activity
20202026
most citedFinite element interpolated neural networks for solving forward and inverse problems

48 citations · 59 across the 5 of their papers we have counts for

collaborators

7 papers

math.NA2026

An intrinsic finite element framework for scalar- and vector-valued partial differential equations on general manifolds

Tamara A. Tambyah, Alberto F. Martín, David Lee +1

We present an intrinsic finite element framework for the numerical approximation of scalar- and vector-valued partial differential equations on general manifolds described by atlas…

math.NA2026

GridapGeosciences.jl: A Julia finite element package for partial differential equations on general manifolds

Tamara A. Tambyah, Alberto F. Martín, David Lee +1

We present GridapGeosciencesjl, a new parallel distributed-memory Julia package for the numerical approximation of partial differential equations on general manifolds. Our abstr…

math.NA2023★ 9 cited

Robust finite element methods and solvers for the Biot--Brinkman equations in vorticity form

Ruben Caraballo, Chansophea Wathanak In, Alberto F. Martín +1

In this paper, we propose a new formulation and a suitable finite element method for the steady coupling of viscous flow in deformable porous media using divergence-conforming filt…

math.NA2023★ 48 cited

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…

math.NA2022★ 2 cited

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…

math.NA2020

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…