An upwind local radial basis functions-differential quadrature (RBF-DQ) method with proper orthogonal decomposition (POD) approach for solving compressible Euler equation

2018 ◽  
Vol 92 ◽  
pp. 244-256 ◽  
Author(s):  
Mehdi Dehghan ◽  
Mostafa Abbaszadeh
Keyword(s):  
Euler Equation ◽  
Proper Orthogonal Decomposition ◽  
Radial Basis Functions ◽  
Orthogonal Decomposition ◽  
Differential Quadrature ◽  
Basis Functions ◽  
Compressible Euler Equation ◽  
Compressible Euler ◽  
Radial Basis ◽  
Proper Orthogonal

scholarly journals Stochastic Fracture Analysis Using Scaled Boundary Finite Element Methods Accelerated by Proper Orthogonal Decomposition and Radial Basis Functions

Geofluids ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Xiaowei Shen ◽  
Haowen Hu ◽  
Zhongwang Wang ◽  
Xiuyun Chen ◽  
Chengbin Du
Keyword(s):  
Finite Element ◽  
Proper Orthogonal Decomposition ◽  
Radial Basis Functions ◽  
Orthogonal Decomposition ◽  
Basis Functions ◽  
Uncertain Variables ◽  
Computation Efficiency ◽  
Radial Basis ◽  
Proper Orthogonal ◽  
Scaled Boundary Finite Element

This paper presents a stochastic analysis method for linear elastic fracture mechanics using the Monte Carlo simulations (MCs) and the scaled boundary finite element method (SBFEM) based on proper orthogonal decomposition (POD) and radial basis functions (RBF). The semianalytical solutions obtained by the SBFEM enable us to capture the stress intensity factors (SIFs) easily and accurately. The adoption of POD and RBF significantly reduces the model order and increases computation efficiency, while maintaining the versatility and accuracy of MCs. Numerical examples of cracks in homogeneous and bimaterial plates are provided to demonstrate the effectiveness and reliability of the proposed method, where the crack inclination angles are set as uncertain variables. It is also found that the larger the scale of the problem, the more advantageous the proposed method is.

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