scholarly journals A New Iterative Method for Linear Systems from XFEM

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Jianping Zhao ◽  
Yanren Hou ◽  
Haibiao Zheng ◽  
Bo Tang
Keyword(s):  
Finite Element Method ◽  
Iterative Method ◽  
Model Problem ◽  
Linear Equations ◽  
Governing Equations ◽  
Numerical Examples ◽  
Cpu Time ◽  
Whole Process ◽  
Linear Elastostatics ◽  
New Iterative Method

The extend finite element method (XFEM) is popular in structural mechanics when dealing with the problem of the cracked domains. XFEM ends up with a linear system. However, XFEM usually leads to nonsymmetric and ill-conditioned stiff matrix. In this paper, we take the linear elastostatics governing equations as the model problem. We propose a new iterative method to solve the linear equations. Here we separate two variablesUand Enr, so that we change the problems into solving the smaller scale equations iteratively. The new program can be easily applied. Finally, numerical examples show that the proposed method is more efficient than common methods; we compare theL2-error and the CPU time in whole process. Furthermore, the new XFEM can be applied and optimized in many other problems.

scholarly journals A New Iterative Method for Finding Approximate Inverses of Complex Matrices

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
M. Kafaei Razavi ◽  
A. Kerayechian ◽  
M. Gachpazan ◽  
S. Shateyi
Keyword(s):  
Iterative Method ◽  
Order Of Convergence ◽  
Complex Matrices ◽  
Approximate Inverse ◽  
Numerical Examples ◽  
Convergence Behavior ◽  
Approximate Inverses ◽  
Nonsingular Matrices ◽  
New Iterative Method

This paper presents a new iterative method for computing the approximate inverse of nonsingular matrices. The analytical discussion of the method is included to demonstrate its convergence behavior. As a matter of fact, it is proven that the suggested scheme possesses tenth order of convergence. Finally, its performance is illustrated by numerical examples on different matrices.

An efficient iterative algorithm for the natural convection equations based on finite element method

2018 ◽  
Vol 28 (3) ◽  
pp. 584-605 ◽  
Author(s):  
Lei Wang ◽  
Jian Li ◽  
Pengzhan Huang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Natural Convection ◽  
Iterative Method ◽  
Error Correction ◽  
Computational Time ◽  
Content Type ◽  
Natural Convection Problem ◽  
New Iterative Method ◽  
Element Method

Purpose This paper aims to propose a new highly efficient iterative method based on classical Oseen iteration for the natural convection equations. Design/methodology/approach First, the authors solve the problem by the Oseen iterative scheme based on finite element method, then use the error correction strategy to control the error arising. Findings The new iterative method not only retains the advantage of the Oseen scheme but also saves computational time and iterative step for solving the considered problem. Originality/value In this work, the authors introduce a new iterative method to solve the natural convection equations. The new algorithm consists of the Oseen scheme and the error correction which can control the errors from the iterative step arising for solving the nonlinear problem. Comparing with the classical iterative method, the new scheme requires less iterations and is also capable of solving the natural convection problem at higher Rayleigh number.

scholarly journals Analyzing a New Third Order Iterative Method for Solving Nonlinear Problems

2021 ◽  
pp. 72-90
Author(s):  
M. S. Ndayawo ◽  
B. Sani
Keyword(s):  
Iterative Method ◽  
Series Expansion ◽  
Nonlinear Problems ◽  
Third Order ◽  
Numerical Examples ◽  
Adomian Method ◽  
The Individual ◽  
New Iterative Method ◽  
Number Of Iterations ◽  
Taylor’S Series

In this paper, we propose and analyse a new iterative method for solving nonlinear equations. The method is constructed by applying Adomian method to Taylor’s series expansion. Using one-way analysis of variance (ANOVA), the method is being compared with other existing methods in terms of the number of iterations and solution to convergence between the individual methods used. Numerical examples are used in the comparison to justify the efficiency of the new iterative method.

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