Log in

Relevant bibliographies by topics / Multilevel Krylov Subspace Splitting / Journal articles

To see the other types of publications on this topic, follow the link: Multilevel Krylov Subspace Splitting.

Journal articles on the topic 'Multilevel Krylov Subspace Splitting'

Author: Grafiati

Published: 6 September 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 20 journal articles for your research on the topic 'Multilevel Krylov Subspace Splitting.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Bai, Zhong-Zhi. "Regularized HSS iteration methods for stabilized saddle-point problems." IMA Journal of Numerical Analysis 39, no. 4 (2018): 1888–923. http://dx.doi.org/10.1093/imanum/dry046.

Full text

Abstract:

Abstract We extend the regularized Hermitian and skew-Hermitian splitting (RHSS) iteration methods for standard saddle-point problems to stabilized saddle-point problems and establish the corresponding unconditional convergence theory for the resulting methods. Besides being used as stationary iterative solvers, this class of RHSS methods can also be used as preconditioners for Krylov subspace methods. It is shown that the eigenvalues of the corresponding preconditioned matrix are clustered at a small number of points in the interval $(0, \, 2)$ when the iteration parameter is close to $0$ and

APA, Harvard, Vancouver, ISO, and other styles

2

Tian, Zhaolu, Xiaojing Li, and Zhongyun Liu. "A general multi-step matrix splitting iteration method for computing PageRank." Filomat 35, no. 2 (2021): 679–706. http://dx.doi.org/10.2298/fil2102679t.

Full text

Abstract:

Based on the general inner-outer (GIO) iteration method [5,34] and the iteration framework [6], we present a general multi-step matrix splitting (GMMS) iteration method for computing PageRank, and analyze its overall convergence property. Moreover, the same idea can be used as a preconditioning technique for accelerating the Krylov subspace methods, such as GMRES method. Finally, several numerical examples are given to illustrate the effectiveness of the proposed algorithm.

APA, Harvard, Vancouver, ISO, and other styles

3

Huang, Yunying, and Guoliang Chen. "A relaxed block splitting preconditioner for complex symmetric indefinite linear systems." Open Mathematics 16, no. 1 (2018): 561–73. http://dx.doi.org/10.1515/math-2018-0051.

Full text

Abstract:

AbstractIn this paper, we propose a relaxed block splitting preconditioner for a class of complex symmetric indefinite linear systems to accelerate the convergence rate of the Krylov subspace iteration method and the relaxed preconditioner is much closer to the original block two-by-two coefficient matrix. We study the spectral properties and the eigenvector distributions of the corresponding preconditioned matrix. In addition, the degree of the minimal polynomial of the preconditioned matrix is also derived. Finally, some numerical experiments are presented to illustrate the effectiveness of

APA, Harvard, Vancouver, ISO, and other styles

4

Xiong, Jin-Song. "Generalized accelerated AOR splitting iterative method for generalized saddle point problems." AIMS Mathematics 7, no. 5 (2022): 7625–41. http://dx.doi.org/10.3934/math.2022428.

Full text

Abstract:

<abstract><p>Generalized accelerated AOR (GAAOR) splitting iterative method for the generalized saddle point problems is proposed in this paper. The iterative scheme and the convergence of the GAAOR splitting method are researched. The eigenvalues distributions of its preconditioned matrix is discussed under {two different choices of the parameter matrix Q}. The resulting GAAOR preconditioner is used to precondition Krylov subspace method such as the restarted generalized minimal residual (GMRES) method for solving the equivalent formulation of the generalized saddle point problems

APA, Harvard, Vancouver, ISO, and other styles

5

Luo, Jia-Min, Hou-Biao Li, and Wei-Bo Wei. "Block splitting preconditioner for time-space fractional diffusion equations." Electronic Research Archive 30, no. 3 (2022): 780–97. http://dx.doi.org/10.3934/era.2022041.

