R. M. Lewis and S. G. Nash, "A multigrid approach to the optimization of systems governed by differential equations," in 8-th AIAA/USAF/ISSMO Symp. Multidisciplinary Analysis and Optimization, Long Beach, CA, 2000. Home/Search Document Not in Database Summary Related Articles Check |
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A General Framework for Nonlinear Multigrid Inversion - Oh, Milstein, Bouman, Webb (Correct)
....the finite element method. In [44] 45] Ye, et al. formulated the multigrid approach directly in an optimization framework, and used the method to solve ODT problems. In related work, Nash and Lewis formulated multigrid algorithms for the solution of a broad class of optimization problems [46] [47]. Importantly, both the approaches of Ye and Nash are based on the matching of cost functional derivatives at different scales. In this paper we propose a method we call multigrid inversion. Multigrid inversion is a general approach for applying nonlinear multigrid optimization to the solution of ....
....be the same at the coarse and fine scales, giving ) y ) 12) This yields the update for y : 13) Intuitively, the term in the bracket compensates for the forward model mismatch between resolutions. Next, we use the condition introduced in [44] 45] 46] [47] to enforce the condition that the gradients of the coarse and fine cost functionals be equal at the current values of x and x . More precisely, we enforce the condition that rc (q 1) I = rc )I (q 1) 14) This condition is essential to assure that the optimum solution is ....
R. M. Lewis and S. G. Nash, "A multigrid approach to the optimization of systems governed by differential equations," in 8-th AIAA/USAF/ISSMO Symp. Multidisciplinary Analysis and Optimization, Long Beach, CA, 2000.
First-Order Frameworks for Managing Models in Engineering.. - Alexandrov, Lewis (2000) Self-citation (Lewis) (Correct)
.... (x) and construct fi c (x) fi(x c ) rfi(x c ) T (x Gamma x c ) 3 1st Int Workshop on Surrogate Modelling and Space Mapping for Eng Opt, 11 16 19 00, TDU Then a c (x) fi c (x)f lo (x) satisfies the consistency conditions (3) 4) For an alternative, additive correction scheme, see [30]. Convergence analysis of the resulting AMMO schemes relies on the consistency conditions and standard assumptions for the convergence analysis of the underlying optimization algorithm [5] For general problems, our current preferred AMMO scheme is based on sequential quadratic programming. ....
....are computed by executing a single physical model on meshes of varying degree of refinement. Such models are frequently available in engineering optimization, and we discuss one instance later. An elaboration of the fundamental AMMO idea leads to the multigrid optimization scheme discussed in [30]. Finally, the most provocative choice of models is that of variable fidelity physics models. For instance, in aerodynamics, the physical models range from linear potential models that describe inviscid, irrotational, incompressible flow to Navier Stokes equations for nonlinear viscous flow. Our ....
R. M. Lewis and S. G. Nash, A multigrid approach to the optimization of systems governed by differential equations. AIAA Paper 2000-4890, 2000.
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