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SUMMARY:An optimization framework for adaptive PDE solutions applied to fl
 uid dynamics - David Darmofal (MIT)
DTSTART:20130118T160000Z
DTEND:20130118T170000Z
UID:TALK42531@talks.cam.ac.uk
CONTACT:Dr Ed Brambley
DESCRIPTION:Improving the autonomy\, efficiency\, and reliability of compu
 tational fluid dynamics algorithms has become increasingly important as po
 werful computers enable characterization of the input-output relationship 
 of complex PDE-governed processes. This work is a step towards the develop
 ment of a versatile PDE solver that accurately predicts output quantities 
 of interest to user-prescribed accuracy in a fully automated manner.   Giv
 en a discretization and a localizable error estimate\, the framework itera
 tes toward a mesh that minimizes the error for a given number of degrees o
 f freedom by considering a continuous optimization problem of the Riemanni
 an metric field. The adaptation procedure consists of three key steps: sam
 pling of the anisotropic error behavior using element-wise local solves\; 
 synthesis of the local errors to construct a surrogate error model based o
 n an affine-invariant metric interpolation framework\; and optimization of
  the surrogate model to drive the mesh toward optimality. The combination 
 of the framework with a discontinuous Galerkin discretization and an a pos
 teriori output error estimate results in a versatile PDE solver for reliab
 le output prediction.\n\nThe versatility and effectiveness of the adaptive
  framework are demonstrated in a number of applications. First\, the optim
 ality of the method is verified against anisotropic polynomial approximati
 on theory in the context of L2 projection. Second\, the behavior of the me
 thod is studied in the context of output-based adaptation using advection-
 diffusion problems with manufactured primal and dual solutions. Third\, th
 e framework is applied to the steady-state Euler and Reynolds-averaged Nav
 ier-Stokes equations. The results highlight the importance of adaptation f
 or high-order discretizations and demonstrate the robustness and effective
 ness of the proposed method in solving complex aerodynamic flows exhibitin
 g a wide range of scales. Fourth\, fully-unstructured space-time adaptivit
 y is realized\, and its competitiveness is assessed for wave propagation p
 roblems.  Finally\, the framework is applied to enable spatial error contr
 ol of parametrized PDEs\, producing universal optimal meshes applicable fo
 r a wide range of parameters.
LOCATION:MR2\, Centre for Mathematical Sciences\, Wilberforce Road\, Cambr
 idge
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