SMOOTH_N

EXPERIMENTAL only.

• Each node point \( i\) establishes its local boundary normal by \begin{align} \tilde{\bf n}_i = \frac{ \sum\limits_{k=\text{AllTrianglesAttachedToPoint}} ({\bf p}_{k,2}-{\bf p}_{k,1}) \times ({\bf p}_{k,3}-{\bf p}_{k,1}) }{ \| ... \|_2 } \end{align} where \( {\bf p}_{k,i}, i=1...N_p\) are the node point coordinates of the shape (in most cases triangles N_p=3, sometimes quads, N_p=4)
• The boundary normal of the MESHFREE point with index \( i\) which is situated inside of the triangle with index \( k\) is computed by its shape functions, i.e. \begin{align} {\bf n}_i = \frac{ \sum\limits_{j=1...N_p} s_j \cdot \tilde{\bf n}_{k,j} }{ \| ... \|_2 } \end{align} where \( N_p\) is the number of nodes of the given boundary element.
• The shape functions are computed for each MESHFREE point in a standard way. The MESHFREE point with index \( i\) situated on the triangle with index \( k\) has the shape functions \begin{align} {\bf x}_i = \sum\limits_{j=1...N_p} s_j \cdot {\bf p}_{k,j} \end{align} with the requirement \( \sum\limits_{j=1...N_p} s_j = 1\)