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It significantly improves the conditioning of the linear systems by approximating the global modes with multilevel techniques, while remaining cheap to update and apply, especially when the mesh changes. For convection-diffusion problems, it achieves a level-independent convergence rate. We then make a few extensions in the MSPAI preconditioner for topology optimization problems, which lead to nearly level-independent convergence rate and better scalability than incomplete factorization type of preconditioners.","Made available in DSpace on 2015-09-25T20:20:29Z (GMT). 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It significantly improves the conditioning of the linear systems by approximating the global modes with multilevel techniques, while remaining cheap to update and apply, especially when the mesh changes. For convection-diffusion problems, it achieves a level-independent convergence rate. We then make a few extensions in the MSPAI preconditioner for topology optimization problems, which lead to nearly level-independent convergence rate and better scalability than incomplete factorization type of preconditioners.","Made available in DSpace on 2015-09-25T20:20:29Z (GMT). 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