152 citations · 616 across the 18 of their papers we have counts for
18 papers
Space-time unfitted finite elements on moving explicit geometry representations
Santiago Badia, Pere A. Martorell, Francesc Verdugo
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the pro…
Designing Structures that Maximize Spatially Averaged Surface-Enhanced Raman Spectra
Wenjie Yao, Francesc Verdugo, Henry O. Everitt +2
We present a general framework for inverse design of nanopatterned surfaces that maximize spatially averaged surface-enhanced Raman (SERS) spectra from molecules distributed random…
A monolithic Finite Element formulation for the hydroelastic analysis of Very Large Floating Structures
Oriol Colomés, Francesc Verdugo, Ido Akkerman
In this work we present a novel monolithic Finite Element Method (FEM) for the hydroelastic analysis of Very Large Floating Structures (VLFS) with arbitrary shapes that is stable,…
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…
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…
Trace formulation for photonic inverse design with incoherent sources
Wenjie Yao, Francesc Verdugo, Rasmus E. Christiansen +1
Spatially incoherent light sources, such as spontaneously emitting atoms, naively require Maxwell's equations to be solved many times to obtain the total emission, which becomes co…
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…
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…
Physics-informed neural networks with hard constraints for inverse design
Lu Lu, Raphael Pestourie, Wenjie Yao +3
Inverse design arises in a variety of areas in engineering such as acoustic, mechanics, thermal/electronic transport, electromagnetism, and optics. Topology optimization is a major…
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…
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 generic finite element framework on parallel tree-based adaptive meshes
Santiago Badia, Alberto F. Martín, Eric Neiva +1
In this work we formally derive and prove the correctness of the algorithms and data structures in a parallel, distributed-memory, generic finite element framework that supports h-…
Distributed-memory parallelization of the aggregated unfitted finite element method
Francesc Verdugo, Alberto F. Martín, Santiago Badia
The aggregated unfitted finite element method (AgFEM) is a methodology recently introduced in order to address conditioning and stability problems associated with embedded, unfitte…
Mixed aggregated finite element methods for the unfitted discretization of the Stokes problem
Santiago Badia, Alberto F. Martín, Francesc Verdugo
In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-…
The aggregated unfitted finite element method for elliptic problems
Santiago Badia, Francesc Verdugo, Alberto F. Martín
Unfitted finite element techniques are valuable tools in different applications where the generation of body-fitted meshes is difficult. However, these techniques are prone to seve…
Robust and scalable domain decomposition solvers for unfitted finite element methods
Santiago Badia, Francesc Verdugo
Unfitted finite element methods, e.g., extended finite element techniques or the so-called finite cell method, have a great potential for large scale simulations, since they avoid…
Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes
Francesc Verdugo, Wolfgang A. Wall
In this paper, we propose and evaluate the performance of a unified computational framework for preconditioning systems of linear equations resulting from the solution of coupled p…