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Meshless Methods and Their Numerical Properties
book

Meshless Methods and Their Numerical Properties

by Hua Li, Shantanu S. Mulay
February 2013
Intermediate to advanced content levelIntermediate to advanced
447 pages
14h 16m
English
CRC Press
Content preview from Meshless Methods and Their Numerical Properties
Formulation of classical meshless methods 15
the FEM. The local nature of the function approximation is preserved as
the WF
w
i
e
vanishes beyond certain distance. The stationarity of J with
respect to
a
e
leads to
ux NxuNxPxAxBx
h
i
i
n
iixj
ji
i
m
() () ,where () () () ()
1
1
1
∑∑
==
=
=
(2.17)
where
Ax wx
PP
i
e
ij
ik
k
m
i
n
() ()
,
11
∑∑
[]
=
==
Bx wxP
i
e
ij
i
n
() ()
1
[]
=
=
(2.18)
The necessary condition to get the nonsingular
Ax()
1
matrix is the existence
of m nodes at least in the local interpolation domain of
ux
e
()
. The approxi-
mate derivative of the function is computed by differentiating p(x) with
respect to x, by considering
a
e
as a constant, and given as
u
x
p
x
a
x
x
x
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Publisher Resources

ISBN: 9781466517462