Results 41 to 50 of about 12,661,880 (175)
Data‐Driven Spectral Prediction for Accelerating Large‐Scale Electronic Structure Calculations
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT Simulating large molecular systems comprising thousands of atoms requires highly scalable methodologies. While modern Density Functional Theory (DFT) codes exhibit linear scaling, solving the associated large, sparse generalized eigenproblems remains a critical computational bottleneck on exascale architectures.
Abhiram Badrinarayanan +6 more
wiley +1 more source
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT For complex geometries, the coarse problem of geometric multigrid can be too large to be solved by a direct solver. Here, we report on the use of domain decomposition applied to the multigrid coarse problem. Additive overlapping Schwarz methods are domain decomposition methods for the iterative solution of partial differential equations whose ...
Stephan Köhler, Oliver Rheinbach
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Energies, 2020 In the transient analysis of an engineering power electronics device, the order of its equivalent circuit model is excessive large. To eliminate this issue, some model order reduction (MOR) methods are proposed in the literature.
Ning Wang, Huifang Wang, Shiyou Yang
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Probing and Graph Coloring Techniques for Trace Estimation in Lattice QCD
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT The computation of Tr[D−1]$\mathrm{Tr}[D^{-1}]$, where D$D$ is the Wilson–Dirac matrix of Lattice QCD, is a fundamental and computationally demanding task with applications to disconnected hadronic correlation functions. Since D−1$D^{-1}$ is a dense matrix of prohibitive size, its trace cannot be computed exactly, and one must resort to ...
Mario Papace +5 more
wiley +1 more source
Krylov Subspace Methods on Supercomputers [PDF]
SIAM Journal on Scientific and Statistical Computing, 1989 This paper presents a short survey of recent research on Krylov subspace methods with emphasis on implementation on vector and parallel computers. Conjugate gradient methods have proven very useful on traditional scalar computers, and their popularity is likely to increase as three-dimensional models gain importance.
openaire +1 more source
Subspace Acceleration for Efficient Nonlinear Water Wave Simulation
International Journal for Numerical Methods in Fluids, Volume 98, Issue 10, Page 1165-1180, October 2026.We introduce an exponentially weighted subspace acceleration technique to reduce GMRES iterations for solving the Poisson equation with time‐dependent coefficients in nonlinear, dispersive free‐surface flows governed by the incompressible Navier‐Stokes equations. The method significantly reduces memory requirements and computational complexity compared
Rasmus Kleist Hørlyck Sørensen +3 more
wiley +1 more source
Polynomial Preconditioning for Indefinite Matrices
Numerical Linear Algebra with Applications, Volume 33, Issue 5, October 2026.ABSTRACT Polynomial preconditioning is an important tool in solving large linear systems and eigenvalue problems. A polynomial from GMRES can be used to precondition restarted GMRES and restarted Arnoldi. Here we give methods for indefinite matrices that make polynomial preconditioning more generally applicable. The new techniques include balancing the
Hayden Henson, Ronald B. Morgan
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Krylov subspace methods in the electronic industry [PDF]
, 2004 Summary. Krylov subspace methods are well-known for their nice properties, but they have to be implemented with care. In this article the mathematical consequences encountered during implementation of Krylov subspace methods in an existing layout ...
Schilders, W.H.A. +3 more
core
Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems
Abstract and Applied Analysis, 2014 Based on the modified Hermitian and skew-Hermitian splitting (MHSS) and preconditioned MHSS (PMHSS) methods, a generalized preconditioned MHSS (GPMHSS) method for a class of complex symmetric linear systems is presented.
Cui-Xia Li, Yan-Jun Liang, Shi-Liang Wu
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Krylov SSP Integrating Factor Runge–Kutta WENO Methods
Mathematics, 2021 Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF ...
Shanqin Chen
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