Most of our developments on multiscale numerical simulators are based on the family of Multiscale Hybrid-Mixed (MHM) methods, which provides a multi-level strategy to approximate the solution of boundary value problems with heterogeneous coefficients.

We devise multiscale numerical simulators to run at scale, exploring massively parallel architectures and developing code with bleeding-edge technologies.

We explore machine learning techniques to predict resource consumption and approximate local solutions in multiscale numerical simulations.

A multidisciplinary group with mathematicians, computer scientists and engineers.

Head of the IPES Research Group, he is a researcher at the National Laboratory for Scientific Computing (LNCC) since 2005. He is currently the executive officer of the Brazilian National System for High-Performance Computing (SINAPAD), and coordinator of the Steering Committee of the Santos Dumont supercomputing facility (SDumont). He received his Ph.D. in Computer Science from the Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Brazil, in 2005. His main research areas are in computer networks, distributed systems, high-performance computing, and software architecture. He is particularly interested in the investigation of software architecture techniques that tame the tension between programming productivity, performance optimization, and parallel computing. He is the main software architect of the MHM Set of Software Libraries (MSL) for implementing multiscale numerical simulators. He is a member of the Association for Computing Machinery (ACM) and the Brazilian Computer Society (SBC).

PhD in applied mathematics from the Sorbonne Universités - Paris VI (1999), France, and pos-doctoral from the University of Colorado at Denver (2006), USA, he holds a senior researcher position at the National Laboratory for Scientific Computing - LNCC (since 2012) where he leads the Department of Computational and Mathematical Methods (since 2017). Also, he holds an INRIA International Chair from 2018 to 2022. His research lies in devising and analyzing innovative numerical methods and mathematical models for multiscale phenomena appearing in engineering and life science problems. His primary tools are partial differential equations, finite element methods, domain decomposition techniques, and numerical and asymptotic analysis. He is also interested in the implementation of numerical algorithms underlying multiscale numerical methods for the new generation of massively parallel architectures.

Researcher at the National Laboratory for Scientific Computing (LNCC), since 2013. He holds a degree in Computational Applied Mathematics (1997) from the Federal University of Rio Grande do Sul (UFRGS), Masters in Remote Sensing (2000) and Ph.D. in Applied Computing (2006) by the National Institute for Space Research (INPE). He works in the area of Computer Science, with emphasis on Scientific Computing, mainly on the following topics: high performance computing, parallel programming and massively parallel architectures.

Senior researcher at LNCC, and holds Ph.D. from PennState University. His research involves the mathematical analysis and development of computational models with applications in mechanics, economics and life science. One of his interests is the development of massively parallel numerical schemes for PDEs using finite element methods.

External consultant at Colorado University Denver (CU Denver), since February 2021, working with software development in the context of the NSF BALLISTIC project. He is a collaborator in the Laboratory of Applied Mathematics (LAMAP) at the Federal University of Juiz de Fora (UFJF) and in the IPES Research Group. He holds a master's degree in Mathematics from UFJF (2015), and a doctor's degree in Computational Modeling from the LNCC (2019). Passionated about Applied Mathematics, he has experience in Numerical Analysis and development of Finite Element Methods. He is member of the Brazilian Society for the Advancement of Science (SBPC).

Bachelor of Mathematics with an emphasis on Computational Mathematics from Federal University Fluminense (UFF - 2017) and master's degree in Computational Modeling from the LNCC (2019). Experience in monitoring pure mathematics subjects. Advanced English. Currently a doctorate student in Computational Modeling at the LNCC and linked to the technical-scientific project Parallelization and Analysis of Accuracy, Performance and Applicability in Simulators based on Finite Element Methods (PADEF).

Bachelor of Mathematics with an emphasis on Computational Mathematics from Federal University Fluminense (UFF) in 2017, where she worked in the areas of statistics and probability. Master's degree in Computational Modeling in UFF, studying Tumor Growth Models, working mainly in the areas of Mathematics and Computational Models. Also at UFF, she played the role of Tutor of Calculus I. Currently, doctorate student at the LNCC where she started working on machine learning applied to MHM-based surrogate models.

Bachelor of Scientific Computing from Universidad Nacional Mayor de San Marcos (Lima, Peru - 2013). Master's degree in Computational Modeling at LNCC (2016), studying calibration of tumor growth models. Currently, doctoral student at the LNCC where he started working on machine learning applied to resource consumption prediction of MHM simulations.

