96 citations · 303 across the 55 of their papers we have counts for
62 papers
Advanced Linear Algebra with Applications - Part I (Numerical linear algebra for PDEs, machine learning, and data assimilation)
Victorita Dolean, Jemima Tabeart
These lecture notes form the first part of a master's-level course on advanced numerical linear algebra. Their aim is not only to present the classical algorithms, but to show why…
Spectral coarse spaces based on indefinite operators: the -GenEO method
Théophile Chaumont-Frelet, Victorita Dolean, Mark Fry +2
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method for constructing coarse spaces used in the preconditioning of iterative solvers for discrete PDEs. This method…
A Guided Tour of Modern Domain Decomposition: From Schwarz Iterations to Robust Preconditioners and HPC Implementations
Victorita Dolean, Pierre Jolivet, Frédéric Nataf +1
Domain decomposition methods (DDMs) provide a unifying framework for the scalable numerical solution of partial differential equations. Originating from Schwarz's alternating metho…
When can a neural operator replace a coarse solve? Architectural principles for two-level preconditioning
Hugo Melchers, Victorita Dolean, Michael Abdelmalik
Neural operators are increasingly used as accelerators inside classical numerical methods, but it is rarely clear which architectural ingredients matter for which application. We a…
Are Deep Learning Based Hybrid PDE Solvers Reliable? Why Training Paradigms and Update Strategies Matter
Yuhan Wu, Jan Willem van Beek, Victorita Dolean +1
Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate conv…
Preconditioning of GMRES for Helmholtz problems with quasimodes
Victorita Dolean, Pierre Marchand, Axel Modave +1
Finite element methods are effective for Helmholtz problems involving complex geometries and heterogeneous media. However, the resulting linear systems are often large, indefinite,…
Neural network-driven domain decomposition for efficient solutions to the Helmholtz equation
Victorita Dolean, Daria Hrebenshchykova, Stéphane Lanteri +1
Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and fin…
Achieving wavenumber robustness in domain decomposition for heterogeneous Helmholtz equation: an overview of spectral coarse spaces
Victorita Dolean, Mark Fry, Matthias Langer +2
Solving time-harmonic wave propagation problems in the frequency domain within heterogeneous media poses significant mathematical and computational challenges, particularly in the…
Local Feature Filtering for Scalable and Well-Conditioned Domain-Decomposed Random Feature Methods
Jan Willem van Beek, Victorita Dolean, Ben Moseley
Random Feature Methods (RFMs) and their variants such as extreme learning machine finite-basis physics-informed neural networks (ELM-FBPINNs) offer a scalable approach for solving…
Convergence analysis of GMRES applied to Helmholtz problems near resonances
Victorita Dolean, Pierre Marchand, Axel Modave +1
The finite element solution of Helmholtz problems near resonant or quasi-resonant frequencies poses significant challenges, as iterative solvers typically suffer from severely degr…
Modal analysis of a domain decomposition method for Maxwell's equations in a waveguide
Victorita Dolean, Antoine Tonnoir, Pierre-Henri Tournier
Time-harmonic wave propagation problems, especially those governed by Maxwell's equations, pose significant computational challenges due to the non-self-adjoint nature of the opera…
An Iterative Block Matrix Inversion (IBMI) Algorithm for Symmetric Positive Definite Matrices with Applications to Covariance Matrices
Ann Paterson, Jennifer Pestana, Victorita Dolean
Obtaining the inverse of a large symmetric positive definite matrix is a continual challenge across many mathematical disciplines. The comput…
ELM-FBPINNs: An Efficient Multilevel Random Feature Method
Samuel Anderson, Victorita Dolean, Ben Moseley +1
Domain-decomposed variants of physics-informed neural networks (PINNs) such as finite basis PINNs (FBPINNs) mitigate some of PINNs' issues like slow convergence and spectral bias t…
Two-level deep domain decomposition method
Victorita Dolean, Serge Gratton, Alexander Heinlein +1
This study presents a two-level Deep Domain Decomposition Method (Deep-DDM) augmented with a coarse-level network for solving boundary value problems using physics-informed neural…
Schwarz preconditioner with -GenEO coarse space for the indefinite Helmholtz problem
Victorita Dolean, Mark Fry, Ivan G. Graham +1
GenEO (`Generalised Eigenvalue problems on the Overlap') is a method from the family of spectral coarse spaces that can efficiently rely on local eigensolves in order to build a ro…
Nonlinear Multilevel Solution Strategies for Diffusive Wave Flood Models in Perforated Domains
Miranda Boutilier, Konstantin Brenner, Victorita Dolean
This article investigates the numerical solution of the Diffusive Wave equation posed on domains containing a large number of polygonal perforations, motivated by urban flood model…
Can Symmetric Positive Definite (SPD) coarse spaces perform well for indefinite Helmholtz problems?
Victorita Dolean, Mark Fry, Matthias Langer
Wave propagation problems governed by the Helmholtz equation remain among the most challenging in scientific computing, due to their indefinite nature. Domain decomposition methods…
Numerical Modeling for Shoulder Injury Detection Using Microwave Imaging
Sahar Borzooei, Pierre-Henri Tournier, Victorita Dolean +4
A portable imaging system for the on-site detection of shoulder injury is necessary to identify its extent and avoid its development to severe condition. Here, firstly a microwave…
A robust and adaptive GenEO-type domain decomposition preconditioner for problems in three-dimensional general topologies
Niall Bootland, Victorita Dolean, Frédéric Nataf +1
In this paper we design, analyse and test domain decomposition methods for linear systems of equations arising from conforming finite element discretisations of positive Maxwell-ty…
Multilevel Scalable Solvers for Stochastic Linear and Nonlinear Problems
Sudhi Sharma, Pierre Jolivet, Victorita Dolean +1
This article discusses the uncertainty quantification (UQ) for time-independent linear and nonlinear partial differential equation (PDE)-based systems with random model parameters…
Robust Methods for Multiscale Coarse Approximations of Diffusion Models in Perforated Domains
Miranda Boutilier, Konstantin Brenner, Victorita Dolean
For the Poisson equation posed in a domain containing a large number of polygonal perforations, we propose a low-dimensional coarse approximation space based on a coarse polygonal…
Multilevel domain decomposition-based architectures for physics-informed neural networks
Victorita Dolean, Alexander Heinlein, Siddhartha Mishra +1
Physics-informed neural networks (PINNs) are a powerful approach for solving problems involving differential equations, yet they often struggle to solve problems with high frequenc…
Travel times and ray paths for acoustic and elastic waves in generally anisotropic media
James Ludlam, Katherine Tant, Victorita Dolean +1
Wavefield travel time tomography is used for a variety of purposes in acoustics, geophysics and non-destructive testing. Since the problem is non-linear, assessing uncertainty in t…
Numerical assessment of PML transmission conditions in a domain decomposition method for the Helmholtz equation
Niall Bootland, Sahar Borzooei, Victorita Dolean +1
The convergence rate of domain decomposition methods (DDMs) strongly depends on the transmission condition at the interfaces between subdomains. Thus, an important aspect in improv…