Full text

Abstract:

<abstract><p>For solving a block lower triangular Toeplitz linear system arising from the time-space fractional diffusion equations more effectively, a single-parameter two-step split iterative method (TSS) is introduced, its convergence theory is established and the corresponding preconditioner is also presented. Theoretical analysis shows that the original coefficient matrix after preconditioned can be expressed as the sum of the identity matrix, a low-rank matrix, and a small norm matrix. Numerical experiments show that the preconditioner improve the calculation efficiency of th

APA, Harvard, Vancouver, ISO, and other styles

6

Lei, Siu-Long, Xu Chen, and Xinhe Zhang. "Multilevel Circulant Preconditioner for High-Dimensional Fractional Diffusion Equations." East Asian Journal on Applied Mathematics 6, no. 2 (2016): 109–30. http://dx.doi.org/10.4208/eajam.060815.180116a.

Full text

Abstract:

AbstractHigh-dimensional two-sided space fractional diffusion equations with variable diffusion coefficients are discussed. The problems can be solved by an implicit finite difference scheme that is proven to be uniquely solvable, unconditionally stable and first-order convergent in the infinity norm. A nonsingular multilevel circulant pre-conditoner is proposed to accelerate the convergence rate of the Krylov subspace linear system solver efficiently. The preconditoned matrix for fast convergence is a sum of the identity matrix, a matrix with small norm, and a matrix with low rank under certa

APA, Harvard, Vancouver, ISO, and other styles

7

Li, Cui-Xia, Yan-Jun Liang, and Shi-Liang Wu. "Generalized Preconditioned MHSS Method for a Class of Complex Symmetric Linear Systems." Abstract and Applied Analysis 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/206821.

Full text

Abstract:

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. Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix. From a practical point of view, we have analyzed and implemented inexact GPMHSS (IGPMHSS) iteration, which employs Krylov subspace methods as its inner processes. Numerical experiments are reported to confirm the efficiency of the proposed methods.

APA, Harvard, Vancouver, ISO, and other styles

8

Chen, Shanqin. "Krylov SSP Integrating Factor Runge–Kutta WENO Methods." Mathematics 9, no. 13 (2021): 1483. http://dx.doi.org/10.3390/math9131483.

Full text

Abstract:

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) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) probl

APA, Harvard, Vancouver, ISO, and other styles

9

Luo, Wei-Hua, and Ting-Zhu Huang. "A Parameterized Splitting Preconditioner for Generalized Saddle Point Problems." Journal of Applied Mathematics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/489295.

Full text

Abstract:

By using Sherman-Morrison-Woodbury formula, we introduce a preconditioner based on parameterized splitting idea for generalized saddle point problems which may be singular and nonsymmetric. By analyzing the eigenvalues of the preconditioned matrix, we find that whenαis big enough, it has an eigenvalue at 1 with multiplicity at leastn, and the remaining eigenvalues are all located in a unit circle centered at 1. Particularly, when the preconditioner is used in general saddle point problems, it guarantees eigenvalue at 1 with the same multiplicity, and the remaining eigenvalues will tend to 1 as

APA, Harvard, Vancouver, ISO, and other styles

10

Li, Yan-Ran, Xin-Hui Shao, and Shi-Yu Li. "New Preconditioned Iteration Method Solving the Special Linear System from the PDE-Constrained Optimal Control Problem." Mathematics 9, no. 5 (2021): 510. http://dx.doi.org/10.3390/math9050510.

Full text

Abstract:

In many fields of science and engineering, partial differential equation (PDE) constrained optimal control problems are widely used. We mainly solve the optimization problem constrained by the time-periodic eddy current equation in this paper. We propose the three-block splitting (TBS) iterative method and proved that it is unconditionally convergent. At the same time, the corresponding TBS preconditioner is derived from the TBS iteration method, and we studied the spectral properties of the preconditioned matrix. Finally, numerical examples in two-dimensions is applied to demonstrate the adva

APA, Harvard, Vancouver, ISO, and other styles

11

Demyanko, Kirill V., Igor E. Kaporin, and Yuri M. Nechepurenko. "Inexact Newton method for the solution of eigenproblems arising in hydrodynamic temporal stability analysis." Journal of Numerical Mathematics 28, no. 1 (2020): 1–14. http://dx.doi.org/10.1515/jnma-2019-0021.

