Chapter 3 Jacobi iteration

SPARK ◽  
2018 ◽  
Author(s):  
Steffen Börm
Keyword(s):  
Jacobi Iteration

scholarly journals Second degree generalized Jacobi iteration method for solving system of linear equations

2016 ◽  
Vol 47 (2) ◽  
pp. 179-192
Author(s):  
Tesfaye Kebede Enyew
Keyword(s):  
Spectral Radius ◽  
Iteration Method ◽  
Linear Equations ◽  
System Of Linear Equations ◽  
Numerical Examples ◽  
Jacobi Iteration ◽  
Optimal Values ◽  
Second Degree

In this paper, a Second degree generalized Jacobi Iteration method for solving system of linear equations, $Ax=b$ and discuss about the optimal values $a_{1}$ and $b_{1}$ in terms of spectral radius about for the convergence of SDGJ method of $x^{(n+1)}=b_{1}[D_{m}^{-1}(L_{m}+U_{m})x^{(n)}+k_{1m}]-a_{1}x^{(n-1)}.$ Few numerical examples are considered to show that the effective of the Second degree Generalized Jacobi Iteration method (SDGJ) in comparison with FDJ, FDGJ, SDJ.

scholarly journals Wavelet Element Modelling for Inviscid Fluid–Solid Coupling Problem based on Partitioned Approach

Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3699
Author(s):  
Zhi-Bo Yang ◽  
Hao-Qi Li ◽  
Bai-Jie Qiao ◽  
Xue-Feng Chen
Keyword(s):  
Inviscid Fluid ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Partitioned Approach ◽  
Complex Shapes ◽  
Jacobi Iteration ◽  
Spatial Domains ◽  
Numerical Formulation ◽  
Alternative Choice ◽  
Element Method

To provide a simple numerical formulation based on fixed grids, a wavelet element method for fluid–solid modelling is introduced in this work. Compared with the classical wavelet finite element method, the presented method can potentially handle more complex shapes. Considering the differences between the solid and fluid regions, a damping-like interface based on wavelet elements is designed, in order to ensure consistency between the two parts. The inner regions are constructed with the same wavelet function in space. In the time and spatial domains, a partitioned approach based on Jacobi iteration is combined with the pseudo-parallel calculation method. Numerical convergence analyses show that the method can serve as an alternative choice for fluid–solid coupling modelling.

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