeiro decil (percentil 96.9). 
Publicación do artigo "Davide Trevisani, José Germán López-Salas, Chris Kenyon, Carlos Vázquez and Mourad Berrahoui. Scope 3 capital design for carbon-emissions-facilitation tax risk, International Journal of Computer Mathematics". A revista "International Journal of Computer Mathematics" está na categoría Q1 do JCR 2023 na categoría MATHEMATICS, APPLIED. Máis concretamente ocupa a posición 83/332, polo que está no percentil 75.2.
Artigo enviado a revista do JCR actualmente en proceso de revisión: "Davide Trevisani, José Germán López-Salas, Carlos Vázquez. Modelling, mathematical analysis and computation of the total value adjustment including KVA and multicurrency."
Boundary Treatment for High-Order IMEX Runge–Kutta Local Discontinuous Galerkin Schemes for Multidimensional Nonlinear Parabolic PDEs.https://doi.org/10.1137/23M1612184
P. Villarino, Joel; Leitao, Álvaro; "On deep learning for computing the dynamic initial margin and margin value adjustment". Applied Mathematics and Computation, Volume 510, 2026
Artículos en revistas internacionales
Sequeiros, Carlos and Pájaro, Manuel and Vázquez, Carlos and Banga, Julio R and Otero-Muras, Irene. IDESS: a toolbox for identification and automated design of stochastic gene circuits. Bioinformatics, 2023. https://doi.org/10.1093/bioinformatics/btad682
Automated Design of Synthetic Gene Circuits in the Presence of Molecular Noise. Sequeiros, Carlos and Vázquez, Carlos and Banga, Julio R. and Otero-Muras, Irene. ACS Synthetic Biology. https://doi.org/10.1021/acssynbio.3c00033
Publicado artículo titulado "High-order well-balanced numerical schemes for one-dimensional shallow-water systems with Coriolis terms" en Applied Mathematics and Computations. https://doi.org/10.1016/j.amc.2023.128528
Enviado artículo sobre High Order Local Discontinuous Galerkin para una revista del SIAM.
Pombo-Romero, J.; Rúas-Barrosa, O.;  Vázquez, C. (2024). Assessing the value and risk of renewable PPAs. Energy Economics, 139, https://doi.org/10.1016/j.eneco.2024.107861.
Otras publicaciones
Title: Parametrized Quantum Circuits and their approximation capacities in the context of quantum machine learning.Authors: Alberto Manzano, David Dechant, Jordi Tura, Vedran Dunjko.Reference: https://arxiv.org/abs/2307.14792
Title: Real Option Pricing using Quantum Computers.Authors: Alberto Manzano, Gonzalo Ferro, Álvaro Leitao, Carlos Vázquez, Andrés GómezReference: https://arxiv.org/abs/2303.06089
Joel P. Villarino, Álvaro Leitao. On Deep Learning for computing the Dynamic Initial Margin and Margin Value Adjustment. 
Artículos en revistas internacionales
Simonella, R. and Vázquez, C., 2023. XVA in a multi-currency setting with stochastic foreign exchange rates. Mathematics and Computers in Simulation207, pp.59-79.
Pombo-Romero, J.; Rúas-Barrosa, O. A Blockchain-Based Financial Instrument for the Decarbonization of Irrigated Agriculture. Sustainability202214, 8848. https://doi.org/10.3390/su14148848
Manzano, A., Musso, D. & Leitao, Á. Real quantum amplitude estimation. EPJ Quantum Technol.10, 2 (2023). https://doi.org/10.1140/epjqt/s40507-023-00159-0
Alberto Pedro Manzano-Herrero, Emanuele Nastasi, Andrea Pallavicini & Carlos Vázquez(2023)Pricing commodity index options,Quantitative Finance,23:2,297-308,DOI: 10.1080/14697688.2022.2138775
SEQUEIROS, Carlos, et al. Global optimization approach for parameter estimation in stochastic dynamic models of biosystems. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2022. https://doi.org/10.1109/TCBB.2022.3225675
Artículo en revisión titulado: "High-order well-balanced numerical schemes for one dimensional shallow-water systems with Coriolis terms" para  Applied Mathematics and Computation (AMC-D-23-01451).
