Spectral meshless radial point interpolation (SMRPI) method to two-dimensional fractional telegraph equation

2015 ◽  
Vol 39 (7) ◽  
pp. 1820-1835 ◽  
Author(s):  
Elyas Shivanian
Keyword(s):  
Telegraph Equation ◽  
Two Dimensional ◽  
Fractional Telegraph Equation ◽  
Radial Point Interpolation ◽  
Point Interpolation

scholarly journals An interaction integral method for evaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method

2015 ◽  
Vol 18 (2) ◽  
pp. 106-113
Author(s):  
Nha Thanh Nguyen ◽  
Hien Thai Nguyen ◽  
Minh Ngoc Nguyen ◽  
Thien Tich Truong
Keyword(s):  
Integral Method ◽  
Interpolation Method ◽  
Two Dimensional ◽  
Radial Point Interpolation Method ◽  
Interaction Integral ◽  
Crack Problems ◽  
Radial Point Interpolation ◽  
T Stress ◽  
Point Interpolation Method ◽  
Point Interpolation

The so-called T-stress, or second term of the William (1957) series expansion for linear elastic crack-tip fields, has found many uses in fracture mechanics applications. In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. The T-stress can be calculated directly from a path independent interaction integral entirely based on the J-integral by simply the auxiliary field. Several benchmark examples in 2D crack problem are performed and compared with other existing solutions to illustrate the correction of the presented approach.

A Coupled FE-Meshfree Triangular Element for Acoustic Radiation Problems

2020 ◽  
pp. 2041002
Author(s):  
Wei Li ◽  
Qifan Zhang ◽  
Qiang Gui ◽  
Yingbin Chai
Keyword(s):  
Acoustic Radiation ◽  
Interpolation Method ◽  
Partition Of Unity ◽  
Local Approximation ◽  
Triangular Element ◽  
Two Dimensional ◽  
Shape Functions ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

To improve the accuracy of the standard finite element (FE) solutions for acoustic radiation computation, this work presents the coupling of a radial point interpolation method (RPIM) with the standard FEM based on triangular (T3) mesh to give a coupled “FE-Meshfree” Trig3-RPIM element for two-dimensional acoustic radiation problems. In this coupled Trig3-RPIM element, the local approximation (LA) is represented by the polynomial-radial basis functions and the partition of unity (PU) concept is satisfied using the standard FEM shape functions. Incorporating the present coupled Trig3-RPIM element with the appropriate non-reflecting boundary condition, the two-dimensional acoustic radiation problems in exterior unbounded domain can be successfully solved. The numerical results demonstrate that the present coupled Trig3-RPIM have significant superiorities over the standard FEM and can be regarded as a competitive numerical techniques for exterior acoustic computation.

Two-Dimensional Legendre Wavelets for Solving Time-Fractional Telegraph Equation

2014 ◽  
Vol 6 (2) ◽  
pp. 247-260 ◽  
Author(s):  
M. H. Heydari ◽  
M. R. Hooshmandasl ◽  
F. Mohammadi
Keyword(s):  
Numerical Solution ◽  
Fractional Integration ◽  
Telegraph Equation ◽  
Operational Matrices ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Fractional Telegraph Equation ◽  
Manageable Method

AbstractIn this paper, we develop an accurate and efficient Legendre wavelets method for numerical solution of the well known time-fractional telegraph equation. In the proposed method we have employed both of the operational matrices of fractional integration and differentiation to get numerical solution of the time-telegraph equation. The power of this manageable method is confirmed. Moreover the use of Legendre wavelet is found to be accurate, simple and fast.

XRPIM versus XFEM

2013 ◽  
Vol 10 (01) ◽  
pp. 1340006 ◽  
Author(s):  
S. LIU
Keyword(s):  
Extended Finite Element Method ◽  
Interpolation Method ◽  
Partition Of Unity ◽  
Moving Boundaries ◽  
Two Dimensional ◽  
Extended Finite Element ◽  
Material Interfaces ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation

We present an extended radial point interpolation method (XRPIM) for modeling cracks and material interfaces in two-dimensional elasto-static problems. Therefore, partition of unity enrichment is incorporated into RPIM. We employ both step enrichment and crack tip enrichment for cracks. The studies are restricted to stationary cracks though the method can be extended easily to moving boundaries. We compare the results to the extended finite element method to show the superiority of our method. We show for two selected problems that the error is of magnitudes lower compared to XFEM simulations.

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