152 citations · 839 across the 37 of their papers we have counts for
41 papers
Model order reduction with novel discrete empirical interpolation methods in space-time
Nicholas Mueller, Santiago Badia
This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) s…
Efficient and reliable divergence-conforming methods for an elasticity-poroelasticity interface problem
S. Badia, M. Hornkjøl, A. Khan +3
We present a finite element discretisation to model the interaction between a poroelastic structure and an elastic medium. The consolidation problem considers fully coupled deforma…
Finite element interpolated neural networks for solving forward and inverse problems
Santiago Badia, Wei Li, Alberto F. Martín
We propose a general framework for solving forward and inverse problems constrained by partial differential equations, where we interpolate neural networks onto finite element spac…
Neural Level Set Topology Optimization Using Unfitted Finite Elements
Connor N. Mallon, Aaron W. Thornton, Matthew R. Hill +1
To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization,…
Adaptive quadratures for nonlinear approximation of low-dimensional PDEs using smooth neural networks
Alexandre Magueresse, Santiago Badia
Physics-informed neural networks (PINNs) and their variants have recently emerged as alternatives to traditional partial differential equation (PDE) solvers, but little literature…
Stability and conditioning of immersed finite element methods: analysis and remedies
Frits de Prenter, Clemens Verhoosel, Harald van Brummelen +2
This review paper discusses the developments in immersed or unfitted finite element methods over the past decade. The main focus is the analysis and the treatment of the adverse ef…
Bound-preserving finite element approximations of the Keller-Segel equations
Santiago Badia, Jesús Bonilla, Juan Vicente Gutiérrez-Santacreu
This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. W…
Space-time unfitted finite element methods for time-dependent problems on moving domains
Santiago Badia, Hridya Dilip, Francesc Verdugo
We propose a space-time scheme that combines an unfitted finite element method in space with a discontinuous Galerkin time discretisation for the accurate numerical approximation o…
A comparison of variational upwinding schemes for geophysical fluids, and their application to potential enstrophy conserving discretisations
David Lee, Alberto F. Martín, Christopher Bladwell +1
Methods for upwinding the potential vorticity in a compatible finite element discretisation of the rotating shallow water equations are studied. These include the well-known antici…
Robust high-order unfitted finite elements by interpolation-based discrete extension
Santiago Badia, Eric Neiva, Francesc Verdugo
In this work, we propose a novel formulation for the solution of partial differential equations using finite element methods on unfitted meshes. The proposed formulation relies on…
A Massively Parallel Implementation of Multilevel Monte Carlo for Finite Element Models
Santiago Badia, Jerrad Hampton, Javier Principe
The Multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty Quantification (UQ) in Partial Differential Equation (P…
Geometrical discretisations for unfitted finite elements on explicit boundary representations
Santiago Badia, Pere A. Martorell, Francesc Verdugo
Unfitted (also known as embedded or immersed) finite element approximations of partial differential equations are very attractive because they have much lower geometrical requireme…
The software design of Gridap: a Finite Element package based on the Julia JIT compiler
Francesc Verdugo, Santiago Badia
We present the software design of Gridap, a novel finite element library written exclusively in the Julia programming language, which is being used by several research groups world…
Conditioning of a Hybrid High-Order scheme on meshes with small faces
Santiago Badia, Jerome Droniou, Liam Yemm
We conduct a condition number analysis of a Hybrid High-Order (HHO) scheme for the Poisson problem. We find the condition number of the statically condensed system to be independen…
Linking ghost penalty and aggregated unfitted methods
Santiago Badia, Eric Neiva, Francesc Verdugo
In this work, we analyse the links between ghost penalty stabilisation and aggregation-based discrete extension operators for the numerical approximation of elliptic partial differ…
A robust and scalable unfitted adaptive finite element framework for nonlinear solid mechanics
Santiago Badia, Manuel Caicedo, Alberto F. Martín +1
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and…
Robust and scalable h-adaptive aggregated unfitted finite elements for interface elliptic problems
Eric Neiva, Santiago Badia
This work introduces a novel, fully robust and highly-scalable, -adaptive aggregated unfitted finite element method for large-scale interface elliptic problems. The new method i…
The aggregated unfitted finite element method on parallel tree-based adaptive meshes
Santiago Badia, Alberto F. Martín, Eric Neiva +1
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel…
Balancing domain decomposition by constraints associated with subobjects
Santiago Badia, Alberto F. Martín, Hieu Nguyen
A simple variant of the BDDC preconditioner in which constraints are imposed on a selected set of subobjects (subdomain subedges, subfaces and vertices between pairs of subedges) i…
Monotonicity-preserving finite element schemes with adaptive mesh refinement for hyperbolic problems
Jesus Bonilla, Santiago Badia
This work is focused on the extension and assessment of the monotonicity-preserving scheme in [3] and the local bounds preserving scheme in [5] to hierarchical octree adaptive mesh…
Embedded multilevel Monte Carlo for uncertainty quantification in random domains
Santiago Badia, Jerrad Hampton, Javier Principe
The multilevel Monte Carlo (MLMC) method has proven to be an effective variance-reduction statistical method for Uncertainty quantification in PDE models. It combines approximation…
On differentiable local bounds preserving stabilization for Euler equations
Santiago Badia, Jesús Bonilla, Sibusiso Mabuza +1
This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integr…
A user-guide to Gridap -- grid-based approximation of partial differential equations in Julia
Francesc Verdugo, Santiago Badia
We present Gridap, a new scientific software library for the numerical approximation of partial differential equations (PDEs) using grid-based approximations. Gridap is an open-sou…
A tutorial-driven introduction to the parallel finite element library FEMPAR v1.0.0
Santiago Badia, Alberto F. Martín
This work is a user guide to the FEMPAR scientific software library. FEMPAR is an open-source object-oriented framework for the simulation of partial differential equations (PDEs)…