Constructing fast numerical solvers for partial differential equations (PDEs) is crucial for
many scientific disciplines. A leading technique for solving large-scale PDEs is using …

Efficient exploitation of exascale architectures requires rethinking of the numerical
algorithms used in many large-scale applications. These architectures favor algorithms that …

Local Fourier analysis is a useful tool for predicting and analyzing the performance of many
efficient algorithms for the solution of discretized PDEs, such as multigrid and domain …

In this paper, we employ local Fourier analysis (LFA) to analyze the convergence properties
of multigrid methods for higher‐order finite‐element approximations to the Laplacian …

Local Fourier analysis is a commonly used tool to assess the quality and aid in the
construction of geometric multigrid methods for translationally invariant operators. In this …

Multigrid methods are popular for solving linear systems derived from discretizing PDEs.
Local Fourier analysis (LFA) is a technique for investigating and tuning multigrid methods. P …

In this work, a local Fourier analysis is presented to study the convergence of multigrid
methods based on additive Schwarz smoothers. This analysis is presented as a general …

Recently, deep learning-based hybrid iterative methods (DL-HIM) have emerged as a
promising approach for designing fast neural solvers to tackle large-scale sparse linear …

The goal of this milestone was to improve the high-order software ecosystem for CEED-
enabled ECP applications by making progress on efficient matrix-free kernels targeting …

This work introduces an extension of the classical local Fourier analysis (LFA) in which the
discrete operator is described by a scalar stencil or stencils. First, we extend the scalar …