A Version of the Bundle Idea for Minimizing a Nonsmooth Function: Conceptual Idea, Convergence Analysis, Numerical Results

1992 ◽  
Vol 2 (1) ◽  
pp. 121-152 ◽  
Author(s):  
Helga Schramm ◽  
Jochem Zowe
Keyword(s):  
Convergence Analysis ◽  
Numerical Results ◽  
Nonsmooth Function

An Adaptive Combined Preconditioner with Applications in Radiation Diffusion Equations

2015 ◽  
Vol 18 (5) ◽  
pp. 1313-1335 ◽  
Author(s):  
Xiaoqiang Yue ◽  
Shi Shu ◽  
Xiao wen Xu ◽  
Zhiyang Zhou
Keyword(s):  
Convergence Analysis ◽  
Estimation Theory ◽  
Numerical Results ◽  
Diffusion Equations ◽  
Condition Numbers ◽  
Radiation Diffusion ◽  
Discrete Problems ◽  
Preconditioned Gmres

AbstractThe paper aims to develop an effective preconditioner and conduct the convergence analysis of the corresponding preconditioned GMRES for the solution of discrete problems originating from multi-group radiation diffusion equations. We firstly investigate the performances of the most widely used preconditioners (ILU(k) and AMG) and their combinations (Bco and Bco), and provide drawbacks on their feasibilities. Secondly, we reveal the underlying complementarity of ILU(k) and AMG by analyzing the features suitable for AMG using more detailed measurements on multiscale nature of matrices and the effect of ILU(k) on multiscale nature. Moreover, we present an adaptive combined preconditioner Bcoα involving an improved ILU(0) along with its convergence constraints. Numerical results demonstrate that Bcoα-GMRES holds the best robustness and efficiency. At last, we analyze the convergence of GMRES with combined preconditioning which not only provides a persuasive support for our proposed algorithms, but also updates the existing estimation theory on condition numbers of combined preconditioned systems.

scholarly journals Prediction of a methane circular pool fire with fireFoam

2018 ◽  
Vol 240 ◽  
pp. 05026
Author(s):  
Camilo Sedano ◽  
Omar López ◽  
Alexander Ladino ◽  
Felipe Muñoz
Keyword(s):  
Large Eddy Simulation ◽  
Convergence Analysis ◽  
Three Dimensional ◽  
Numerical Results ◽  
Pool Fire ◽  
Medium Scale ◽  
Eddy Simulation ◽  
Large Eddy

In the present work, the fireFoam solver was used with Large Eddy Simulation (LES) and the Eddy Dissipation Concept (EDC) for modelling a medium-scale methane pool fire. A convergence analysis performed, showed that a 2 Million elements three-dimensional mesh, is good enough to attain good numerical results. By comparing the numerical results obtained, with the experimental ones, as well as numerical results from previous studies, it was proven that the fireFoam solver is able to obtain satisfactory results.

scholarly journals An improvement of H. Wang preconditioner for L-matrices

2016 ◽  
Vol 5 (4) ◽  
pp. 182
Author(s):  
Hamideh Nasabzadeh
Keyword(s):  
Iterative Method ◽  
Convergence Analysis ◽  
Diagonal Element ◽  
Numerical Results

In this paper, we improve the preconditioner, that introduced by H. Wang et al [6]. The H. Wang preconditioner \(P\in R^{n\times n}\) has only one non-zero, non-diagonal element in \(P_{n1}\) or \(P_{1n}\) , when \(a_{1n}a_{n1}\ne 0\) . But the new preconditioner has only one non-zero, non-diagonal element in  \(P_{ij}\) or  \(P_{ji}\) if \(a_{ij}a_{ji}\ne 0\), so the H. Wang preconditioner is a spacial case of the new preconditioner for L-matrices. Also we present two models to construct a better \(I+S\) type preconditioner for the   \(AOR\) iterative method. Convergence analysis are given, numerical results are presented which show the effectiveness of the new preconditioners.

scholarly journals Anderson Acceleration of the Arnoldi-Inout Method for Computing PageRank

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 636
Author(s):  
Xia Tang ◽  
Chun Wen ◽  
Xian-Ming Gu ◽  
Zhao-Li Shen
Keyword(s):  
Fixed Point ◽  
Convergence Analysis ◽  
Linear Combination ◽  
Computational Cost ◽  
Numerical Results ◽  
New Method ◽  
Fixed Point Iteration ◽  
Anderson Acceleration

Anderson(m0) extrapolation, an accelerator to a fixed-point iteration, stores m0+1 prior evaluations of the fixed-point iteration and computes a linear combination of those evaluations as a new iteration. The computational cost of the Anderson(m0) acceleration becomes expensive with the parameter m0 increasing, thus m0 is a common choice in most practice. In this paper, with the aim of improving the computations of PageRank problems, a new method was developed by applying Anderson(1) extrapolation at periodic intervals within the Arnoldi-Inout method. The new method is called the AIOA method. Convergence analysis of the AIOA method is discussed in detail. Numerical results on several PageRank problems are presented to illustrate the effectiveness of our proposed method.

Sign in / Sign up

Export Citation Format

Share Document