Research projects funded by public agencies
Finite Element Data Driven Computational approaches for Complex Materials and Microfluidics
Funded by Fapesp - (Proc. 2025/00975-9)
2026-2028 (3 years)
The primary motivation of this project is investigating a novel Data Driven approach for solving problems involving elliptic PDEs, whether the scalar Poisson problem or the elasticity problem, that incorporates experimental or synthetic constitutive data without relying on a smooth constitutive relation-between fluxes and gradients in the former case, or to stresses and deformations in the latter. This approach is known as the Data-Driven Computational Mechanics paradigm, which can be seen as a form of unsupervised machine learning applied to continuum mechanics. The ultimate goal of this work is to formulate a discrete-continuous optimization problem that seeks, under certain constraints, the fluxes-gradients (or stresses-deformations) that minimize the distance between the dataset and the subspace of corresponding compatible fields in equilibrium. Given the challenging nature of this optimization problem, we begin by analyzing a finite element formulation in which the data set is prescribed over the domain. Next, we develop strategies to initialize the data distribution, enabling the solution of a class of optimization subproblems. We then propose iterative strategies to approximate the global optimization problem. Additionally, we discuss other data-driven approaches of interest, along with potential extensions to parabolic problems and Stokes flows. These include applications in microfluidics, such as fluid-structure finite element formulations for simulating the behavior of microswimmers.
Development of algebraic multiscale preconditioners for the simulation of oil reservoirs
Collaborative Research project with Petrobras
2024-2027 (3 years)
Neste projeto de pesquisa iremos desenvolver um método de precondicionamento baseado na família de métodos multiescala mistos "Multiscale Robin Coupled Method" que foi desenvolvida nos últimos anos pelo grupo de pesquisa proponente com apoio da Petrobras. Para tal fim, primeiramente iremos estudar as propriedades do método e a sua eficácia como precondicionador no caso de discretizações conhecidas, para posteriormente motivar a sua extensão ao caso mais geral quando a informação e detalhes da discretização subjacente que dá origem ao sistema linear é limitada ou não encontra-se disponível.
Multiscale methods for the Numerical modeling of Oil Reservoirs
Collaborative Research project with Petrobras
2017-2022 (5 years)
The focus of this project is the development of multiscale methods for elliptic and parabolic problems aimed for the parallel numerical simulation of multiphase flows arising in hydrocarbon reservoirs of current interest to the Oil & Gas industry. State-of-the-art commercial software have shown to be inadequate to simulate the large (and deep) Brazilian reservoirs in the pre-salt and therefore new simulation tools must be developed, capable of dealing with large heterogeneities and realistic rock properties so as to accurately and efficiently solve the governing equations by means of HPC, taking advantage of Multicore and GPU architectures. This is a joint project between ICMC/USP, IMECC/UNICAMP and University of Texas at Dallas - EUA.
Modeling of complex interfaces in microfluidics with applications to emulsions
Funded by CNPq - (Proc. 447607/2014-6)
2014-2018 (3 years)
The aim is the development and improvement of finite element formulations when a level set technique is used to parametrize the interface separating the fluids in multiphase microflows dominated by surface tension, thermocapillarity, interfacial viscous effects and bending forces in lipidic membranes, with applications to the study of emulsions. Also, Lagrangian formulations which are currently under study will be considered to complement the survey and for comparison purposes.
Computational Fluid Dynamics of Complex Interfaces: Applications to the study of Emulsions and the Micromechanics of Biological Membranes
Funded by Fapesp - (Proc. 14/19249-1)
2015-2016 (2 years)
The main research topic considered here is that of the finite element modeling of complex phenomena on moving microfluidic interfaces with both, Eulerian and Lagrangian methods, based on variational formulations. Among the physical phenomena of interest in this project, we consider the capillarity and surface tension effects, interfacial viscous effects, surfactant transport, elastic forces on cellular membranes and surface inextensibility restrictions. The aim is at developing robust numerical schemes so as to complement experimental studies meeting the expectations of the existing technologies.
