19 citations · 51 across the 13 of their papers we have counts for
14 papers
Stable time-stepping via residual minimization: finite-element and neural-network approximations for transient parabolic problems
Judit Muñoz-Matute, Sergio Rojas
We propose a time-stepping minimum-residual (MinRes) framework for transient coercive variational problems, applicable to finite-element and neural-network trial approximations. Fo…
Parametric Neural r-Adaptivity for Isogeometric Analysis via Residual Minimization
Elías Caru, David Pardo, Judit Muñoz-Matute
We propose an r-adaptive neural algorithm for Isogeometric Analysis (IGA) based on residual minimization. The boundary-value problem is solved using a standard conforming Galerkin…
Tracking controllability on moving targets for parabolic equations
Jone Apraiz, Jon Asier Bárcena-Petisco, Judit Muñoz-Matute
In this paper, we study the tracking controllability of a 1D parabolic-type equation. Notably, with controls acting on the boundary, we seek to approximately control the solution o…
A Space-Time Discontinuous Petrov-Galerkin Finite Element Formulation for a Modified Schrödinger Equation for Laser Pulse Propagation in Waveguides
Ankit Chakraborty, Judit Munoz-Matute, Leszek Demkowicz +1
In this article, we propose a modified nonlinear Schrödinger equation for modeling pulse propagation in optical waveguides. The proposed model bifurcates into a system of elliptic…
Regularity-Conforming Neural Networks (ReCoNNs) for solving Partial Differential Equations
Jamie M. Taylor, David Pardo, Judit Muñoz-Matute
Whilst the Universal Approximation Theorem guarantees the existence of approximations to Sobolev functions -- the natural function spaces for PDEs -- by Neural Networks (NNs) of su…
Augmenting MRI scan data with real-time predictions of glioblastoma brain tumor evolution using faster exponential time integrators
Magdalena Pabisz, Judit Muñoz-Matute, Maciej Paszyński
We present a MATLAB code for exponential integrators method simulating the glioblastoma tumor growth. It employs the Fisher-Kolmogorov diffusion-reaction tumor brain model with log…
Multistage DPG time-marching scheme for nonlinear problems
Judit Muñoz-Matute, Leszek Demkowicz
In this article, we employ the construction of the time-marching Discontinuous Petrov-Galerkin (DPG) scheme we developed for linear problems to derive high-order multistage DPG met…
Robust Variational Physics-Informed Neural Networks
Sergio Rojas, Paweł Maczuga, Judit Muñoz-Matute +2
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-Galer…
A Deep Double Ritz Method (DRM) for solving Partial Differential Equations using Neural Networks
Carlos Uriarte, David Pardo, Ignacio Muga +1
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…
Exploiting Kronecker structure in exponential integrators: fast approximation of the action of -functions of matrices via quadrature
Matteo Croci, Judit Muñoz-Matute
In this article, we propose an algorithm for approximating the action of functions of matrices against vectors, which is a key operation in exponential time integrators. In par…
Isogeometric Residual Minimization Method (iGRM) with Direction Splitting for Non-Stationary Advection-Diffusion Problems
Marcin Los, Judit Munoz-Matute, Ignacio Muga +1
In this paper, we propose a novel computational implicit method, which we call Isogeometric Residual Minimization (iGRM) with direction splitting. The method mixes the benefits res…
Alternating directions implicit higher-order finite element method for simulations of time-dependent electromagnetic wave propagation in non-regular biological tissues
Maciej Paszynski, Marcin Los, Judit Munoz-Matute
We focus on non-stationary Maxwell equations defined on a regular patch of elements as considered in the isogeometric analysis (IGA). We apply the time-integration scheme following…
Isogeometric Residual Minimization (iGRM) for Non-Stationary Stokes and Navier-Stokes Problems
Marcin Los, Ignacio Muga, Judit Munoz-Matute +1
We show that it is possible to obtain a linear computational cost FEM-based solver for non-stationary Stokes and Navier-Stokes equations. Our method employs a technique developed b…
Variational Formulations for Explicit Runge-Kutta Methods
Judit Muñoz-Matute, David Pardo, Victor M. Calo +1
Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have v…