Bachelor of Computer Engeneer by Pontifical of Catholic University of Goias (PUC GO 2012). Ph.D. Student of Molecular Modeling at the National Laboratory for Scientific Computing (LNCC). Has a Master degree in Computational Modeling in Quantum Computing at LNCC. Linked to INCT-Inofar and Molecular Modeling of Biological Systems Group at LNCC, and to the technical-scientific project Parallelization and Analysis of Accuracy, Performance and Applicability in Simulators based on Finite Element Methods (PADEF).

Bachelor of Physics with an emphasis on Computacional Physics from Federal University Fluminense (UFF) in 2017. Worked with some projects related to computational physics, such as the econophysics model of Harris-Todaro and the Brunel Network model in the theoretical neuroscience field. Obtained a Master's degree in material physics at UFF (2019) studying, computationally, thermoelectric properties via Boltzmann model and Density Functional Theory. Linked to the technical-scientific project Parallelization and Analysis of Accuracy, Performance and Applicability in Simulators based on Finite Element Methods (PADEF).

Bachelor of Information Systems from Estácio de Sá University (UNESA - 2016). Has experience in High Performance Computing, having worked in research projects related with Numerical Weather Prediction Models. He is linked to the technical-scientific project Parallelization and Analysis of Accuracy, Performance and Applicability in Simulators based on Finite Element Methods (PADEF).

External collaborator of the IPES Research group, Assistant Professor at the Mathematical Engineering Department (DIM), and Researcher at the Center for Research in Mathematical Engineering (CI²MA), both based in the University of Concepción (UDEC), Chile. He received his D.Sc. in Computational Modelling from the National Laboratory for Scientific Computing (LNCC) in 2013, then obtained a post-doctoral position at the same institute and later at the National Institute for Research in Computer Science and Automation (INRIA). From 2014 to 2018, he worked at the Institute of Mathematics (IMA) of the Pontifical Catholic University of Valparaiso (PUCV), Chile. His research is focused on development, mathematical analysis, and efficient computational implementation of numerical methods. He is particularly interested in proposing new numerical schemes to solve multiscale problems related to fluid flow in porous media and wave propagation models.

Currently an Associate Professor at Metropolitan State University of Denver, Chris completed his Ph.D. in Applied Mathematics at the University of Colorado Denver. He spent two years working as a post-doc at LNCC working on finite element methods suitable for massively parallel architectures. His interests include partial differential equations, multiscale finite element methods, and domain decomposition methods.

Henrique Versieux (UFMG, Brazil)

Honório Fernando (UFF, Brazil)

Sonia Gomes, Philippe Devloo (UNICAMP, Brazil)

Rodolfo Araya (Universidad de Concepción, Chile)

Stephane Lanteri, Claire Scheid, Théophile Chaumont (Inria, France)

Gabriel Barrenechea (University of Straitclyde, UK)

Fabrice Jaillet (IUT-Lyon, France)

Jean-François Méhaut (LIG-UGA, France)

Marcus Sarkis (WPI, EUA)

Contributing to the advancement of science and technology, and to transferring knowledge to industry.

This project aims at refactoring simulation software from Petrobras (the Brazilian Oil Company) in order to improve quality attributes related to its functionality and interoperability with other systems, as well as its performance in parallel architectures. It also proposes the integration of the family of MHM methods within this software.

This project aims at developing, analyzing and performing parallel implementations of innovative multiscale finite element methods for wave propagation models in grating media motivated by its use in the simulation of photovoltaic solar cells. This two-year international collaboration involves universities and research laboratories from Brazil, Chile, and France.

This project aimed to apply the new exascale HPC techniques to energy industry simulations, customizing them, and going beyond the state-of-the-art in the required HPC exascale simulations for different energy sources: wind energy production and design, efficient combustion systems for biomass-derived fuels (biogas), and exploration geophysics for hydrocarbon reservoirs. FUNDING FROM THE EUROPEAN UNION'S HORIZON 2020 PROGRAMME (2014-2020) AND FROM BRAZILIAN MINISTRY OF SCIENCE,TECHNOLOGY AND INNOVATION THROUGH REDE NACIONAL DE PESQUISA (RNP) UNDER THE HPC4E PROJECT (WWW.HPC4E.EU), GRANT AGREEMENT N° 689772.

The main scientific goals of this collaboration were: (i) to design and analyze new MHM methods for the system of time-domain Maxwell equations coupled to models of physical dispersion, in view of their application to light interaction with nanometer-scale structures; (ii) to design and analyze new MHM methods for the system of time-domain elastodynamic equations for modeling elastic wave propagation in anisotropic media; (iii) to devise appropriate discrete versions of the proposed MHM methods using DG (Discontinuous Galerkin) formulations for the discretization of the local solvers, and to study the mathematical properties (stability, convergence) of the combined MHM-DGTD strategies.

