Dr Alberto F. Martin

Research Overview

My research is framed within the broad field of Scientific Computing (SC), with a particular focus on the numerical solution of Partial Differential Equations (PDEs) via Finite Element (FE) methods.

My contributions so far to this field span:

1. The design and mathematical analysis of new, application-tailored FE discretizations and solution methods, or innovative algorithmic adaptations of state-of-the-art ones towards different goals.
2. The efficient parallel implementation of these in open source HPC software packages provided to the general SC community.
3. The application these advances for the computer simulation of large-scale, real-world challenges in the sciences and engineering, in collaboration with application-problem specialists.

I am co-author of FEMPAR, a software package which provides state-of-the-art numerical discretizations for PDEs and highly scalable numerical solvers. It has attained perfect weak scalability up to 458,672 cores in JUQUEEN (Germany) solving up to 60 billion  unknowns.

I am also contributor to Gridap.jl, and co-author of GridapDistributed.jl, its parallel version, which provide a new FE framework written in Julia for the numerical simulation of models governed by PDEs, from desktop/laptops to supercomputers. Gridap.jl exploits the modern features of the Julia language in order to strike a remarkable balance among performance and generality via appropriate mathematically-driven software abstractions.

Selected Publications

[1] Neiva, Eric ; Badia, Santiago ; Martín, Alberto F. ; Chiumenti, Michele. "A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing". In: International Journal for Numerical Methods in Engineering. 2019 ; Vol. 119, No. 11. pp. 1098-1125. https://doi.org/10.1002/nme.6085

[2] Badia, Santiago ; Martin, Alberto F. ; Verdugo, Francesc. "Mixed aggregated finite element methods for the unfitted discretization of the stokes problem". In: SIAM Journal on Scientific Computing. 2018 ; Vol. 40, No. 6. pp. B1541-B1576. https://doi.org/10.1137/18M1185624

[3] Badia, Santiago ; Martín, Alberto F. ; Principe, Javier. "FEMPAR : An Object-Oriented Parallel Finite Element Framework". In: Archives of Computational Methods in Engineering. 2018 ; Vol. 25, No. 2. pp. 195-271. https://doi.org/10.1007/s11831-017-9244-1

[4] 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

[5] Badia, Santiago ; Martín, Alberto F. ; Planas, Ramon. "Block recursive LU preconditioners for the thermally coupled incompressible inductionless MHD problem". In: Journal of Computational Physics. 2014 ; Vol. 274. pp. 562-591. https://doi.org/10.1016/j.jcp.2014.06.028