Prof Santiago Badia

Research Overview

Prof. Badia works on the numerical approximation of partial differential equations (PDEs). He develops and analyses finite element methods and also works on their application in modelling fluid and solid mechanics, electromagnetics, and multiphysics problems. He works on unfitted techniques that do not require body-fitted mesh generation, adaptive finite element methods for these techniques, and interface problems in space-time. He also works on efficient (non)linear solvers for the resulting systems of equations, e.g., domain decomposition methods, and is particularly focused on the design and implementation of highly scalable algorithms.

As a by-product of his research, Prof Badia leads some high-performance scientific projects, like FEMPAR, which attained perfect weak scalability up to 458,672 cores in JUQUEEN (Germany) solving up to 60 billion unknowns, and Gridap, that he initiated in 2019 and heavily relies on functional programming and multiple dispatching in Julia, with the aim to create easy-to-use but very efficient and scalable PDE solvers. His algorithms and codes have solved complex application problems, e.g., in metal additive manufacturing, superconductor devices, breeding blankets in fusion reactors, or nuclear waste repositories.

Selected Publications

[1] Badia, Santiago ; Verdugo, Francesc ; Martín, Alberto F. "The aggregated unfitted finite element method for elliptic problems". In: Computer Methods in Applied Mechanics and Engineering. 2018 ; Vol. 336. pp. 533-553. https://doi.org/10.1016/j.cma.2018.03.022

[2] Badia, Santiago ; Bonilla, Jesús. "Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization". In: Computer Methods in Applied Mechanics and Engineering. 2017 ; Vol. 313. pp. 133-158. https://doi.org/10.1016/j.cma.2016.09.035

[3] Badia, Santiago ; Martín, Alberto F. ; Principe, Javier. "Multilevel balancing domain decomposition at extreme scales". In: SIAM Journal on Scientific Computing. 2016 ; Vol. 38, No. 1. pp. C22-C52. https://doi.org/10.1137/15M1013511

[4] Badia, Santiago ; Codina, Ramon. "Unified Stabilized Finite Element Formulations for the Stokes and the Darcy Problems". In: SIAM Journal on Numerical Analysis. 2009 ; Vol. 47, No. 3. pp. 1971-2000. https://doi.org/10.1137/08072632X

[5] Badia, Santiago ; Quaini, Annalisa ; Quarteroni, Alfio. "Splitting methods based on algebraic factorization for fluid-structure interaction". In: SIAM Journal on Scientific Computing. 2008 ; Vol. 30, No. 4. pp. 1778-1805. https://doi.org/10.1137/070680497