The HOSCAR project is a CNPq - INRIA collaborative project between Brazilian and French researchers, in the field of computational sciences. The project was also sponsored by the French Embassy in Brazil. The general objective of the project was to setup a multidisciplinary Brazil-France collaborative effort for taking full benefits of future high-performance massively parallel architectures. The targets were the very large-scale datasets and numerical simulations relevant to a selected set of applications in natural sciences: (i) resource prospection, (ii) reservoir simulation, (iii) ecological modeling, (iv) astronomy data management, and (v) simulation data management. The project involved computer scientists and numerical mathematicians divided in 3 fundamental research groups: (i) numerical schemes for PDE models (Group 1), (ii) scientific data management (Group 2), and (iii) high-performance software systems (Group 3).

High-impact research and developement results, and associated training of human resources with a strong multidisciplinary character.

- Devloo, P. R. B.; Farias, A. M.; Gomes, S. M.; Pereira, W.; Santos, J. B.; Valentin, F. New H(div)-conforming multiscale hybrid-mixed methods for the elasticity problem on polygonal meshes. To appear in ESAIM: Math. Model. Num. Anal., 2021.
- Araya, R.; Cárcamo, C.; Poza, A. H.; Valentin, F. An adaptive multiscale hybrid-mixed method for the Oseen equations. Adv. Comput. Math. 47(15), 2021.
- Araya, R.; Rebolledo, R.; Valentin, F. On a multiscale a posteriori error estimator for the stokes and Brinkman equations. IMA J. Numer. Anal. 41(1):344–380, 2021.
- Gomes, A.T.A.; Molion, E.; Souto, R.P.; Méhaut, J.F. Memory allocation anomalies in high-performance computing applications: A study with numerical simulations. CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE. p.e6094 - , 2020.
- Barrenechea, G.; Jaillet, F.; Paredes, D.; Valentin, F. The multiscale hybrid mixed method in general polygonal meshes. Numer. Math., 145:197–237, 2020.
- Chaumont-Frelet, T.; Valentin, F. A multiscale hybrid-mixed method for the helmholtz equation in heterogeneous domains. SIAM J. Numer. Anal., 58(2):1029–1067, 2020.
- Penna, P.; Gomes, A.T.A.; Castro, M.; Plentz, P.; Freitas, H.; Broquedis, F.; Méhaut, J.F. A comprehensive performance evaluation of the BinLPT workload-aware loop scheduler. CONCURRENCY AND COMPUTATION-PRACTICE & EXPERIENCE. p.e5170 - , 2019.
- Lanteri, S.; Paredes, D.; Scheid, C.; Valentin, F. The multiscale hybrid-mixed method for the Maxwell equations in heterogeneous media. SIAM Multiscale Model. Simul., 16(4):1648–1683, 2018.
- Paredes, D.; Valentin, F.; Versieux, H. M. On the robustness of multiscale hybrid-mixed methods. Math. Comp., 86(304):525–548, 2017.
- Harder, C.; Madureira, A.; Valentin, F. A hybrid-mixed method for elasticity. ESAIM: Math. Model. Num. Anal., 50(2):311–336, 2016.
- Harder C.; Valentin, F. Foundations of the MHM method. In G. R. Barrenechea, F. Brezzi, A. Can- giani, and E. H. Georgoulis, editors, Building Bridges: Connections and Challenges in Modern Approaches to Numerical Partial Differential Equations, Lecture Notes in Computational Science and Engineering. Springer, 2016.
- Harder, C.; Paredes, D.; Valentin, F. On a multiscale hybrid-mixed method for advective-reactive dominated problems with heterogenous coefficients. SIAM Multiscale Model. and Simul., 13(2):491–518, 2015.
- Harder, C.; Paredes, D.; Valentin, F. A family of multiscale hybrid-mixed finite element methods for the Darcy equation with rough coefficients. J. Comput. Phys., 245:107–130, 2013.
- Araya, R.; Harder, C.; Paredes, D.; Valentin, F. Multiscale hybrid-mixed method. SIAM J. Numer. Anal., 51(6):3505–3531, 2013.

