Dimensional Reduction of Highly Nonlinear Multiscale Models Using Most Appropriate Local Reduced-Order Bases

Abstract

Higher-fidelity mathematical models, better approximation methods, and faster numerical algorithms have been developed for the solution of many computational problems. Linux clusters are now ubiquitous, GPUs (Graphics Processing Units) have shattered computing speed barriers, and exascale machines will increase computational power by at least two orders of magnitude. Most importantly, the potential of simulation based engineering science for providing a deeper understanding of complex engineering systems, improving design reliability, reducing design-cycle time, and enhancing their performance is well recognized today in many fields. Yet, in many applications such as turbulent flow computations at high Reynolds numbers, high-fidelity simulations remain so computationally intensive that they cannot be performed as often as needed. Consequently, their impact on engineering has been strong so far for the analysis and verification of carefully selected system configurations, system verification, and forensic applications. However, it has not been as strong for routine analysis, what-ifscenarios, parametric studies, and time-critical applications such as design, design optimization, optimal control, and test support. Such applications demand a game-changing computational technology that leverages the power of high performance computing with the unique ability of low-dimensional computational models to perform in real-time. Nonlinear, Projection-based Model Order Reduction (PMOR) can provide this leverage. For this reason, this three-year basic research effort focuses on developing a rigorous, systematic approach for parametric, highly nonlinear, multiscale PMOR based on the recently developed mathematical concept of local reduced-order bases.

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Document Details

Document Type
Technical Report
Publication Date
Aug 15, 2020
Accession Number
AD1108188

Entities

People

  • Charbel Farhat

Organizations

  • Stanford University

Tags

Communities of Interest

  • Autonomy
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Aeroelasticity
  • Algorithms
  • Computational Complexity
  • Computational Fluid Dynamics
  • Computational Science
  • Data Compression
  • Differential Equations
  • Fluid Dynamics
  • Fluid Flow
  • Fluid Mechanics
  • Large Eddy Simulation
  • Mathematical Models
  • Mechanical Properties
  • Mechanics
  • Military Research
  • Multiscale Models
  • Reliability

Fields of Study

  • Engineering

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Computational Fluid Dynamics (CFD)
  • Distributed Systems and Data Platform Development