Application of reproducing kernel particle method and element-free Galerkin method on the simulation of the membrane of capacitive micromachined microphone in viscothermal air

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.

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Element free Galerkin approach based on the reproducing kernel particle method for solving 2D fractional Tricomi-type equation with Robin boundary condition

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2016.11.020 ◽

2017 ◽

Vol 73 (6) ◽

pp. 1270-1285 ◽

Cited By ~ 34

Author(s):

Mehdi Dehghan ◽

Mostafa Abbaszadeh

Keyword(s):

Reproducing Kernel ◽

Type Equation ◽

Particle Method ◽

Robin Boundary Condition ◽

Reproducing Kernel Particle Method ◽

Galerkin Approach ◽

Element Free Galerkin ◽

Reproducing Kernel Particle ◽

Element Free ◽

Robin Boundary

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Penyelesaian Numerik Advection Equation 1 Dimensi dengan EFG-DGM

MEDIA KOMUNIKASI TEKNIK SIPIL ◽

10.14710/mkts.v22i1.12406 ◽

2016 ◽

Vol 22 (1) ◽

pp. 51

Author(s):

Kresno Wikan Sadono

Keyword(s):

Galerkin Method ◽

Reproducing Kernel ◽

Time Integration ◽

Particle Method ◽

Advection Equation ◽

Reproducing Kernel Particle Method ◽

Domain Space ◽

Reproducing Kernel Particle ◽

The One ◽

Element Free

Differential equation can be used to model various phenomena in science and engineering. Numerical method is the most common method used in solving DE. Numerical methods that popular today are finite difference method (FDM), finite element method (FEM) dan discontinuous Galerkin method (DGM), which the method includes mesh based. Lately, the developing methods, that are not based on a mesh, which the nodes directly spread in domain, called meshfree or meshless. Element free Galerkin method (EFG), Petrov-Galerkin meshless (MLPG), reproducing kernel particle method (RKPM) and radial basis function (RBF) fall into the category meshless or meshfree. Time integration generally use an explicit Runge Kutta 4th order, Newmark- , HHT- , Wilson- dll. This research was carried out numerical simulations DE, by combining the EFG method to solve the domain space and time integration with DGM methods. EFG using the complete order polynomial 1, and DGM used polynomial order 1. The equation used advection equation in one dimension. EFG-DGM comparison with analytical results also performed. The simulation results show the method EFG-DGM match the one-dimensional advection equations well.

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Bernstein polynomials in element-free Galerkin method

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406211401677 ◽

2011 ◽

Vol 225 (8) ◽

pp. 1808-1815 ◽

Cited By ~ 4

Author(s):

O F Valencia ◽

F J Gómez-Escalonilla ◽

D Garijo ◽

J L Díez

Keyword(s):

Boundary Conditions ◽

Galerkin Method ◽

Bernstein Polynomials ◽

Partition Of Unity ◽

Particle Method ◽

Moving Least Squares ◽

Shape Functions ◽

Element Free Galerkin Method ◽

Element Free Galerkin ◽

Element Free

In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves, can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.

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Application of an Element-free Galerkin Method to Water Wave Propagation Problems

Archives of Hydro-Engineering and Environmental Mechanics ◽

10.2478/heem-2013-0010 ◽

2014 ◽

Vol 60 (1-4) ◽

pp. 87-105 ◽

Cited By ~ 3

Author(s):

Ryszard Staroszczyk

Keyword(s):

Wave Propagation ◽

Galerkin Method ◽

Present Model ◽

Free Surface Elevation ◽

Element Free Galerkin Method ◽

Plane Flow ◽

Element Free Galerkin ◽

Proposed Model ◽

Sloping Bed ◽

Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

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