Skip to main content

An adaptive sampling approach for solving PDEs with uncertain inputs and evaluating risk

Publication ,  Conference
Zou, Z; Kouri, D; Aquino, W
Published in: 19th AIAA Non-Deterministic Approaches Conference, 2017
January 1, 2017

© 2017, American Institute of Aeronautics and Astronautics Inc, AIAA. All rights reserved. When solving partial differential equations (PDEs) with random inputs, it is often computationally inefficient to merely propagate samples of the input probability law (or an approximation thereof) because the input law may not accurately capture the behavior of critical system responses that depend on the PDE solution. To further complicate matters, in many applications it is critical to accurately approximate the “risk” associated with the statistical tails of the system responses, not just the statistical moments. In this paper, we develop an adaptive sampling and local reduced basis method for approximately solving PDEs with random inputs. Our method determines a set of parameter atoms and an associated (implicit) Voronoi partition of the parameter domain on which we build local reduced basis approximations of the PDE solution. In addition, we extend our adaptive sampling approach to accurately compute measures of risk evaluated at quantities of interest that depend on the PDE solution.

Duke Scholars

Published In

19th AIAA Non-Deterministic Approaches Conference, 2017

ISBN

9781624104527

Publication Date

January 1, 2017
 

Citation

APA
Chicago
ICMJE
MLA
NLM
Zou, Z., Kouri, D., & Aquino, W. (2017). An adaptive sampling approach for solving PDEs with uncertain inputs and evaluating risk. In 19th AIAA Non-Deterministic Approaches Conference, 2017.
Zou, Z., D. Kouri, and W. Aquino. “An adaptive sampling approach for solving PDEs with uncertain inputs and evaluating risk.” In 19th AIAA Non-Deterministic Approaches Conference, 2017, 2017.
Zou Z, Kouri D, Aquino W. An adaptive sampling approach for solving PDEs with uncertain inputs and evaluating risk. In: 19th AIAA Non-Deterministic Approaches Conference, 2017. 2017.
Zou, Z., et al. “An adaptive sampling approach for solving PDEs with uncertain inputs and evaluating risk.” 19th AIAA Non-Deterministic Approaches Conference, 2017, 2017.
Zou Z, Kouri D, Aquino W. An adaptive sampling approach for solving PDEs with uncertain inputs and evaluating risk. 19th AIAA Non-Deterministic Approaches Conference, 2017. 2017.

Published In

19th AIAA Non-Deterministic Approaches Conference, 2017

ISBN

9781624104527

Publication Date

January 1, 2017