Calculation of numerical boundary measure for wavelet-Galerkin approximations in aeroelasticity

Jeonghwan Ko, Andrew J. Kurdila, Sang Young Park, Thomas Strganac

Research output: Contribution to journalConference article

1 Citation (Scopus)

Abstract

Wavelet analysis is regarded as an extremely promising tool for approximate solution of multi-field problems, such as those arising in aeroelasticity and fluid structure interaction, due to its inherent multi-resolution/multi-scale nature. However, wavelet analysis has been conducted primarily within the fields of signal and image processing due to the difficulty in defining wavelet bases that satisfy specified boundary conditions. This paper employs an embedded domain technique to ameliorate the difficulty associated with deriving a wavelet basis for a specific multi-field initial/boundary value problem. Instead of constructing an explicit wavelet basis over the domain of interest, boundary conditions are enforced using a penalty formulation that requires the calculation of a numerical boundary measure. This paper presents strategies for the rapid calculation of numerical boundary measures employed in wavelet-Galerkin approximations of problems in aeroelastic transient response and control. In addition, the impact of new wavelet quadrature truncation error bounds is discussed in the context of aeroelastic simulation and control.

Original languageEnglish
Pages (from-to)2009-2019
Number of pages11
JournalCollection of Technical Papers - AIAA/ASME Structures, Structural Dynamics and Materials Conference
Issue numberpt 4
Publication statusPublished - 1993 Jan 1

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Aeroelasticity
Wavelet analysis
Boundary conditions
Fluid structure interaction
Transient analysis
Boundary value problems
Signal processing
Image processing

All Science Journal Classification (ASJC) codes

  • Architecture
  • Materials Science(all)
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

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abstract = "Wavelet analysis is regarded as an extremely promising tool for approximate solution of multi-field problems, such as those arising in aeroelasticity and fluid structure interaction, due to its inherent multi-resolution/multi-scale nature. However, wavelet analysis has been conducted primarily within the fields of signal and image processing due to the difficulty in defining wavelet bases that satisfy specified boundary conditions. This paper employs an embedded domain technique to ameliorate the difficulty associated with deriving a wavelet basis for a specific multi-field initial/boundary value problem. Instead of constructing an explicit wavelet basis over the domain of interest, boundary conditions are enforced using a penalty formulation that requires the calculation of a numerical boundary measure. This paper presents strategies for the rapid calculation of numerical boundary measures employed in wavelet-Galerkin approximations of problems in aeroelastic transient response and control. In addition, the impact of new wavelet quadrature truncation error bounds is discussed in the context of aeroelastic simulation and control.",
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Calculation of numerical boundary measure for wavelet-Galerkin approximations in aeroelasticity. / Ko, Jeonghwan; Kurdila, Andrew J.; Park, Sang Young; Strganac, Thomas.

In: Collection of Technical Papers - AIAA/ASME Structures, Structural Dynamics and Materials Conference, No. pt 4, 01.01.1993, p. 2009-2019.

Research output: Contribution to journalConference article

TY - JOUR

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AB - Wavelet analysis is regarded as an extremely promising tool for approximate solution of multi-field problems, such as those arising in aeroelasticity and fluid structure interaction, due to its inherent multi-resolution/multi-scale nature. However, wavelet analysis has been conducted primarily within the fields of signal and image processing due to the difficulty in defining wavelet bases that satisfy specified boundary conditions. This paper employs an embedded domain technique to ameliorate the difficulty associated with deriving a wavelet basis for a specific multi-field initial/boundary value problem. Instead of constructing an explicit wavelet basis over the domain of interest, boundary conditions are enforced using a penalty formulation that requires the calculation of a numerical boundary measure. This paper presents strategies for the rapid calculation of numerical boundary measures employed in wavelet-Galerkin approximations of problems in aeroelastic transient response and control. In addition, the impact of new wavelet quadrature truncation error bounds is discussed in the context of aeroelastic simulation and control.

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