Analytical Benchmark Problems for Multifidelity Optimization Methods

The paper presents a collection of analytical benchmark problems specifically selected to provide a set of stress tests for the assessment of multifidelity optimization methods. In addition, the paper discusses a comprehensive ensemble of metrics and criteria recommended for the rigorous and meaningful assessment of the performance of multifidelity strategies and algorithms

Slice Stretching at the Event Horizon when Geodesically Slicing the Schwarzschild Spacetime with Excision

Slice-stretching effects are discussed as they arise at the event horizon when geodesically slicing the extended Schwarzschild black-hole spacetime while using singularity excision. In particular, for Novikov and isotropic spatial coordinates the outward movement of the event horizon (``slice sucking'') and the unbounded growth there of the radial metric component (``slice wrapping'') are analyzed. For the overall slice stretching, very similar late time behavior is found when comparing with maximal slicing. Thus, the intuitive argument that attributes slice stretching to singularity avoidance is incorrect.Comment: 5 pages, 2 figures, published version including minor amendments suggested by the refere

An Adjoint-based Derivative Evaluation Method for Time-dependent Aeroelastic Optimization of Flexible Aircraft

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106483/1/AIAA2013-1530.pd

Adaptive N-Fidelity Metamodels for Noisy CFD Data

International audienceAn adaptive-fidelity approach to metamodeling from noisy data is presented for design-space exploration and design optimization. Computational fluid dynamics (CFD) simulations with different numerical accuracy (spatial discretization) provides metamodel training sets affected by unavoidable numerical noise. The-fidelity approximation is built by an additive correction of a low-fidelity metamodel with metamodels of differences (errors) between higher-fidelity levels whose hierarchy needs to be provided. The approach encompasses two core metamodeling techniques, namely: i) stochastic radial-basis functions (SRBF) and ii) Gaussian process (GP). The adaptivity stems from the sequential training procedure and the auto-tuning capabilities of the metamodels. The method is demonstrated for an analytical test problem and a CFD-based optimization of a NACA airfoil, where the fidelity levels are defined by an adaptive grid refinement technique of a Reynolds-averaged Navier-Stokes (RANS) solver. The paper discusses: i) the effect of using more than two fidelity levels; ii) the use of least squares regression as opposed to exact interpolation; iii) the comparison between SRBF and GP; and iv) the use of two sampling approaches for GP. Results show that in presence of noise, the use of more than two fidelity levels improves the model accuracy with a significant reduction of the number of high-fidelity evaluations. Both least squares SRBF and GP provide promising results in dealing with noisy data