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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 45
Matrix G is symmetric. The solution of Equation (2.115) leads to
aGU
0
1
S
=
(2.118)
Substituting Equation (2.118) into Equation (2.108) results in
uxx
h
Q
TT
S
(, )R(x)p(x)GU
1
{}
=
(2.119)
uxx
h
Q
T
S
T
TT
(, )(x) U,where(x)
R(x) p(x)
G
1
{}
∴=
ΦΦ=
(2.120)
Equation (2.120) can be rewritten as
ux
xu
h
Q
T
Si
i
i
n
(, )(x) U
1
=
(2.121)
Equation (2.121) is the nal expression of the RBF shape functions. The
approximate derivatives of the eld variables are computed by simply dif-
ferentiating Equation (2.121) as
u
d
l
d
T
S
(x
)(
x) U
,,
(2.122)
where,
d
denotes the derivative in either the x or y coordinate direction.
The working ...
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Publisher Resources

ISBN: 9781466517462