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Related papers: Resta-like preconditioning for self-consistent fie…

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We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…

Numerical Analysis · Mathematics 2017-12-27 Gustavo Chávez , George Turkiyyah , Stefano Zampini , David Keyes

We propose the complex-plane generalization of a powerful algebraic sequence acceleration algorithm, the Method of Weighted Averages (MWA), to guarantee exponential-cum-algebraic convergence of Fourier and Fourier-Hankel (F-H) integral…

Computational Physics · Physics 2016-02-17 Kamalesh Sainath , Fernando Teixeira , Burkay Donderici

This paper introduces the sparsifying preconditioner for the pseudospectral approximation of highly indefinite systems on periodic structures, which include the frequency-domain response problems of the Helmholtz equation and the…

Numerical Analysis · Mathematics 2014-09-18 Lexing Ying

Full-potential electronic structure calculations for periodic systems retain the Coulomb singularity at the nuclei, which induces cusp behavior of the orbitals near the nuclei while leaving the interstitial region smooth. This multiscale…

Numerical Analysis · Mathematics 2026-05-26 Baowei Lai , Xucheng Meng , Xiaoxu Li

A thermo-elastoplastic finite element approach is used to perform the simulation of a laser beam welding (LBW) process. This results in a nonlinear, nonsymmetric saddle point multiphysics system, for which the nonlinearity is handled via…

Numerical Analysis · Mathematics 2025-02-28 Tommaso Bevilacqua , Axel Klawonn , Martin Lanser

We introduce a preconditioner for a hybridizable discontinuous Galerkin discretization of the linearized Navier-Stokes equations at high Reynolds number. The preconditioner is based on an augmented Lagrangian approach of the full…

Numerical Analysis · Mathematics 2025-12-03 Alexander D. Lindsay , Sander Rhebergen , Ben S. Southworth

In this report, we present a versatile and efficient preconditioned Anderson acceleration (PAA) method for fixed-point iterations. The proposed framework offers flexibility in balancing convergence rates (linear, super-linear, or quadratic)…

Numerical Analysis · Mathematics 2023-10-09 Kewang Chen , Ye Ji , Matthias Möller , Cornelis Vuik

We present an ab initio pseudopotential local density functional calculation for stoichiometric high-Tc cuprate YBa_2Cu_3O_7 using the plane-wave basis set. We have overcome well-known difficulties in applying pseudopotential methods to…

Condensed Matter · Physics 2009-10-22 Hanchul Kim , Jisoon Ihm

We present an implementation of the linear density response function within the projector-augmented wave (PAW) method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response…

Materials Science · Physics 2011-06-28 Jun Yan , Jens. J. Mortensen , Karsten W. Jacobsen , Kristian S. Thygesen

The Projected Augmented Waves (PAW) method is based on a linear transformation between the pseudo wavefunctions and the all electron wavefunctions. To obtain high accuracy with this method, it is important that the local part of the linear…

Other Condensed Matter · Physics 2025-04-15 Garry Goldstein

We deal with interval parametric systems of linear equations and the goal is to solve such systems, which basically comes down to finding an enclosure for a parametric solution set. Obviously we want this enclosure to be as tight as…

Numerical Analysis · Mathematics 2025-10-07 Iwona Skalna , Milan Hladík

In this paper, we propose and analyze an efficient preconditioning method for the elliptic problem based on the reconstructed discontinuous approximation method. We reconstruct a high-order piecewise polynomial space that arbitrary order…

Numerical Analysis · Mathematics 2024-07-16 Ruo Li , Qicheng Liu , Fanyi Yang

It is tested whether machine learning methods can be used for preconditioning to increase the performance of the linear solver -- the backbone of the semi-implicit, grid-point model approach for weather and climate models. Embedding the…

Atmospheric and Oceanic Physics · Physics 2020-10-07 Jan Ackmann , Peter D. Düben , Tim N. Palmer , Piotr K. Smolarkiewicz

In this article, a two-level overlapping domain decomposition preconditioner is developed for solving linear algebraic systems obtained from simulating Darcy flow in high-contrast media. Our preconditioner starts at a mixed finite element…

Numerical Analysis · Mathematics 2024-03-29 Changqing Ye , Shubin Fu , Eric T. Chung , Jizu Huang

This paper studies the solution of nonsymmetric linear systems by preconditioned Krylov methods based on the normal equations, LSQR in particular. On some examples, preconditioned LSQR is seen to produce errors many orders of magnitude…

Numerical Analysis · Mathematics 2025-03-06 Ethan N. Epperly , Anne Greenbaum , Yuji Nakatsukasa

We present optimal preconditioners for a recently introduced hybridized discontinuous Galerkin finite element discretization of the Stokes equations. Typical of hybridized discontinuous Galerkin methods, the method has degrees-of-freedom…

Numerical Analysis · Mathematics 2023-07-06 Sander Rhebergen , Garth N. Wells

We discuss techniques for accelerating the self consistent field (SCF) iteration for solving the Kohn-Sham equations. These techniques are all based on constructing approximations to the inverse of the Jacobian associated with a fixed point…

Computational Physics · Physics 2015-03-20 Lin Lin , Chao Yang

In this paper, we address the efficient numerical solution of linear and quadratic programming problems, often of large scale. With this aim, we devise an infeasible interior point method, blended with the proximal method of multipliers,…

Numerical Analysis · Mathematics 2021-01-18 Luca Bergamaschi , Jacek Gondzio , Ángeles Martínez , John W. Pearson , Spyridon Pougkakiotis

A general technique for synthesizing both planar and conformal beamforming metasurfaces is presented that utilizes full-wave modeling techniques and rapid optimization methods. The synthesized metasurfaces consist of a patterned metallic…

Optics · Physics 2022-06-22 Jordan Budhu , Luke Szymanski , Anthony Grbic

We derive a linearized rotating shallow water system modeling tides, which can be discretized by mixed finite elements. Unlike previous models, this model allows for multiple layers stratified by density. Like the single-layer…

Numerical Analysis · Mathematics 2022-07-06 Colin J. Cotter , Robert C. Kirby , Hunter Morris