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Robust variational physics-informed neural networks
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 …
(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
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 …
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
Code generation technology has been transformative to the field of numerical partial
differential equations (PDEs), allowing domain scientists and engineers to automatically …
differential equations (PDEs), allowing domain scientists and engineers to automatically …
SUPG-YZβ computation of chemically reactive convection-dominated nonlinear models
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 …
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
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 …
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
We explore how recent advances in Isogeometric analysis, Galerkin Least-Squares
methods, and Augmented Lagrangian techniques can be applied to solve nonstandard …
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
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 …
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
In this paper, we introduce the isoGeometric Residual Minimization (iGRM) method. The
method solves stationary advection-dominated diffusion problems. We stabilize the method …
method solves stationary advection-dominated diffusion problems. We stabilize the method …
A spatio-temporal adaptive phase-field fracture method
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 …
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
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 …
which solves a discretely stable saddle‐point problem to approximate the velocity‐pressure …