Results 61 to 70 of about 3,994 (221)
Toward a Mixed‐Precision ADI Method for Lyapunov Equations
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT We apply mixed‐precision to the low‐rank Lyapunov ADI (LR‐ADI) by performing certain aspects of the algorithm in a lower working precision. Namely, we accumulate the overall solution, solve the linear systems comprising the ADI iteration, and store the inner low‐rank factors of the residuals in various combinations of IEEE 754 single and ...
Jonas Schulze, Jens Saak
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Monolithic Multi‐Level Overlapping Schwarz Preconditioners for Fluid Problems
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 2, June 2026.ABSTRACT Additive overlapping Schwarz methods are iterative methods of the domain decomposition type for the solution of partial differential equations. Numerical and parallel scalability of these methods can be achieved by adding coarse levels. A successful coarse space, inspired by iterative substructuring, is the generalized Dryja–Smith–Widlund ...
Stephan Köhler, Oliver Rheinbach
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Inexact Krylov Subspace Methods for Linear Systems [PDF]
SIAM Journal on Matrix Analysis and Applications, 2004 This paper is devoted to the impact of perturbations of the matrix-vector product in various Krylov subspace solvers. This problem is related to the rounding errors analysis of Krylov subspace methods since in the latter case an inexact matrix-vector product is one source of errors.
Eshof, J. van den, Sleijpen, G.L.G.
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Journal of Computational Chemistry, Volume 47, Issue 14, 30 May 2026.We propose a hybrid quantum and classical method for accurately evaluating molecular total energies with limited logical qubits. In our subspace dynamic correlation (SDC) method, electron correlation involving core and external orbitals that are not encoded on the quantum computer is recovered using an approximate wavefunction reconstructed on ...
Nobuki Inoue, Hisao Nakamura
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Krylov Subspace Recycling for Evolving Structures
CoRR, 2020 Krylov subspace recycling is a powerful tool for solving long series of large, sparse linear systems that change slowly. In PDE constrained shape optimization, these appear naturally, as hundreds or more optimization steps are needed with only small changes in the geometry.
Matthias Bolten +2 more
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Preserving Symmetry in Preconditioned Krylov Subspace Methods [PDF]
SIAM Journal on Scientific Computing, 1998 The authors consider the problem of solving linear systems of equations with coefficient matrices which are ``nearly'' (very close to be) symmetric and when symmetric positive definite preconditioners are used. They show that it is possible to improve upon the standard practice of using nonsymmetric preconditioners for that matrices along with a left ...
Tony F. Chan +3 more
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Parametric Model Order Reduction by Box Clustering With Applications in Mechatronic Systems
International Journal for Numerical Methods in Engineering, Volume 127, Issue 10, 30 May 2026.ABSTRACT High temperatures and structural deformations can compromise the functionality and reliability of new components for mechatronic systems. Therefore, high‐fidelity simulations (HFS) are employed during the design process, as they enable a detailed analysis of the thermal and structural behavior of the system.
Juan Angelo Vargas‐Fajardo +4 more
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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. +5 more
core
Explicit‐Implicit Material Point Method for Dense Granular Flows With a Novel Regularized µ(I) Model
International Journal for Numerical and Analytical Methods in Geomechanics, Volume 50, Issue 7, Page 3256-3273, May 2026.ABSTRACT The material point method (MPM) is widely employed to simulate granular flows. Although explicit time integration is favored in most current MPM implementations for its simplicity, it cannot rigorously incorporate the incompressible µ(I)‐rheology, an efficient model ubiquitously adopted in other particle‐based numerical methods. While operator‐
Hang Feng, Zhen‐Yu Yin
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Forward and Adjoint Calculations of Gravitational Potential in Heterogeneous, Aspherical Planets
Earth and Space Science, Volume 13, Issue 5, May 2026.Abstract We have developed a computational package for the calculation of numerically exact internal and external gravitational potential, its functional derivatives and sensitivity kernels, in an aspherical, heterogeneous planet. We detail our implementation, utilizing a transformation of the Poisson equation into a spherical reference domain, as well
Alex D. C. Myhill +2 more
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