# Interdisciplinary Applied Mathematics

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у) ^

/ j    0.9

i =1

dy2

NP

E

d2N!{x, y) „ dxdy 1

The finite cloud method uses a point collocation technique (Aluru, 2000) to discretize the governing equations. Point collocation is the easiest way to discretize the governing equations. In a point collocation approach, the governing equations for a physical problem can be written in the following general form:

L(u(x, y)) = f (x,y)    in Q,

G(u(x,y)) = g(x,y)    on Гд,

H(u(x,y)) = h(x,y)    on Гн,

I”5

0 2    0 3

0 4    0 5

x position

0 6    0 7    0 8    0 9

,mm)

0 5

 •; • • • •. •… • *. 9 ‘ * ’. ‘ •» . 8 ’* * : *•’ * ’ — 7 * **. • .• * ‘ • •• ’. “■ ‘.. 6 — * ’ ‘: • • ‘ 5- . * **. • .’ •A . : • •. ■ • • •• • 4-‘ .• •. •. . • *• *. ’* • ..■• •’ * • , .•••.: • • ’ v 2 ■■ V * ». •’ t . ‘ .

1    0    0 1    0 2    0 3    0 4    0 5

x position

0 6    0 7    0 8    0 9    1

(mm)

FIGURE 14.10. Meshless method: Uniform (left) and random (right) point distribution.

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