Interdisciplinary Applied Mathematics

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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,


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x position


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(mm)


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

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