I am trying to develop a mathematical method to calculate the pressure field on offshore structures.
We are given the resultant force on the structure F, and a pressure
profile model pi = p0 dot(ni,nF) that our solution should follow. Where:
{pi}_{i=1}^{Nel}are the pressures defined in the elements of the structure (see figure);niare the outward normals of the elements (dot is the scalar prod)Aiare element areas;nf=F/|F|;p0is the effective pressure of the model.
I am using an optimazition algorithm using an objective function with two terms:
PHI = \alpha * ||F-F_rec ||_2^2 + \Sum_i (p0*dot(ni,nF) - pi)^2
to get the figures I am showing. where F_rec = \sum_i pi Ai ni.
I would like to add a new term in the objective accounting for continuity in the pressure field. So far I have been thinking in a third term like:
\beta * \sum_i 1/3(\sum_{j=neig(i) (pi*dot(nj,nF) - pj*dot(ni,nF))^2})
Where \alpha and \beta are constants controlling the importance of each term in the objective.
Other possibility is that the third term accounts for the total variation of the
pressure field (or maybe pi/dot(ni,nF) field). Do you have any idea of how I can define a third term measuring the total variation in a surface like this?
Thanks a lot!
