A Meshless Particle Method for Poisson and Diffusion Problems with Discontinuous Coefficients and Inhomogeneous Boundary Conditions

2013 ◽  
Vol 35 (6) ◽  
pp. A2469-A2493 ◽  
Author(s):  
Nicolas Fiétier ◽  
Ömer Demirel ◽  
Ivo F. Sbalzarini
Keyword(s):  
Boundary Conditions ◽  
Particle Method ◽  
Discontinuous Coefficients ◽  
Meshless Particle Method ◽  
And Diffusion ◽  
Diffusion Problems

Implementing of Displacement Boundary Conditions of Element-Free Galerkin Method and its Applications Used in Fracture Mechanics

2012 ◽  
Vol 629 ◽  
pp. 606-610
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Dun Fu Zhang
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Transformation Method ◽  
Computational Method ◽  
Reproducing Kernel Particle Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

The main draw back of the Moving Least Squares (MLS) approximate used in element free Galerkin method (EFGM) is its lack the property of the delta function. To alleviate difficulties in the treatment of essential boundary conditions in EFGM, the local transformation method and the boundary singular weight method, which are used in the reproducing kernel particle method, is combined with the element free Galerkin method. The computational method is given to analyze the stress intensity factors and the numerical simulation of crack propagation of two-dimentional problems of the elastic fracture analysis. The application examples reveal the effectiveness and feasibility of the present methods.

ON A RESCALED NONLOCAL DIFFUSION PROBLEM WITH NEUMANN BOUNDARY CONDITIONS

2021 ◽  
Vol 10 (8) ◽  
pp. 3013-3022
Author(s):  
C.A. Gomez ◽  
J.A. Caicedo
Keyword(s):  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Neumann Boundary ◽  
Diffusion Problem ◽  
Neumann Boundary Conditions ◽  
Nonlocal Diffusion ◽  
Banach Fixed Point Theorem ◽  
Positive Continuous Function ◽  
Normalization Constant ◽  
Diffusion Problems

In this work, we consider the rescaled nonlocal diffusion problem with Neumann Boundary Conditions \[ \begin{cases} u_t^{\epsilon}(x,t)=\displaystyle\frac{1}{\epsilon^2} \int_{\Omega}J_{\epsilon}(x-y)(u^\epsilon(y,t)-u^\epsilon(x,t))dy\\ \qquad \qquad+\displaystyle\frac{1}{\epsilon}\int_{\partial \Omega}G_\epsilon(x-y)g(y,t)dS_y,\\ u^\epsilon(x,0)=u_0(x), \end{cases} \] where $\Omega\subset\mathbb{R}^{N}$ is a bounded, connected and smooth domain, $g$ a positive continuous function, $J_\epsilon(z)=C_1\frac{1}{\epsilon^N}J(\frac{z}{\epsilon}), G_\epsilon(x)=C_1\frac{1}{\epsilon^N}G(\frac{x}{\epsilon}),$ $J$ and $G$ well defined kernels, $C_1$ a normalization constant. The solutions of this model have been used without prove to approximate the solutions of a family of nonlocal diffusion problems to solutions of the respective analogous local problem. We prove existence and uniqueness of the solutions for this problem by using the Banach Fixed Point Theorem. Finally, some conclusions are given.

scholarly journals Numerical Study of Quantum Wave Packet in Meshless Particle Method

2019 ◽  
Vol 18 (3) ◽  
pp. 159-161 ◽  
Author(s):  
Fumiaki HIRONO ◽  
Misako IWASAWA ◽  
Satoru S. KANO ◽  
Yasunari ZEMPO
Keyword(s):  
Wave Packet ◽  
Numerical Study ◽  
Particle Method ◽  
Quantum Wave ◽  
Meshless Particle Method

Boundary conditions for a dual particle method

2005 ◽  
Vol 83 (17-18) ◽  
pp. 1476-1486 ◽  
Author(s):  
P.W. Randles ◽  
L.D. Libersky
Keyword(s):  
Boundary Conditions ◽  
Particle Method
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