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Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations |
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| Authors: | Valery Agoshkov Paola Gervasio Alfio Quarteroni |
| Institution: | 1. Institute of Numerical Mathematics, Russian Academy of Sciences, 119991, GSP-1, Moscow, Russia 2. Dipartimento di Matematica, Universit? di Brescia, 25133, Brescia, Italy 3. MOX, Dipartimento di Matematica, Politecnico di Milano, 20133, Milano, Italy 4. CMCS-EPFL, CH-1015, Lausanne, Switzerland |
| Abstract: | New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem, and the convergence of iterative processes is analyzed. The work was supported by the Russian Foundation for Basic Research (04-01-00615) and it was partly carried out while the first author was visiting the IACS at EPFL. |
| Keywords: | Primary 65N55 Secondary 35B37 49N45 |
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