My current research focuses on two main topics in the field of computational mechanics: to develop error estimators for the uncertainty quantification of numerical solutions and to develop novel numerical algorithms for the simulation of complex solid dynamics.
The main interest regarding the error estimators is to define algorithms able to quantify the error of a simulation that could be applied in a general framework, both from the numerical point of view (using different numerical methods such as the Finite Element or Finite Volume methods) and the physical point of view (solving multiphysics problems).
With respect to the simulation of complex solid dynamics, I am interested in the development of numerical algorithms for the simulation of viscoelastic or viscoplastic solids subjected to large deformations.
When trying to quantify the uncertainty of a given simulation, one has to identify the sources of such uncertainty. These sources can be classified into input uncertainty, numerical approximation uncertainty, or modelling uncertainty. In the Computational Modelling Lab at Duke University, we focus on the quantification of numerical approximation uncertainty (also combined with input uncertainty) using Variational Multiscale error estimators.
Our main goal in this topic is the development of a family of Variational Multiscale error estimators for the Uncertainty Quantification of Mesh Discretization Error under uncertain input parameters. We are developing error estimators that could be used in most numerical approximation frameworks and that can be applied to several physical problems.
Currently, we are applying such algorithms for the uncertainty quantification of turbulent reacting flows.
The objective of my PhD thesis was to develop efficient Finite Element (FE) solvers for turbulent incompressible flow problems. In particular, I worked with stabilized FE methods and their application to the simulation of turbulent flows. In addition, I also worked on efficient time integration techniques through implicit-explicit Runge-Kutta schemes. All my research was done in FEMPAR, a scientific software for the simulation of problems governed by partial differential equations (PDEs), which was originally designed to efficiently exploit distributed-memory supercomputers and easily handle multiphysics problems, one of the main objectives of the CIMNE/LSSC group.
The study of the Variational MultiScale (VMS) methods as a Large Eddy Simulation (LES) model for turbulent incompressible flows is one of the CIMNE/LSSC research topics. We are interested on the performance of VMS methods when turbulent incompressible flows are simulated without adding any kind of physical-based model. We consider VMS models obtained by different subgrid scale approximations wich include either static or dynamic subscales, linear or nonlinear multiscale splitting and different choices of the subscale space.
Sometimes, when simulating transient problems one needs to use very small time steps in order to face the small time scales inherent to the problem, e.g. turbulent flows. The solution of these kind of problems usually involve a huge amount of time steps, which increase the computational cost of the simulation. In order to deal with this issue, we are developing efficient and accurate time integration techniques throuhg Implicit-Explicit Runge-Kutta schemes.
Turbulent flows are characterized by having a wide range of temporal and spatial scales. Accurate solutions require the resolution of the smallest scales, which increases the computational cost. The resulting system of equations can reach several millions of unknowns, so in order to solve such problems we must use Supercomputers. The solver scalability is mandatory when using distributed memory machines, where the problems are being solved in parallel with a large amount of processors. In our group we use the so called Balanced Domain Decomposition with Constrains (BDDC), which have been proven to have excelent scalability problems for laplacian type problems. Additionally, a block preconditioning technique is used to better condition the system.
See my publications for a deeper description of these topics.