scholarly journals Randomized algorithms for generalized Hermitian eigenvalue problems with application to computing Karhunen-Loève expansion

2015 ◽  
Vol 23 (2) ◽  
pp. 314-339 ◽  
Author(s):  
Arvind K. Saibaba ◽  
Jonghyun Lee ◽  
Peter K. Kitanidis
Keyword(s):  
Randomized Algorithms ◽  
Eigenvalue Problems

scholarly journals A Revisit to CMFD Schemes: Fourier Analysis and Enhancement

Energies ◽  
2021 ◽  
Vol 14 (2) ◽  
pp. 424
Author(s):  
Dean Wang ◽  
Zuolong Zhu
Keyword(s):  
Fourier Analysis ◽  
Eigenvalue Problems ◽  
Neutron Transport ◽  
Coarse Mesh ◽  
Successive Overrelaxation ◽  
Computational Cell ◽  
Artificial Diffusion ◽  
Acceleration Method ◽  
The Stability ◽  
Partial Current

The coarse-mesh finite difference (CMFD) scheme is a very effective nonlinear diffusion acceleration method for neutron transport calculations. CMFD can become unstable and fail to converge when the computational cell optical thickness is relatively large in k-eigenvalue problems or diffusive fixed-source problems. Some variants and fixups have been developed to enhance the stability of CMFD, including the partial current-based CMFD (pCMFD), optimally diffusive CMFD (odCMFD), and linear prolongation-based CMFD (lpCMFD). Linearized Fourier analysis has proven to be a very reliable and accurate tool to investigate the convergence rate and stability of such coupled high-order transport/low-order diffusion iterative schemes. It is shown in this paper that the use of different transport solvers in Fourier analysis may have some potential implications on the development of stabilizing techniques, which is exemplified by the odCMFD scheme. A modification to the artificial diffusion coefficients of odCMFD is proposed to improve its stability. In addition, two explicit expressions are presented to calculate local optimal successive overrelaxation (SOR) factors for lpCMFD to further enhance its acceleration performance for fixed-source problems and k-eigenvalue problems, respectively.

Entropy numbers of embedding maps between Besov spaces with an application to eigenvalue problems

1981 ◽  
Vol 90 (1-2) ◽  
pp. 63-70 ◽  
Author(s):  
Bernd Carl
Keyword(s):  
Banach Space ◽  
Asymptotic Behaviour ◽  
Besov Spaces ◽  
Eigenvalue Problems ◽  
Function Spaces ◽  
Sequence Spaces ◽  
Entropy Numbers ◽  
Diagonal Operators

SynopsisIn this paper we determine the asymptotic behaviour of entropy numbers of embedding maps between Besov sequence spaces and Besov function spaces. The results extend those of M. Š. Birman, M. Z. Solomjak and H. Triebel originally formulated in the language of ε-entropy. It turns out that the characterization of embedding maps between Besov spaces by entropy numbers can be reduced to the characterization of certain diagonal operators by their entropy numbers.Finally, the entropy numbers are applied to the study of eigenvalues of operators acting on a Banach space which admit a factorization through embedding maps between Besov spaces.The statements of this paper are obtained by results recently proved elsewhere by the author.

Indefinite Eigenvalue Problems with Several Singular Points and Turning Points

2001 ◽  
Vol 229 (1) ◽  
pp. 51-71 ◽  
Author(s):  
Walter Eberhard ◽  
Gerhard Freiling ◽  
Kerstin Wilcken-Stoeber
Keyword(s):  
Eigenvalue Problems ◽  
Turning Points ◽  
Singular Points

Tensor solutions in irregular domains: Eigenvalue problems

2021 ◽  
Author(s):  
Osvaldo Guimarães ◽  
William Labecca ◽  
José R.C. Piqueira
Keyword(s):  
Eigenvalue Problems ◽  
Irregular Domains
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