Numerical integration of the Galerkin weak form in meshfree methods

1999 ◽  
Vol 23 (3) ◽  
pp. 219-230 ◽  
Author(s):  
John Dolbow ◽  
Ted Belytschko
Keyword(s):  
Numerical Integration ◽  
Weak Form ◽  
Meshfree Methods

scholarly journals A New Meshless “Fragile Points Method (FPM)” Based on a Galerkin Weak-Form for 2D Flexoelectric Analysis

2020 ◽  
Author(s):  
Yue Guan ◽  
Leiting Dong ◽  
Satya N. Atluri
Keyword(s):  
Numerical Integration ◽  
Sparse Matrices ◽  
Weak Form ◽  
Test Functions ◽  
The Finite Element Method ◽  
Element Free Galerkin ◽  
Piezoelectric Effects ◽  
Numerical Fluxes ◽  
Element Free ◽  
Methods Numerical

Abstract A meshless Fragile Points Method (FPM) is presented for analyzing 2D flexoelectric problems. Local, simple, polynomial and discontinuous trial and test functions are generated with the help of a local meshless differential quadrature approximation of the first three derivatives. Interior Penalty Numerical Fluxes are employed to ensure the consistency of the method. Based on a Galerkin weak-form formulation, the present FPM leads to symmetric and sparse matrices, and avoids the difficulties of numerical integration in the previous meshfree methods. Numerical examples including isotropic and anisotropic materials with flexoelectric and piezoelectric effects are provided as validations. The present method is much simpler than the Finite Element Method, or the Element-Free Galerkin (EFG) and Meshless Local Petrov-Galerkin (MLPG) methods, and the numerical integration of the weak form is trivially simple.

A background decomposition method for domain integration in weak-form meshfree methods

2014 ◽  
Vol 142 ◽  
pp. 64-78 ◽  
Author(s):  
M.R. Hematiyan ◽  
A. Khosravifard ◽  
G.R. Liu
Keyword(s):  
Decomposition Method ◽  
Weak Form ◽  
Meshfree Methods ◽  
Domain Integration

The orbit of Pluto over a long interval of time

1966 ◽  
Vol 25 ◽  
pp. 227-229 ◽  
Author(s):  
D. Brouwer
Keyword(s):  
Periodic Orbit ◽  
Numerical Integration ◽  
Restricted Problem ◽  
Three Dimensional ◽  
The Third ◽  
Circular Restricted Problem ◽  
Resonance Relation

The paper presents a summary of the results obtained by C. J. Cohen and E. C. Hubbard, who established by numerical integration that a resonance relation exists between the orbits of Neptune and Pluto. The problem may be explored further by approximating the motion of Pluto by that of a particle with negligible mass in the three-dimensional (circular) restricted problem. The mass of Pluto and the eccentricity of Neptune's orbit are ignored in this approximation. Significant features of the problem appear to be the presence of two critical arguments and the possibility that the orbit may be related to a periodic orbit of the third kind.

NUMERICAL INTEGRATION IN THE PRESENCE OF SINGULARITIES

1981 ◽  
Vol 1 (1) ◽  
pp. 83-85 ◽  
Author(s):  
Moran P.A.P.
Keyword(s):  
Numerical Integration
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