31 citations · 85 across the 9 of their papers we have counts for
9 papers
Integrating Additive Multigrid with Multipreconditioned Conjugate Gradient Method
Hardik Kothari, Maria Giuseppina Chiara Nestola, Marco Favino +1
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial dif…
Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies
Alena Kopaničáková, Hardik Kothari, George Em Karniadakis +1
We propose to enhance the training of physics-informed neural networks (PINNs). To this aim, we introduce nonlinear additive and multiplicative preconditioning strategies for the w…
Nonlinear Schwarz preconditioning for nonlinear optimization problems with bound constraints
Hardik Kothari, Alena Kopaničáková, Rolf Krause
We propose a nonlinear additive Schwarz method for solving nonlinear optimization problems with bound constraints. Our method is used as a "right-preconditioner" for solving the fi…
Nonlinear Schwarz preconditioning for Quasi-Newton methods
Hardik Kothari
We propose the nonlinear restricted additive Schwarz (RAS) preconditioning strategy to improve the convergence speed of limited memory quasi-Newton (QN) methods. We consider both "…
Nonlinear Field-split Preconditioners for Solving Monolithic Phase-field Models of Brittle Fracture
Alena Kopaničáková, Hardik Kothari, Rolf Krause
One of the state-of-the-art strategies for predicting crack propagation, nucleation, and interaction is the phase-field approach. Despite its reliability and robustness, the phase-…
A Generalized Multigrid Method for Solving Contact Problems in Lagrange Multiplier based Unfitted Finite Element Method
Hardik Kothari, Rolf Krause
Internal interfaces in a domain could exist as a material defect or they can appear due to propagations of cracks. Discretization of such geometries and solution of the contact pro…
A Multigrid Preconditioner for Jacobian-free Newton-Krylov Methods
Hardik Kothari, Alena Kopaničáková, Rolf Krause
In this work, we propose a multigrid preconditioner for Jacobian-free Newton-Krylov (JFNK) methods. Our multigrid method does not require knowledge of the Jacobian at any level of…
Multigrid and saddle-point preconditioners for unfitted finite element modelling of inclusions
Hardik Kothari, Rolf Krause
In this work, we consider the modeling of inclusions in the material using an unfitted finite element method. In the unfitted methods, structured background meshes are used and onl…
A Multigrid Method for a Nitsche-based Extended Finite Element Method
Hardik Kothari, Rolf Krause
We present a tailored multigrid method for linear problems stemming from a Nitsche-based extended finite element method (XFEM). Our multigrid method is robust with respect to highl…