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A Domain Decomposition Method for the Polar Factorization of Vector-Valued Mappings

J.-D. Benamou
SIAM Journal on Numerical Analysis
Vol. 32, No. 6 (Dec., 1995), pp. 1808-1838
Stable URL: http://www.jstor.org/stable/2158530
Page Count: 31
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A Domain Decomposition Method for the Polar Factorization of Vector-Valued Mappings
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Abstract

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.

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