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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…
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…