Partial optimal transport for a constant-volume Lagrangian mesh with free boundaries

This article introduces a representation of dynamic meshes, adapted to some numerical simulations that require controlling the volume objects with free boundaries, such as incompressible fluid simulation, astrophysical at cosmological scale, and shape/topology optimization. The algorithm decomposes simulated object into set convex cells called Laguerre diagram, parameterized by position N points in 3D additional parameters control volumes cells. These are found (unique) solution optimization problem – semi-discrete Monge-Ampère equation stemming from optimal transport theory. In this article, setting is extended boundaries arbitrary topology, evolving domain shape, solving partial problem. resulting Lagrangian scheme makes it possible accurately object, while precisely computing intersections boundary, interactions, collisions, changes topology.