Most of our developments on 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 numerical simulators to run at scale, exploring massively parallel architectures and developing code with bleeding-edge technologies.

Machine learning

We explore machine learning techniques to predict resource consumption and to act as surrogates of numerical simulations.


A multidisciplinary group with mathematicians, computer scientists and engineers.


Antônio Tadeu Gomes

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 is also the current deputy coordinator of the LNCC's Graduate Program in Computational Modeling (PPG-LNCC). He received his Ph.D. in Computer Science from the Pontifical Catholic University of Rio de Janeiro (PUC-Rio), Brazil, in 2005. His main interests are in the broad area of systems modeling, encompassing networked systems, distributed systems, numerical simulation systems, high-performance computing systems, and machine learning systems. He is particularly interested in the investigation of software architecture techniques that tame the tension between programming productivity, performance optimization, and parallel computing in the development of scientific software. 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). He was recipient of the productivity research award PQ-2 from the Brazilian Research Council (CNPq) from 2010 to 2018.

Frédéric Valentin

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 led the Department of Computational and Mathematical Methods (2017-2021). Also, he held an INRIA International Chair from 2018 to 2023. 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 with machine learning techniques.

Roberto Souto

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.

Alexandre Madureira

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.

Juan Humberto Leonardo Fabian

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. Doctor degree in Computational Modeling at LNCC (2022), working on machine learning applied to resource consumption prediction of MHM simulations.

Julio César David da Fonseca

He has a degree in Mechanical Engineering from the Federal University of Uberlândia and a master's and doctorate in Physics from USP. He has professional experience in the areas of Physics, Engineering and Computing. His current research activities are in the field of Scientific Machine Learning.

Lucas Rocha

Bachelor of Mathematics from Federal University of Ouro Preto (UFOP - 2016), master's degree in Mathematics from Federal University of Minas Gerais (UFMG - 2018), doctor's degree in Mathematics at UFMG (2023). Specially interested in the MHM method for parabolic type PDEs.

Larissa Martins

Bachelor of Mathematics with an emphasis on Computational Mathematics from Federal University Fluminense (UFF - 2017) and master's degree in Computational Modeling from LNCC (2019). Experience in monitoring pure mathematics subjects. Advanced English. From 2018 to 2020 worked on a technical-scientific project Parallelization and Analysis of Accuracy, Performance and Applicability in Simulators based on Finite Element Methods (PADEF). Winner of SBMAC Odelar Leite Linhares award (2021). Currently a doctorate student in Computational Modeling at LNCC.

Larissa Miguez

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.

Haron Calegari

Bachelor in Production Engineering from Multivix-ES (2014), with experience in Industry and Teaching in higher education. Master in Computational Modeling from LNCC (2017) with emphasis on Complex Networks and Mobility Analysis. Currently, doctorate student at LNCC with emphasis on the use of Physical Principles applied in Machine Learning Models, and also Substitute Professor at the Federal Institute of Espírito Santo (IFES).

Franklin da Conceição de Barros

PhD candidate in Computational Modeling at the National Scientific Computing Laboratory - LNCC, since 2023. Master in Computational Modeling at the National Scientific Computing Laboratory / LNCC. Bachelor's degree in Mathematics with an emphasis on Computational Mathematics from the Institute of Exact Sciences of the Universidade Federal Fluminense / ICEX-UFF.

Juan Felipe Pacazuca Santiago

MSc candidate in Computational Modeling at the National Scientific Computing Laboratory - LNCC, since 2024.

External Collaborators

Weslley da Silva Pereira (University of Colorado Denver)

External collaborator of the IPES Research group, and Research Associate at the University of Colorado Denver. Master in Mathematics (2015) from Universidade Federal de Juiz de Fora, and D.Sc. in Computational Modeling (2019) from Laboratório Nacional de Computação Científica (LNCC). Passionate about Applied Mathematics and Scientific Software Development, with extensive experience in Numerical Analysis and in developing numerical software. Maintainer of the Netlib BLAS, LAPACK and ScaLAPACK libraries; designer and developer of <T>LAPACK, a new numerical linear algebra library based on modern C++. His research is on (1) MHM methods for linear elasticity and elastodynamics; (2) improvements in the MHM methods; and (3) numerical linear algebra software and standards.

Diego Paredes (Universidad de Concepción)

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.

Christopher Harder (Metropolitan State University of Denver)

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.

Other collaborators

CEFET-RJ, Brazil: Eduardo Ogasawara
Inria Bordeaux, France: Francieli Zanon-Boito, Laércio Pilla
Inria Saclay, France: Aline Carneiro Viana
Inria Sophia-Antipolis, France: Stephane Lanteri, Claire Scheid, Théophile Chaumont
IUT-Lyon, France: Fabrice Jaillet
LIG-UGA, France: Jean-François Méhaut
UdeC, Chile: Rodolfo Araya
UFMG, Brazil: Henrique Versieux
UFF, Brazil: Honório Fernando
UNICAMP, Brazil: Sonia Gomes, Philippe Devloo
UStrathclyde, UK: Gabriel Barrenechea
WPI, US: Marcus Sarkis


Aaron Bruno Leão (D.Sc., LNCC, 2022)
João Victor Caccavo Wanderley (B.Sc., UFRJ, --)
Lucas Prett (M.Sc. UFF, 2019)
Mateus Silva de Melo (B.Sc., UNESA, 2016)


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

INVMULTIFIS: Development of multi-physics data inversion software with optimization via artificial intelligence (2022-2025)

The project proposes the development of an innovative inversion technology for the characterization and monitoring of deep water reservoirs for Petrobras (the Brazilian Oil Company) using CSEM (Controlled-Source Electromagnetic Methods), a robust risk reduction tool in the drilling of oil basins, using multiphysics data in the 3D domain. One of the main objectives of this project is to develop, optimize and parallelize CSEM codes, aiming at improving their performance. The construction of inversion algorithms will be also performed, such as Deep Neural Networks (DNNs) trained to transform CSEM data into models.

EOLIS: Efficient Off-LIne numerical Strategies formulti-query problems (2021-2023)

Project involving Inria, represented by Théophile Chaumont from the Atlantis Project-Team, LNCC with the PI Frederic Valentin and UdeC (Universidad de Concepcion, Chile) featuring the researcher Manuel Solano. This project targets multi-query problems that involve the solution of a parametrized boundary value problem (BVP) for a set of parameters. Notable examples include parameter identification, optimal design and uncertainty quantification, each having concrete applications.

PADEF: Parallelism and Analysis of Accuracy, Performance and Applicability in Simulators based on Finite Element Methods (2018-2020)

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.

PHOTOM: Photovoltaic Solar Devices in Multiscale Computational Simulations (2018-2020)

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.

HPC4e: High-Performance Computing for Energy (2016-2019)

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 (, GRANT AGREEMENT N° 689772.

HOMAR: High-performance Multiscale Algorithms for wave pRopagation problems (2015-2018)

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.

HOSCAR: High performance cOmputing and SCientific dAta management dRiven by highly demanding applications (2013-2015)

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.



Previous years

Conference papers


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PhD Theses

Master Theses



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Training of human resources with a strong multidisciplinary character.

Regular courses



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Invited Talks and Keynotes


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Our research is deeply connected with the development of high-quality software. All of our implementations are made available on GitLab, under request.

MSL Core

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.

MSL Python

Simple Python wrapper over the FEniCS platform for implementing simulators based on the the family of MHM methods.


Simple implementation of the MHM method on the FreeFEM++ platform.


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