IPES Research Group @ LNCC
Innovative Parallel finite Element Solvers

Members of the IPES Research Group participated in the 9th Brazil InterPore Chapter Meeting, held from August 10 to 13, 2026, at the Brazilian Center for Physics Research (CBPF) in Rio de Janeiro.
The conference brought together researchers from different scientific fields to discuss recent advances in porous media research, including mathematical and computational modeling, energy applications, and carbon capture and storage.
During the event, Leonardo Mello presented the work entitled “DeepONet-Based Stress Path Prediction Using a Multiscale Finite Element Method.”
Diego Volpatto presented the work entitled “A Locally Conservative Equal-Order Stabilized Mixed Finite Element Method for the Brinkman Problem in Highly Heterogeneous Porous Media.”
Juan Pacazuca presented the work entitled “Stabilized Multiscale Hybrid-Mixed Methods for Reaction-Advection-Dominated Models.”
Guilherme Osanski presented the work entitled “Neural Galerkin Operator.”
Their participation provided an excellent opportunity to share the group’s latest research, exchange ideas with the porous media community, and strengthen scientific collaborations.

Last month, researchers associated with our group participated in the 17th World Congress on Computational Mechanics (WCCM) and the 10th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), held in Munich, Germany.
WCCM-ECCOMAS 2026 brought together researchers and professionals from academia, government, and industry worldwide. As one of the largest international events in the field, the congress provided a forum for discussing recent advances in computational mechanics and computational methods in applied sciences and engineering.
During the event, Frédéric Valentin presented the work entitled “H(div, Ω)-Conforming MHM Methods for Elasticity with Weak and Strong Symmetry,” co-authored by Gabriel R. Barrenechea, Josué Barroso, Larissa Martins, Weslley Pereira, and Frédéric Valentin. The study addresses H(div, Ω)-conforming formulations for the Multiscale Hybrid-Mixed (MHM) method, considering stress tensor reconstructions with both weak and strong symmetry.
Ramiro Rebolledo, from Universidad de Concepción, presented the work entitled “An H(div, Ω)-Conforming Post-Processing of the Cauchy Stress Tensor in Multiscale Hybrid-Mixed Approximations of the Stokes-Brinkman Problem.” The study was developed in collaboration with Larissa Martins, Juan F. Pacazuca, Weslley Pereira, and Frédéric Valentin from the National Laboratory for Scientific Computing (LNCC). It proposes an H(div, Ω)-conforming post-processing technique for reconstructing the Cauchy stress tensor in MHM approximations of the Stokes–Brinkman problem.
Participation in the congress provided an important opportunity to disseminate the group's research results, exchange knowledge with international experts, and strengthen scientific collaborations in numerical methods and computational modeling.

The poster “A Stabilized Multiscale Hybrid-Mixed Method for Reaction-Dominated Models” was presented by PhD student Juan Pacazuca at the Inria-Brasil (hybrid) Workshop on HPC, held at LNCC, Petrópolis, Brazil, on April 15–16, 2026. The event brought together French and Brazilian researchers to foster collaboration in high-performance computing, artificial intelligence, scientific computing, and data science. The work highlights ongoing research on advanced numerical methods for challenging multiscale problems.

During the workshop “Taming the PDEs: Tailored Methods, Multiscale Approaches, and Real-World Application”, held on March 9–13, 2026 as part of the Junior Trimester Program at the Hausdorff Research Institute for Mathematics in Bonn, Larissa Martins presented the talk “H(div, Ω)-Conforming Multiscale Hybrid-Mixed Methods for Elasticity with Weak and Strong Symmetry.” The presentation introduced new elementwise reconstruction strategies within the Multiscale Hybrid-Mixed (MHM) framework for linear elasticity that produce H(div; Ω)-conforming stress tensors while enforcing either weak or strong symmetry. The proposed approach restores local conservation and improves the quality of stress approximations obtained from continuous Galerkin local solvers. Theoretical analysis proves optimal convergence of the reconstructed stress in the H(div; Ω)-norm, while numerical experiments demonstrate the robustness and effectiveness of the method in multilayer elasticity problems relevant to real-world applications such as faulted subsurface reservoirs.
🎥 Presentation recording: https://youtu.be/noJqq1eotX4

At the XLVI Ibero-Latin American Congress on Computational Methods in Engineering (CILAMCE 2025), Juan Felipe Pacazuca Santiago presented the work “A Multiscale Hybrid-Mixed Method with Local Stabilization.” The talk introduced the MHM-UNUSUAL method, a new approach that combines the Multiscale Hybrid-Mixed (MHM) framework with the Unusual Stabilized Finite Element Method (UNUSUAL). The proposed strategy improves the approximation of multiscale basis functions in challenging scenarios, such as reaction-dominated and highly heterogeneous problems. By incorporating stabilization terms in the local problems, the method mitigates spurious oscillations and allows the use of coarser local meshes, reducing computational cost while maintaining accuracy. Numerical experiments on boundary layer problems and the SPE-10 benchmark demonstrate the potential of the approach for efficient and reliable multiscale simulations.

Larissa Martins and Diego Paredes presented recent advances on Multiscale Hybrid-Mixed (MHM) methods at the workshop Reduced-Order Modeling for Complex Engineering Problems: From Analysis to Practical Implementation, held from January 29 to February 7, 2025, at the Institute for Mathematical and Statistical Innovation (IMSI), in Chicago, USA. The event focused on numerical simulation of engineering problems in complex and heterogeneous media, highlighting multiscale methods, reduced-order modeling, and practical implementation in industrial contexts. Diego Paredes (Universidad de Concepción) delivered the talk "Multiscale Hybrid Methods: Theoretical Foundations and Computational Analysis". In a lightning talk, Larissa Martins presented "An H(div, Ω)-conforming flux reconstruction for the MHM method".

Members of the IPES Research Group participated in CNMAC 2024, held on September 19–20 in Porto de Galinhas, Brazil, presenting recent developments in multiscale numerical methods and scientific machine learning. During the mini-symposium “New Challenges in the Numerical Simulation of Partial Differential Equations” (MS08), Frédéric Valentin presented recent advances in the Multiscale Hybrid-Mixed (MHM) method. The talk focused on a local post-processing strategy for recovering optimal convergence of the dual variable in H(div, Ω), as well as a fully computable a posteriori error estimator based on equilibrated flux techniques.
Larissa Miguez presented the talk “Interplay of Physics-Informed Neural Networks and Multiscale Numerical Methods,” which explored the integration of Physics-Informed Neural Networks (PINNs) with the MHM framework. In the proposed approach, PINN models are used to approximate the multiscale basis functions arising from the independent local problems of the method. Numerical experiments for the Poisson problem demonstrated the potential of this strategy as a surrogate approach for efficiently capturing multiscale features in partial differential equation simulations.
The participation of the group in CNMAC 2024 provided an important opportunity to disseminate complementary research results and discuss the interplay between multiscale finite element methods, post-processing techniques, error estimation, and machine learning.