Unsteady Output-Based Adaptation Using Continuous-in-Time Adjoints

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143081/1/6.2017-0529.pd

An Output-Based Dynamic Order Refinement Strategy for Unsteady Aerodynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97140/1/AIAA2012-77.pd

Airfoil Shape Optimization Using Output-Based Adapted Meshes

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143055/1/6.2017-3102.pd

Output Error Control Using r-Adaptation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143062/1/6.2017-4111.pd

Output‐based mesh optimization for hybridized and embedded discontinuous Galerkin methods

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/154431/1/nme6248.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/154431/2/nme6248_am.pd

Constrained pseudo‐transient continuation

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/111771/1/nme4858.pd

A Probabilistic Approach to Inverse Convection-Diffusion

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90616/1/AIAA-2011-824-287.pd

Error Estimation and Adaptation in Hybridized Discontinous Galerkin Methods

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/140705/1/6.2014-0078.pd

Non-intrusive reduced-order modeling using convolutional autoencoders

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB methods perform poorly, failing to provide an efficient subspace for the solution space. The use of nonlinear manifolds for ROMs has gained traction in recent years, showing increased performance for certain nonlinear problems over linear methods. Deep learning has been popular to this end through the use of autoencoders for providing a nonlinear trial manifold for the solution space. In this work, we present a non-intrusive ROM framework for steady-state parameterized partial differential equations (PDEs) that uses convolutional autoencoders (CAEs) to provide a nonlinear solution manifold and is augmented by Gaussian process regression (GPR) to approximate the expansion coefficients of the reduced model. When applied to a numerical example involving the steady incompressible Navier-Stokes equations solving a lid-driven cavity problem, it is shown that the proposed ROM offers greater performance in prediction of full-order states when compared to a popular method employing POD and GPR over a number of ROM dimensions

Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90641/1/AIAA-53965-537.pd