Full text

Abstract:

AbstractThe inexact Newton method developed earlier for computing deflating subspaces associated with separated groups of finite eigenvalues of regular linear large sparse non-Hermitian matrix pencils is specialized to solve eigenproblems arising in the hydrodynamic temporal stability analysis. To this end, for linear systems to be solved at each step of the Newton method, a new efficient MLILU2 preconditioner based on the multilevel 2nd order incomplete LU-factorization is proposed. A special variant of Krylov subspace method IDR2 with right preconditioning is developed. In comparison with GM

APA, Harvard, Vancouver, ISO, and other styles

12

Ran, Yu-Hong, Jun-Gang Wang, and Dong-Ling Wang. "On Preconditioners Based on HSS for the Space Fractional CNLS Equations." East Asian Journal on Applied Mathematics 7, no. 1 (2017): 70–81. http://dx.doi.org/10.4208/eajam.190716.051116b.

Full text

Abstract:

AbstractThe space fractional coupled nonlinear Schrödinger (CNLS) equations are discretized by an implicit conservative difference scheme with the fractional centered difference formula, which is unconditionally stable. The coefficient matrix of the discretized linear system is equal to the sum of a complex scaled identity matrix which can be written as the imaginary unit times the identity matrix and a symmetric Toeplitz-plusdiagonal matrix. In this paper, we present new preconditioners based on Hermitian and skew-Hermitian splitting (HSS) for such Toeplitz-like matrix. Theoretically, we show

APA, Harvard, Vancouver, ISO, and other styles

13

Yuan, Yu-Xin, A.-Man Li, Ting Hu, and Hong Liu. "An anisotropic multilevel preconditioner for solving the Helmholtz equation with unequal directional sampling intervals." GEOPHYSICS 85, no. 6 (2020): T293—T300. http://dx.doi.org/10.1190/geo2019-0330.1.

Full text

Abstract:

An efficient finite-difference method for solving the isotropic Helmholtz equation relies on a discretization scheme and an appropriate solver. Accordingly, we have adopted an average-derivative optimal scheme that has two advantages: (1) it can be applied to unequal directional sampling intervals and (2) it requires less than four grid points of sampling per wavelength. Direct methods are not of interest for industry-sized problems due to the high memory requirements; Krylov subspace methods such as the biconjugate gradient stabilized method and the flexible generalized minimal residual metho

APA, Harvard, Vancouver, ISO, and other styles

14

Axelsson, Owe, Maya Neytcheva, and Zhao-Zheng Liang. "PARALLEL SOLUTION METHODS AND PRECONDITIONERS FOR EVOLUTION EQUATIONS." Mathematical Modelling and Analysis 23, no. 2 (2018): 287–308. http://dx.doi.org/10.3846/mma.2018.018.

Full text

Abstract:

The recent development of the high performance computer platforms shows a clear trend towards heterogeneity and hierarchy. In order to utilize the computational power, particular attention must be paid to ﬁnding new algorithms or adjust existing ones so that they better match the HPC computer architecture. In this work we consider an alternative to classical time-stepping methods based on use of time-harmonic properties and discuss solution approaches that allow eﬃcient utilization of modern HPC resources. The method in focus is based on a truncated Fourier expansion of the solution of an evol

APA, Harvard, Vancouver, ISO, and other styles

15

Mo, Tieqiang, and Renfa Li. "Iteratively solving sparse linear system based on PaRSEC task scheduling." International Journal of High Performance Computing Applications 34, no. 3 (2020): 306–15. http://dx.doi.org/10.1177/1094342019899997.

