Discrete Adjoint Formulation for Continuum Sensitivity Analysis

Kulkarni, Mandar D.; Cross, David M.; Canfield, Robert A.

doi:10.2514/1.j053827

Cited by 11 publications

(4 citation statements)

References 19 publications

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“…Spatial gradient reconstruction (SGR) was demonstrated as a means to improve CSA accuracy in a controllable and nonintrusive manner. Three journal articles [1][2][3] were published and four others [4][5][6][7] submitted for publication documenting the funded research. Seven conference papers were presented during the performance period [8][9][10][11][12][13][14].…”

Section: Discussionmentioning

confidence: 99%

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Continuum Shape Sensitivity For Nonlinear Aeroelastic Gust Response

Canfield¹

2014

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Section: Discussionmentioning

confidence: 99%

“…• A hybrid adjoint was derived to efficiently compute static shape derivatives for many design variables, using a discrete adjoint with CSA for which accuracy is controlled by SGR [7,14].…”

mentioning

confidence: 99%

Continuum Shape Sensitivity For Nonlinear Aeroelastic Gust Response

Canfield¹

2014

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“…To obtain the spatial derivatives it is possible to apply the FDM or the Spatial Gradients Reconstruction (SGR). The latter technique was proposed by Cross and Canfield [17,39,40] and is based on the least-squares patch-recovery approach used by Duvigneau and Pelletier [41]. Being the domain one-dimensional, the two approaches can be applied indifferently.…”

Section: Csa Applicationmentioning

confidence: 99%

“…By employing the Spatial Gradient Reconstruction (SGR) method [15] it is possible to obtain accurate spatial gradients and apply CSA in a nonintrusive way, that is, without any modification to the black-box programs used for analysis, such as NASTRAN or FLUENT. CSA has already been applied and validated for isotropic materials for one-dimensional (1D) [17], three-dimensional (3D) problems [18,19] and on some particular two-dimensional (2D) problems [15,16] for the static analysis case. An initial attempt to apply CSA to vibration problems was made in [20] where the scalar Helmholtz equation has been differentiated in a 1D (string) and 2D (membrane) domain.…”

Section: Introductionmentioning

confidence: 99%

Continuum and Discrete Analytical Methods for Vibration and Buckling Eigenvalues Shape Sensitivities

Gagliardi,

Kulkarni,

Marulo

2024

Preprint

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Gradient-based optimization techniques need precise and efficient sensitivities. Numerical sensitivity methods such as finite differences are easy to implement but imprecise and computationally inefficient. In contrast, analytical sensitivity methods, such as the discrete and continuum ones are highly accurate and efficient. Continuum Sensitivity Analysis (CSA) is an analytical method used to calculate derivatives of shape or value parameters. While CSA has been successfully applied in static analysis and dynamic problems in the time domain, this work presents an extension of the approach to eigenvalue sensitivities for the first time. However, CSA revealed limitations, prompting the exploration of an alternative approach based on discrete analytical differentiation. This method is employed for the first time in shape sensitivities. The derivatives of the stiffness and mass matrices required by the method are calculated analytically, resulting in high accuracy and computational efficiency. In addition, an element-agnostic approach has been developed leveraging primary analysis matrices to calculate their derivative. This characteristic, along with the nonintrusivity, makes the method employable with standard commercial software. Both approaches have been applied and validated in a wide range of scenarios, involving vibration and buckling problems.

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Continuum shape sensitivity analysis for aeroelastic gust using an arbitrary lagrangian-eulerian reference frame

Canfield

Sandler

2018

Struct Multidisc Optim

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Discrete Adjoint Formulation for Continuum Sensitivity Analysis

Cited by 11 publications

References 19 publications

Continuum Shape Sensitivity For Nonlinear Aeroelastic Gust Response

Continuum Shape Sensitivity For Nonlinear Aeroelastic Gust Response

Continuum and Discrete Analytical Methods for Vibration and Buckling Eigenvalues Shape Sensitivities

Continuum shape sensitivity analysis for aeroelastic gust using an arbitrary lagrangian-eulerian reference frame

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