Convergence and Resilience of the Fine-Grained Parallel Incomplete LU Factorization for Non-Symmetric Problems

2017 ◽  
Keyword(s):  
Lu Factorization ◽  
Fine Grained ◽  
Incomplete Lu Factorization

Fine-Grained Parallel Incomplete LU Factorization

2015 ◽  
Vol 37 (2) ◽  
pp. C169-C193 ◽  
Author(s):  
Edmond Chow ◽  
Aftab Patel
Keyword(s):  
Lu Factorization ◽  
Fine Grained ◽  
Incomplete Lu Factorization

Boundary Element Algorithm for Modeling and Simulation of Dual-Phase Lag Bioheat Transfer and Biomechanics of Anisotropic Soft Tissues

2018 ◽  
Vol 10 (10) ◽  
pp. 1850108 ◽  
Author(s):  
Mohamed Abdelsabour Fahmy
Keyword(s):  
Boundary Element ◽  
Soft Tissues ◽  
Bioheat Transfer ◽  
Phase Lag ◽  
Dual Phase ◽  
Lu Factorization ◽  
Governing Equations ◽  
Complex Shapes ◽  
Incomplete Lu Factorization ◽  
Element Algorithm

The main aim of this paper is to propose a new boundary element algorithm for describing thermomechanical interactions in anisotropic soft tissues. The governing equations are studied based on the dual-phase lag bioheat transfer and Biot’s theory. Due to the advantages of convolution quadrature boundary element method (CQBEM), such as low CPU usage, low memory usage and suitability for treatment of soft tissues that have complex shapes, it is a versatile and powerful method for modeling of bioheat distribution in anisotropic soft tissues and the related deformation. The resulting linear systems for bioheat and mechanical equations are solved by Transpose-free quasi-minimal residual (TFQMR) solver with a dual-threshold incomplete LU factorization technique (ILUT) preconditioner that reduces the iterations number and total CPU time. Numerical results demonstrate the validity, efficiency and accuracy of the proposed algorithm and technique.

scholarly journals Spectral properties of discrete models of multi-dimensional elliptic problems with mixed derivatives

2019 ◽  
Vol 55 (2) ◽  
pp. 207-215
Author(s):  
A. U. Prakonina
Keyword(s):  
Convergence Rate ◽  
Iterative Methods ◽  
Imaginary Part ◽  
Conjugate Gradient ◽  
Discrete Models ◽  
Lu Factorization ◽  
The Matrix ◽  
Mixed Derivatives ◽  
Incomplete Lu Factorization ◽  
Number Of Iterations

The influence of the spectrum of original and preconditioned matrices on a convergence rate of iterative methods for solving systems of finite-difference equations applicable to two-dimensional elliptic equations with mixed derivatives is investigated. It is shown that the efficiency of the bi-conjugate gradient iterative methods for systems with asymmetric matrices significantly depends not only on the matrix spectrum boundaries, but also on the heterogeneity of the distribution of the spectrum components, as well as on the magnitude of the imaginary part of complex eigenvalues. For test matrices with a fixed condition number, three variants of the spectral distribution were studied and the dependences of the number of iterations on the dimension of matrices were estimated. It is shown that the non-uniformity in the eigenvalue distribution within the fixed spectrum boundaries leads to a significant increase in the number of iterations with increasing dimension of the matrices. The increasing imaginary part of the eigenvalues has a similar effect on the convergence rate. Using as an example the model potential distribution problem in a square domain, including anisotropic ring inhomogeneity, a comparative analysis of the matrix structure and the convergence rate of the bi-conjugate gradient method with Fourier – Jacobi and incomplete LU factorization preconditioners is performed. It is shown that the advantages of the Fourier – Jacobi preconditioner are associated with a more uniform distribution of the spectrum of the preconditioned matrix along the real axis and a better suppression of the imaginary part of the spectrum compared to the preconditioner based on the incomplete LU factorization.

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