Computing constrained energy-minimizing flows

Conservative flows that minimize the kinetic energy have be linked to the problem of optimal transport, a field with numerous applications in many areas of mathematics, science and engineering ranging from probability theory, fluid dynamics meteorology, oceanography to antenna design, image registration and shape analysis among others. This paper solves the problem of computing energy-minimizing flows under prescribed constraints. In addition to mass conservation, which is imposed through the continuity equation, the density and the momentum of the flow can be constrained to belong to a given feasible set. A family of algorithms is introduced to solve a class of constrained saddle point problems, which has computing constrained energy-minimizing flows as a special case. Numerical experiments demonstrating the working of the algorithms and measuring their performance are presented.