Santiago Badia is Professor of Computational Mathematics at Monash since June 2019. He obtained his PhD at Universitat Politècnica de Catalunya (UPC) in 2006. Previously, he worked at the Applied Mathematics departments at Politecnico di Milano (Italy) in 2006 and Sandia National Labs (New Mexico, USA) in 2007-08. He joined UPC in 2009, where he was appointed Professor of Computational Science and Engineering in 2017. He is adjoint researcher at CIMNE (Barcelona), where he leads the Large Scale Scientific Computing Department.
He works on the numerical approximation of partial differential equations (PDEs), e.g., using finite element methods, for modelling fluid and solid mechanics, electromagnetics, and multiphysics problems. He is particularly interested in large scale scientific computing and numerical linear algebra.
As a by-product of his research, Prof Badia leads some high-performance scientific projects, like FEMPAR. FEMPAR provides state-of-the-art numerical discretizations of PDEs and highly scalable numerical linear algebra solvers. FEMPAR has been used to model metal additive manufacturing, superconductor devices, breeding blankets in fusion reactors, or nuclear waste repositories. It has attained perfect weak scalability up to 458,672 cores in JUQUEEN (Germany) solving up to 60 billion unknowns. In 2019 he co-started the Gridap project, which heavily relies on functional programming and multiple dispatching in Julia, with the aim to create an easy-to-use but very efficient PDE solver.
In this talk, we explore the novel capabilities of Gridap to solve Partial Differential Equations (PDEs) in Julia. This includes new features like a high-level API to write the PDE weak form with a syntax almost identical to the math notation, support for automatic differentiation, and simulation of PDEs on manifolds and domains of mixed geometrical dimensions. We will showcase these techniques with representative applications and performance comparisons against codes implemented in C/C++.