Meshless method with ridge basis functions for modified Helmholtz equations

2010 ◽  
Author(s):  
Xinqiang Qin ◽  
Zhigang Wang ◽  
Baoshan Miao ◽  
Faning Dang
Keyword(s):  
Meshless Method ◽  
Basis Functions ◽  
Helmholtz Equations ◽  
Modified Helmholtz Equations

A Meshless Method for Solving the Mathematical Model Associated the Leakage Problem in Gas Pipeline

2014 ◽  
Vol 986-987 ◽  
pp. 1418-1421
Author(s):  
Jun Shan Li
Keyword(s):  
Differential Equation ◽  
Mathematical Model ◽  
Partial Differential Equation ◽  
Inverse Problem ◽  
Basis Function ◽  
Meshless Method ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Gas Pipeline ◽  
The Mathematical Model

In this paper, we propose a meshless method for solving the mathematical model concerning the leakage problem when the pressure is tested in the gas pipeline. The method of radial basis function (RBF) can be used for solving partial differential equation by writing the solution in the form of linear combination of radius basis functions, that is, when integrating the definite conditions, one can find the combination coefficients and then the numerical solution. The leak problem is a kind of inverse problem that is focused by many engineers or mathematical researchers. The strength of the leak can find easily by the additional conditions and the numerical solutions.

Solution for fractional distributed optimal control problem by hybrid meshless method

2016 ◽  
Vol 24 (11) ◽  
pp. 2149-2164 ◽  
Author(s):  
Majid Darehmiraki ◽  
Mohammad Hadi Farahi ◽  
Sohrab Effati
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Least Squares ◽  
Meshless Method ◽  
Basis Functions ◽  
Moving Least Squares ◽  
Distributed Optimal Control

We use a hybrid local meshless method to solve the distributed optimal control problem of a system governed by parabolic partial differential equations with Caputo fractional time derivatives of order α ∈ (0, 1]. The presented meshless method is based on the linear combination of moving least squares and radial basis functions in the same compact support, this method will change between interpolation and approximation. The aim of this paper is to solve the system of coupled fractional partial differential equations, with necessary and sufficient conditions, for fractional distributed optimal control problems using a combination of moving least squares and radial basis functions. To keep matters simple, the problem has been considered in the one-dimensional case, however the techniques can be employed for both the two- and three-dimensional cases. Several test problems are employed and results of numerical experiments are presented. The obtained results confirm the acceptable accuracy of the proposed method.

Meshless method with ridge basis functions for time fractional two-flow domain model

2020 ◽  
Vol 14 (4) ◽  
pp. 375-385
Author(s):  
Xinqiang Qin ◽  
Keyuan Li ◽  
Gang Hu
Keyword(s):  
Meshless Method ◽  
Basis Functions ◽  
Domain Model ◽  
Flow Domain

Coupling of 2D discretized Peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour

2017 ◽  
Vol 34 (5) ◽  
pp. 1334-1366 ◽  
Author(s):  
Arman Shojaei ◽  
Mirco Zaccariotto ◽  
Ugo Galvanetto
Keyword(s):  
Meshless Method ◽  
Design Methodology ◽  
Surface Effect ◽  
Boundary Region ◽  
Basis Functions ◽  
Gradual Transition ◽  
Classical Elasticity ◽  
Content Type ◽  
Future Studies ◽  
The Road

Purpose The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems. Design/methodology/approach The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place. Findings The new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points. Originality/value The current study paves the road for future studies on dynamic and static crack propagation problems.

Sign in / Sign up

Export Citation Format

Share Document