How to evaluate natural coordinates from global coordinates?
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For 3D isoparametric elements, we could easily find evaluate x(r,s,t), y(r,s,t) and z(r,s,t) from (r,s,t). Given a global point (x,y,z), how could we find/derive the corresponding nature coordinate (r,s,t)? Is there any equation? Even for linear element, the coordinate transformation is not linear.
This is a practical FEM implementation issue, if a user wants to query a displacement at a given global point, how can we do that? If we know the (r, s, t), then we could easily find the U(r, s, t) = ΣNi(r, s, t)Ui