Full text

Abstract:

With the new architecture and new programming paradigms such as task-based scheduling emerging in the parallel high performance computing area, it is of great importance to utilize these features to tune the monolithic computing codes. In this article, the classical conjugate gradient algorithms targeting at sparse linear system Ax = b in Krylov subspace are pipelining to execute interdependent tasks on Parallel Runtime Scheduling and Execution Controller (PaRSEC) runtime. Firstly, the sparse matrix A is split in rows to unfold more coarse-grained parallelism. Secondly, the partitioned sub-vec

APA, Harvard, Vancouver, ISO, and other styles

16

Alpert, C. J., A. E. Caldwell, T. F. Chan, et al. "Analytical Engines are Unnecessary in Top-down Partitioning-based Placement." VLSI Design 10, no. 1 (1999): 99–116. http://dx.doi.org/10.1155/1999/93607.

Full text

Abstract:

The top-down “quadratic placement” methodology is rooted in such works as [36, 9, 32] and is reputedly the basis of commercial and in-house VLSI placement tools. This methodology iterates between two basic steps: solving sparse systems of linear equations to achieve a continuous placement solution, and “legalization” of the placement by transportation or partitioning. Our work, which extends [5], studies implementation choices and underlying motivations for the quadratic placement methodology. We first recall some observations from [5], e.g., that (i) Krylov subspace engines for solving sparse

APA, Harvard, Vancouver, ISO, and other styles

17

Kong, Fande, Yaqi Wang, Derek R. Gaston, et al. "A Highly Parallel Multilevel Newton--Krylov--Schwarz Method with Subspace-Based Coarsening and Partition-Based Balancing for the Multigroup Neutron Transport Equation on Three-Dimensional Unstructured Meshes." SIAM Journal on Scientific Computing 42, no. 5 (2020): C193—C220. http://dx.doi.org/10.1137/19m1249060.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Hajibeygi, H., S. H. H. Lee, and I. Lunati. "Accurate and Efficient Simulation of Multiphase Flow in a Heterogeneous Reservoir With Error Estimate and Control in the Multiscale Finite-Volume Framework." SPE Journal 17, no. 04 (2012): 1071–83. http://dx.doi.org/10.2118/141954-pa.

Full text

Abstract:

Summary The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be d

APA, Harvard, Vancouver, ISO, and other styles

19

Trivedi, Rahul, Logan Su, Jesse Lu, Martin F. Schubert, and Jelena Vuckovic. "Data-driven acceleration of photonic simulations." Scientific Reports 9, no. 1 (2019). http://dx.doi.org/10.1038/s41598-019-56212-5.

Full text

Abstract:

AbstractDesigning modern photonic devices often involves traversing a large parameter space via an optimization procedure, gradient based or otherwise, and typically results in the designer performing electromagnetic simulations of a large number of correlated devices. In this paper, we investigate the possibility of accelerating electromagnetic simulations using the data collected from such correlated simulations. In particular, we present an approach to accelerate the Generalized Minimal Residual (GMRES) algorithm for the solution of frequency-domain Maxwell’s equations using two machine lea

APA, Harvard, Vancouver, ISO, and other styles

20

Dufrechou, Ernesto. "Accelerating advanced preconditioning methods on hybrid architectures." CLEI Electronic Journal 24, no. 1 (2021). http://dx.doi.org/10.19153/cleiej.24.1.6.

Full text

Abstract:

Many problems, in diverse areas of science and engineering, involve the solution of largescale sparse systems of linear equations. In most of these scenarios, they are also a computational bottleneck, and therefore their efficient solution on parallel architectureshas motivated a tremendous volume of research.This dissertation targets the use of GPUs to enhance the performance of the solution of sparse linear systems using iterative methods complemented with state-of-the-art preconditioned techniques. In particular, we study ILUPACK, a package for the solution of sparse linear systems via Kryl

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!