- MADUREIRA, A.; SARKIS, M. Robust Model Reduction Discretizations Based on Adaptive BDDC Techniques. In: Domain Decomposition Methods in Science and Engineering XXV. Lecture Notes in Computational Science and Engineering 158. pp. 41–52, 2020.
- FABIAN, J. H. L. ; GOMES, A. T. A. ; OGASAWARA, E. Estimating the execution time of the coupled stage in multiscale numerical simulations. In: Latin America High Performance Computing Conference (CARLA), 2020, Cuenca, EQ. Proceedings of the 7th Latin America High Performance Computing Conference (CARLA2020), 2020.
- FABIAN, J. H. L. ; GOMES, A. T. A. ; OGASAWARA, E. Estimating the execution time of fully-online multiscale numerical simulations. In: Simpósio em Sistemas Computacionais de Alto Desempenho (WSCAD), 2020, Santo André, SP. Anais do XXI Simpósio em Sistemas Computacionais de Alto Desempenho (WSCAD2020). Porto Alegre, RS: SBC, 2020.
- Gomes, A. T. A.; Molion, E.; Méhaut, J.F.; Souto, R.P. Identification and Characterization of Memory Allocation Anomalies in High-Performance Computing Applications. In: Simpósio Brasileiro de Sistemas Computacionais de Alto Desempenho (WSCAD), 2019, Campo Grande, MS. Anais do XX Simpósio Brasileiro de Sistemas Computacionais de Alto Desempenho (WSCAD 2019). Porto Alegre, RS: SBC, 2019. v. 1. p. 1-12.
- Gomes, A.T.A.; Zillmer, F. Avaliação de desempenho de um simulador numérico distribuı́do e tolerante a falhas baseado no modelo de atores. In: Workshop em Clouds e Aplicações (WCGA), 2018, Campos do Jordão, SP. Anais do XVI Workshop em Clouds e Aplicações (WCGA 2018). Porto Alegre, RS: SBC, 2018.
- Gomes, A.T.A.; Zillmer, F. Experimentos no uso do modelo de atores para simulações numéricas distribuídas baseadas em elementos finitos. In: Workshop de Computação em Clouds e Aplicações (WCGA), 2017, Belém-PA. Anais do XV Workshop de Computação em Clouds e Aplicações (WCGA 2017). Porto Alegre-RS: SBC, 2017. p. 144-157.
- Gomes, A.T.A.; Paredes, D.; Pereira, W.S.; Souto, R.P.; Valentin, F. Performance analysis of the MHM simulator in a petascale machine. In: XXXVIII IberianLatin American Congress on Computational Methods in Engineering, 2017, Florianopolis, 2017.
- Gomes, A.T.A.; Paredes, D.; Pereira, W.S.; Souto, R.P.; Valentin, F. A Multiscale Hybrid-Mixed Method for the Elastodynamic Model with Rough Coefficients. In: XXXVIII IberianLatin American Congress on Computational Methods in Engineering, 2017, Florianopolis, 2017.
- Paszynski, M.; Gomes, A.T.A. A wrapper around parallel MUMPS solver to reduce its memory usage and execution time for finite element method computations. PROCEDIA COMPUTER SCIENCE, v. 108, p. 838-847, 2017.
- Gomes, A.T.A.; Paredes, D.; Valentin, F. Supporting the Perpetuation and Reproducibility of Numerical Method Publications. Procedia Computer Science. , v.4, p.688 - 696, 2011.

- Weslley Pereira. Multiscale Hybrid-Mixed Methods for Heterogeneous Elastic Models. 2019.
- Franklin Zillmer. A Fault-Tolerant Framework Based on the Actor Model for the Numerical Solution of Differential Equations. 2019.
- Diego Fabian Paredes Concha. New Multiscale Finite Element Methods: Theory and Applications. 2013.

- Larissa Martins. A Petrov-Galerkin Multiscale Hybrid-Mixed method for the Darcy Equation on Polytope. 2019.

- Gomes, A.T.A.; Pereira, W.S.; Valentin, F. The MHM Method for Elasticity on Polytopal Meshes. 2020.
- Gomes, A.T.A.; Pereira, W.S.; Valentin, F.; Paredes, D. On the Implementation of a Scalable Simulator for Multiscale Hybrid-Mixed Methods. 2017.

Training of human resources with a strong multidisciplinary character.

- Numerical Analysis of Finite Elements.
- Architecture, Design and Implementation of Software-Intensive Systems.
- Data Structures.
- Algorithms.

- MC-A: Multiscale Methods: Theory and Practice (LNCC Summer School - March/2020).

- Antônio Tadeu Gomes, Developing scientific software with qualityand productivity: a 15-year endeavor, LNCC seminars, 06/July/2020.
- Frédéric Valentin, The origin of the Multiscale Hybrid-Mixed Method: an overview, LNCC seminars, 23/November/2020.

C++ library for implementing key concepts present in most FEM-based simulators.

C++ library for implementing key concepts present in Continuous Galerkin-based simulators.

C++ library for implementing simulators based on the the family of MHM methods.

"Knowledge can only be volunteered it cannot be conscripted" (David Snowden)