scholarly journals On the robustness of elliptic resolvents computed by means of the technique of hierarchical matrices

2008 ◽  
Vol 58 (12) ◽  
pp. 1844-1851
Author(s):  
M. Espig ◽  
W. Hackbusch
Keyword(s):  
Hierarchical Matrices

scholarly journals Solution of Large Scale Algebraic Matrix Riccati Equations by Use of Hierarchical Matrices

Computing ◽  
2003 ◽  
Vol 70 (2) ◽  
pp. 121-165 ◽  
Author(s):  
L. Grasedyck ◽  
W. Hackbusch ◽  
B. N. Khoromskij
Keyword(s):  
Large Scale ◽  
Riccati Equations ◽  
Hierarchical Matrices

scholarly journals Preconditioners for hierarchical matrices based on their extended sparse form

2016 ◽  
Vol 31 (1) ◽  
Author(s):  
Darya A. Sushnikova ◽  
Ivan V. Oseledets
Keyword(s):  
Numerical Solution ◽  
Linear Systems ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Hierarchical Matrices ◽  
Dense Matrices

AbstractIn this paper we consider linear systems with dense-matrices which arise from numerical solution of boundary integral equations. Such matrices can be well-approximated with ℋ

scholarly journals Parallel Hierarchical Matrices with Adaptive Cross Approximation on Symmetric Multiprocessing Clusters

2014 ◽  
Vol 22 (4) ◽  
pp. 642-650 ◽  
Author(s):  
Akihiro Ida ◽  
Takeshi Iwashita ◽  
Takeshi Mifune ◽  
Yasuhito Takahashi
Keyword(s):  
Hierarchical Matrices ◽  
Adaptive Cross Approximation ◽  
Symmetric Multiprocessing

scholarly journals Modeling of spatial uncertainties in the magnetic reluctivity

2017 ◽  
Vol 36 (4) ◽  
pp. 1151-1167 ◽  
Author(s):  
Radoslav Jankoski ◽  
Ulrich Römer ◽  
Sebastian Schöps
Keyword(s):  
Hierarchical Matrices ◽  
Electrical Machines ◽  
Computationally Efficient ◽  
Standard Deviation Increase ◽  
Suggested Approach ◽  
Content Type ◽  
Efficient Approach ◽  
Dense Matrices ◽  
The Impact ◽  
Matrix Vector

Purpose The purpose of this paper is to present a computationally efficient approach for the stochastic modeling of an inhomogeneous reluctivity of magnetic materials. These materials can be part of electrical machines such as a single-phase transformer (a benchmark example that is considered in this paper). The approach is based on the Karhunen–Loève expansion (KLE). The stochastic model is further used to study the statistics of the self-inductance of the primary coil as a quantity of interest (QoI). Design/methodology/approach The computation of the KLE requires solving a generalized eigenvalue problem with dense matrices. The eigenvalues and the eigenfunction are computed by using the Lanczos method that needs only matrix vector multiplications. The complexity of performing matrix vector multiplications with dense matrices is reduced by using hierarchical matrices. Findings The suggested approach is used to study the impact of the spatial variability in the magnetic reluctivity on the QoI. The statistics of this parameter are influenced by the correlation lengths of the random reluctivity. Both, the mean value and the standard deviation increase as the correlation length of the random reluctivity increases. Originality/value The KLE, computed by using hierarchical matrices, is used for uncertainty quantification of low frequency electrical machines as a computationally efficient approach in terms of memory requirement, as well as computation time.

scholarly journals Likelihood approximation with hierarchical matrices for large spatial datasets

2019 ◽  
Vol 137 ◽  
pp. 115-132 ◽  
Author(s):  
Alexander Litvinenko ◽  
Ying Sun ◽  
Marc G. Genton ◽  
David E. Keyes
Keyword(s):  
Hierarchical Matrices ◽  
Likelihood Approximation ◽  
Spatial Datasets

LDRD Final Report: Fast and Robust Linear Solvers based on Hierarchical Matrices.

2019 ◽  
Author(s):  
Erik Gunnar Boman ◽  
Eric Darve ◽  
Richard B. Lehoucq ◽  
Sivasankaran Rajamanickam ◽  
Raymond S. Tuminaro ◽  
...  
Keyword(s):  
Hierarchical Matrices ◽  
Final Report ◽  
Linear Solvers
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