P. Villarino, Joel; Leitao, Álvaro; García Rodríguez, J.A. Boundary-safe PINNs extension: Application to non-linear parabolic PDEs in counterparty credit risk. Journal of Computational and Applied Mathematics, 425 (2023).
Hiram Varela and María González. An improved model for the drying of porous solids with abruptly changing permeability. Dry. Technol., 0(0): 1-16, 2023.https://www.tandfonline.com/doi/full/10.1080/07373937.2023.2227433
Libro
https://gei-cal.github.io/JB-Calculo1-UDC/capitulos/README.html    Licencia CC BY 4.0
Otras publicaciones
Arregui, I., Simonella, R. and Vázquez, C., 2022. Modelling and Computing the Total Value Adjustment for European Derivatives in a Multi-Currency Setting. In Progress in Industrial Mathematics at ECMI 2021 (pp. 313-319). Cham: Springer International Publishing.
-Redacción de un artículo científico que lleva por título “Experimental validation of a coupled acoustic fluid-poroelastic-plate model with frontal and lateral source Excitations” para su publicación en revista científica.
Artículos en revistas internacionales
Arregui, Iñigo, Roberta Simonella, and Carlos Vázquez. "Total value adjustment for European options in a multi‐currency setting." Applied Mathematics and Computation 413 (2022): 126647.
Di Francesco, Marco, and Roberta Simonella. "A stochastic Asset Liability Management model for life insurance companies." Financial Markets and Portfolio Management (2022): 1-34.
Gómez, A., Leitao, Á., Manzano, A. et al. "A Survey on Quantum Computational Finance for Derivatives Pricing and VaR." Arch Computat Methods Eng (2022). https://doi.org/10.1007/s11831-022-09732-9
Manzano, A.; Musso, D.; Leitao, Á.; Gómez, A.; Vázquez, C.; Ordóñez, G.; Nogueiras, M.R. A "Modular Framework for Generic Quantum Algorithms." Mathematics (2022), 10, 785. https://doi.org/10.3390/math10050785
M. GONZÁLEZ AND H. VARELA, A posteriori errorestimates for stabilised mixed finite element methods for a nonlinear elliptic problem, Electron. Trans. Numer. Anal., 55(2022), pp. 706-725.
Otras publicaciones
González, M.; Varela, H. On the Adaptive Numerical Solution to the Darcy-Forchheimer Model. Eng. Proc. 2021, 7, 36
Artículos en revistas internacionales
Numerical solution of a nonlinear PDE model for pricing Renewable Energy Certificates (RECs)Applied Mathematics and Computation 404 (2021) 126199
Ráfales, J., Vázquez, C. (2021). Equilibrium models with heterogeneous agents under rational expectations and its numerical solution. Communications in Nonlinear Science and Numerical Simulation, 96: 105673.
Otras publicaciones
Auer, Naomi, Barral, PatriciaI, Benamou, Jean-David, Baermann, Andreas, Binder, Andreas, Comesaña, Daniel Fernández, … Vergara, Christian. (2020). Reports about 8 selected benchmark cases of model hierarchies (Version 3.0). Zenodo, https://doi.org/10.5281/zenodo.3888124
Bannenberg, Marcus, Barral, Patricia, Bärmann, Andreas, Benamou, Jean-David, Bianco, Federico, Binder, Andreas, … Vergara, Christian. (2020). Software-based representation of selected benchmark hierarchies equipped with publically available data (Version 2.0). Zenodo, https://doi.org/10.5281/zenodo.3888145
Bannenberg, Marcus, Barral, Patricia, Bianco, Federico, Fernández Comesaña, Daniel, Marconi, Gianfranco, Martinolli, Marco, … Vergara, Christian. (2020). Report on common coupling framework, error and complexity measures (Version 1.0). Zenodo, https://doi.org/10.5281/zenodo.3606282
Bannenberg, Marcus, Barral, Patricia, Bianco, Federico, Fernández-Comesaña, Daniel, Marconi, Gianfranco, Martinolli, Marco, … Vergara, Christian. (2020). Reports on specific model hierarchies for different coupling applications and the corresponding error analyses (Version 1.0). Zenodo. https://doi.org/10.5281/zenodo.3606326
Martín Ortega, Elena, Nayak, Ashwin Sadanand, & Varas, Fernando. (2019). Simplified Modeling of Brazing Furnaces (Version 1.0). In Proceedings of the 139 European Study Group with Industry (139ESGI) (pp. 27–46). Spanish Network for Mathematics & Industry (math-in). http://doi.org/10.5281/zenodo.3610123
González, M.; Varela, H. Numerical Simulation of a Nonlinear Problem Arising in Heat Transfer and Magnetostatics. Proceedings202054, 13.
