A finite point method for the fractional cable equation using meshless smoothed gradients

2022 ◽  
Vol 134 ◽  
pp. 453-465
Author(s):  
Xiaolin Li ◽  
Shuling Li
Keyword(s):  
Point Method ◽  
Cable Equation ◽  
Finite Point ◽  
Finite Point Method ◽  
Fractional Cable Equation

scholarly journals Real-Time Computer Simulation of Three Dimensional Elastostatics Using the Finite Point Method

2011 ◽  
Vol 110-116 ◽  
pp. 2740-2745
Author(s):  
Kirana Kumara P. ◽  
Ashitava Ghosal
Keyword(s):  
Real Time ◽  
Graphics Processing Unit ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Point Method ◽  
Processing Unit ◽  
Finite Point ◽  
Deformable Solids ◽  
Finite Point Method ◽  
Linear Elastostatics

Real-time simulation of deformable solids is essential for some applications such as biological organ simulations for surgical simulators. In this work, deformable solids are approximated to be linear elastic, and an easy and straight forward numerical technique, the Finite Point Method (FPM), is used to model three dimensional linear elastostatics. Graphics Processing Unit (GPU) is used to accelerate computations. Results show that the Finite Point Method, together with GPU, can compute three dimensional linear elastostatic responses of solids at rates suitable for real-time graphics, for solids represented by reasonable number of points.

Two Implicit Meshless Finite Point Schemes for the Two-Dimensional Distributed-Order Fractional Equation

2019 ◽  
Vol 19 (4) ◽  
pp. 813-831
Author(s):  
Rezvan Salehi
Keyword(s):  
Reproducing Kernel ◽  
Point Method ◽  
Least Square ◽  
Computationally Efficient ◽  
Finite Point ◽  
Moving Least Square ◽  
Point Collocation ◽  
Finite Point Method ◽  
Distributed Order ◽  
Fractional Equation

AbstractIn this paper, the distributed-order time fractional sub-diffusion equation on the bounded domains is studied by using the finite-point-type meshless method. The finite point method is a point collocation based method which is truly meshless and computationally efficient. To construct the shape functions of the finite point method, the moving least square reproducing kernel approximation is employed. Two implicit discretisation of order{O(\tau)}and{O(\tau^{1+\frac{1}{2}\sigma})}are derived, respectively. Stability and{L^{2}}norm convergence of the obtained difference schemes are proved. Numerical examples are provided to confirm the theoretical results.

Improvement of the flow formulation by recovery of the hydrostatic pressure using the finite point method

2006 ◽  
Vol 65 (9) ◽  
pp. 1403-1418
Author(s):  
H. Dalayeli ◽  
H. Hashemolhosseini ◽  
M. Farzin ◽  
B. Soltani
Keyword(s):  
Hydrostatic Pressure ◽  
Point Method ◽  
Finite Point ◽  
Finite Point Method

scholarly journals Free Transverse Vibration Analysis of Axially Functionally Graded Tapered Euler-Bernoulli Beams through Spline Finite Point Method

2016 ◽  
Vol 2016 ◽  
pp. 1-23 ◽  
Author(s):  
Peng Liu ◽  
Kun Lin ◽  
Hongjun Liu ◽  
Rong Qin
Keyword(s):  
Boundary Conditions ◽  
Transverse Vibration ◽  
Spline Interpolation ◽  
Computational Cost ◽  
Functionally Graded ◽  
Point Method ◽  
Finite Point ◽  
Various Boundary Conditions ◽  
Finite Point Method ◽  
Free Transverse Vibration

A new model for the free transverse vibration of axially functionally graded (FG) tapered Euler-Bernoulli beams is developed through the spline finite point method (SFPM) by investigating the effects of the variation of cross-sectional and material properties along the longitudinal directions. In the proposed method, the beam is discretized with a set of uniformly scattered spline nodes along the beam axis instead of meshes, and the displacement field is approximated by the particularly constructed cubic B-spline interpolation functions with good adaptability for various boundary conditions. Unlike traditional discretization and modeling methods, the global structural stiffness and mass matrices for beams of the proposed model are directly generated after spline discretization without needing element meshes, generation, and assembling. The proposed method shows the distinguished features of high modeling efficiency, low computational cost, and convenience for boundary condition treatment. The performance of the proposed method is verified through numerical examples available in the published literature. All results demonstrate that the proposed method can analyze the free vibration of axially FG tapered Euler-Bernoulli beams with various boundary conditions. Moreover, high accuracy and efficiency can be achieved.

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