11 papers · 1 filter
Multilevel Isogeometric Projection Stabilization via Quasi-Interpolation for Advection-Dominated Problems
Zakaria El Hasnaoui, Ahmed Ratnani
This paper presents a novel multilevel projection-based stabilization method for advection-dominated convection--diffusion problems within the framework of Isogeometric Analysis. T…
Block Schwarz methods and preconditioning strategies using Generalized locally Toeplitz tools - part I: analysis of the preconditioners and numerical validation
Abdessadek Rifqui, Ahmed Ratnani, Stefano Serra-Capizzano
In the current work we present a spectral analysis of the additive and multiplicative Schwarz methods within the framework of domain decomposition techniques, by investigating the…
Higher order multi-dimension reduction methods via Einstein product
Alaeddine Zahir, Khalide Jbilou, Ahmed Ratnani
This paper explores the extension of dimension reduction (DR) techniques to the multi-dimension case by using the Einstein product. Our focus lies on graph-based methods, encompass…
Trace Ratio vs Ratio Trace Methods for Multidimensional Dimensionality Reduction
Alaeddine Zahir, Franck Dufrenois, Khalide Jbilou +1
We propose a higher-order dimensionality reduction framework based on the Trace Ratio (TR) optimization problem. We establish conditions for existence and uniqueness of solutions a…
Quaternion tensor low rank Quaternion tensor low-rank approximation using a family of non-convex norms
Alaeddine Zahir, Ahmed Ratnani, Khalide Jbilou
In this paper, we propose a new approaches for low rank approximation of quaternion tensors \cite{chen2019low,zhang1997quaternions,hamilton1866elements}. The first method uses quas…
IGA Laplace Eigenfrequencies Distributions and Estimations: Impact of Reparametrization on Eigenfrequency Behavior
Lamsahel Noureddine, Abdeladim El Akri, Ahmed Ratnani
This work addresses the Galerkin isogeometric discretization of the one-dimensional Laplace eigenvalue problem subject to homogeneous Dirichlet boundary conditions on a bounded int…