A Domain Decomposition Method for the Polar Factorization of Vector-Valued Mappings
Jean‐David Benamou · SIAM Journal on Numerical Analysis · 1995
We prove the convergence of an overlapping domain decomposition method for the polar factorization of vector-valued mappings. We introduce a consistent discretization of this problem under the form of an assignment problem. The domain decomposition method applied to the discrete problem does not necessarily produce the wanted discrete solution. However, we prove that the sequence of outputs it produces when we refine the discretization tends to the solution of the continuous problem.