Artículos en revistas internacionales
J. Carbajo, A. Prieto, J. Ramis, L. Río-Martín, A non-parametric fluid-equivalent approach for the acoustic characterization of rigid porous materials, Applied Mathematical Modelling, Volume 76, 2019, Pages 330-347, ISSN 0307-904X, https://doi.org/10.1016/j.apm.2019.05.046. (http://www.sciencedirect.com/science/article/pii/S0307904X19303439) Abstract: The acoustic characterization of porous materials with rigid solid frame plays a key role in the prediction of the acoustic behavior of any dynamic system that incorporates them. In order to obtain an accurate prediction of its frequency-dependent response, a suitable choice of the parametric models for each material is essential. However, such models could be inadequate for a given material or only valid in a specific frequency range. In this work, a novel non-parametric methodology is proposed for the characterization of the acoustic properties of rigid porous materials. Unlike most widespread methodologies, this technique is based on the solution of a sequence of frequency-by-frequency well-posed inverse problems, thus increasing the characterization accuracy. Once a reduced number of experimental measurements is available, the proposed method avoids the a priori choice of a parametric model. Keywords: Material characterization; Porous materials; Inverse problem; Non-parametric model; Acoustic properties
Artículos en revistas internacionales
Iñigo Arregui; B. Salvador; Carlos Vázquez.. A Monte Carlo approach to American options pricing including counterparty risk. INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. , -. ISSN:0020-7160
Iñigo Arregui; B. Salvador; Daniel Sevcovic; Carlos Vázquez. 2018. Total value adjustment for European options with two stochastic factors. Mathematical model, analysis and numerical simulation.COMPUTERS AND MATHEMATICS WITH APPLICATIONS(1987). , -.76 (2018)4, 725-740
Otras publicaciones
J. Carbajo, A. Prieto, J. Ramis, L. del Río. Data-driven characterization of porous materials by using frequency-dependent measurements. Proceedings from 48º Congreso Español de Acústica - Encuentro Ibérico de Acústica, 2017. 
Artículos en revistas internacionales
I.Arregui, B.Salvador, C.Vázquez, PDE models and numerical methods for total value adjustment in European and American options with counterparty risk. Applied Mathematics and Computation, 308 (2017) 31-53
Artículos en revistas internacionales
Numerical methods for a nonlinear reaction-diffusion system modelling a batch culture of biofilm, Balsa-Canto E., López-Núñez A., Vázquez C., Applied Mathematical Modelling, In Press, DOI: 10.1016/j.apm.2016.08.020
Capítulo de Libro
Balsa-Canto E., Alonso A. A., Arias-Méndez A., Garca M. R., López-Núñez A., Mosquera-Fernández, M., Vázquez C., Vilas C., Modelling and optimisation techniques with applications in food processes, bio-processes and bio-systems, SEMA SIMAI Springer Series, 9, Cap. 4, pp 187-216, 2016.
Artículos en revistas internacionales
I. Arregui, B. Salvador, C. Vázquez, A numerical strategy for telecommuications networks capacity planning under demand and price uncertainty, Journal of Computational and Applied Mathematics (2016), http://dx.doi.org/10.1016/j.cam.2016.01.056 

Offer places

Offer available places last year and, for degree studies, you can also check the cut notes of those admitted by PAAU.

academic year 2025/2026
General offer 7