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Isogeometric Analysis of New Efficient Moving Mesh Technique for elliptic problems based on Optimal Transport Problem
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We propose a new approach based on the optimal transport problem, in particular, a solution of the Monge-Ampere equation using a method proposed by Benamou et al. Thus, our process preserves the exact geometry using optimal one-to-one mapping. The performance of the computation of adapted mesh on a more complex general geometry is given by a new proposed illustration of mesh adaptation that allows us to solve Monge-Ampère always in the patch and to use the fast diagonalization method based on Kronecker algebra. Finally, the global efficiency of our new method is then the independent has each complex geometry but just the initial mapping in two- and three-dimensional spaces.
