Robust variational physics-informed neural networks

S Rojas, P Maczuga, J Muñoz-Matute, D Pardo… - Computer Methods in …, 2024‏ - Elsevier
We introduce a Robust version of the Variational Physics-Informed Neural Networks method
(RVPINNs). As in VPINNs, we define the quadratic loss functional in terms of a Petrov …

[HTML][HTML] A deep double Ritz method (D2RM) for solving partial differential equations using neural networks

C Uriarte, D Pardo, I Muga, J Muñoz-Matute - Computer Methods in Applied …, 2023‏ - Elsevier
Residual minimization is a widely used technique for solving Partial Differential Equations in
variational form. It minimizes the dual norm of the residual, which naturally yields a saddle …

Leveraging code generation for transparent immersogeometric fluid–structure interaction analysis on deforming domains

GE Neighbor, H Zhao, M Saraeian, MC Hsu… - Engineering with …, 2023‏ - Springer
Code generation technology has been transformative to the field of numerical partial
differential equations (PDEs), allowing domain scientists and engineers to automatically …

SUPG-YZβ computation of chemically reactive convection-dominated nonlinear models

S Cengizci, Ö Uğur, S Natesan - International Journal of Computer …, 2023‏ - Taylor & Francis
In this computational study, we deal with the stabilized finite element solutions of convection-
dominated models having nonlinear reaction mechanisms. The existence of advection terms …

Automatically adaptive, stabilized finite element method via residual minimization for heterogeneous, anisotropic advection–diffusion–reaction problems

RJ Cier, S Rojas, VM Calo - Computer Methods in Applied Mechanics and …, 2021‏ - Elsevier
We describe a stable finite element formulation for advection–diffusion–reaction problems
that allows for the easy implementation of robust automatic adaptivity. We consider locally …

Isogeometric analysis and Augmented Lagrangian Galerkin Least Squares Methods for residual minimization in dual norm

E Burman, P Hansbo, MG Larson, K Larsson - Computer Methods in …, 2023‏ - Elsevier
We explore how recent advances in Isogeometric analysis, Galerkin Least-Squares
methods, and Augmented Lagrangian techniques can be applied to solve nonstandard …

An adaptive in space, stabilized finite element method via residual minimization for linear and nonlinear unsteady advection–diffusion–reaction equations

JF Giraldo, VM Calo - Mathematical and Computational Applications, 2023‏ - mdpi.com
We construct a stabilized finite element method for linear and nonlinear unsteady advection–
diffusion–reaction equations using the method of lines. We propose a residual minimization …

[HTML][HTML] Isogeometric Residual Minimization Method (iGRM) with direction splitting preconditioner for stationary advection-dominated diffusion problems

VM Calo, M Łoś, Q Deng, I Muga… - Computer Methods in …, 2021‏ - Elsevier
In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The
method solves stationary advection-dominated diffusion problems. We stabilize the method …

A spatio-temporal adaptive phase-field fracture method

NA Labanda, L Espath, VM Calo - Computer Methods in Applied Mechanics …, 2022‏ - Elsevier
We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in
an Eulerian–Lagrangian formulation, where a second-order phase-field equation controls …

Incompressible flow modeling using an adaptive stabilized finite element method based on residual minimization

FE Kyburg, S Rojas, VM Calo - International Journal for …, 2022‏ - Wiley Online Library
We model incompressible Stokes flows with an adaptive stabilized finite element method,
which solves a discretely stable saddle‐point problem to approximate the velocity‐pressure …