Model reduction in computational homogenization for transient heat conduction

Abdullah Waseem, Thomas Heuze, Laurent Stainier , Marc Geers, Varvara Kouznetsova (Corresponding author)

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Abstract

This paper presents a computationally efficient homogenization method for transient heat conduction problems. The notion of relaxed separation of scales is introduced and the homogenization framework is derived. Under the assumptions of linearity and relaxed separation of scales, the microscopic solution is decomposed into a steady-state and a transient part. Static condensation is performed to obtain the global basis for the steady-state response and an eigenvalue problem is solved to obtain a global basis for the transient response. The macroscopic quantities are then extracted by averaging and expressed in terms of the coefficients of the reduced basis. Proof-of-principle simulations are conducted with materials exhibiting high contrast material properties. The proposed homogenization method is compared with the conventional steady-state homogenization and transient computational homogenization methods. Within its applicability limits, the proposed
homogenization method is able to accurately capture the microscopic thermal inertial effects with significant computational efficiency.
Original languageEnglish
JournalComputational Mechanics
Early online date18 Sep 2019
DOIs
Publication statusE-pub ahead of print - 18 Sep 2019

Fingerprint

Transient Heat Conduction
Homogenization method
Homogenization Method
Model Reduction
Heat conduction
Homogenization
Transient Response
Computational efficiency
Condensation
Linearity
Transient analysis
Computational Methods
Computational Efficiency
Material Properties
Eigenvalue Problem
Averaging
Materials properties
Coefficient
Simulation

Keywords

  • Homogenization
  • Inclusions
  • Model reduction
  • Non-homogeneous media
  • Transient

Cite this

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abstract = "This paper presents a computationally efficient homogenization method for transient heat conduction problems. The notion of relaxed separation of scales is introduced and the homogenization framework is derived. Under the assumptions of linearity and relaxed separation of scales, the microscopic solution is decomposed into a steady-state and a transient part. Static condensation is performed to obtain the global basis for the steady-state response and an eigenvalue problem is solved to obtain a global basis for the transient response. The macroscopic quantities are then extracted by averaging and expressed in terms of the coefficients of the reduced basis. Proof-of-principle simulations are conducted with materials exhibiting high contrast material properties. The proposed homogenization method is compared with the conventional steady-state homogenization and transient computational homogenization methods. Within its applicability limits, the proposedhomogenization method is able to accurately capture the microscopic thermal inertial effects with significant computational efficiency.",
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Model reduction in computational homogenization for transient heat conduction. / Waseem, Abdullah; Heuze, Thomas; Stainier , Laurent; Geers, Marc; Kouznetsova, Varvara (Corresponding author).

In: Computational Mechanics, 18.09.2019.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Model reduction in computational homogenization for transient heat conduction

AU - Waseem, Abdullah

AU - Heuze, Thomas

AU - Stainier , Laurent

AU - Geers, Marc

AU - Kouznetsova, Varvara

PY - 2019/9/18

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N2 - This paper presents a computationally efficient homogenization method for transient heat conduction problems. The notion of relaxed separation of scales is introduced and the homogenization framework is derived. Under the assumptions of linearity and relaxed separation of scales, the microscopic solution is decomposed into a steady-state and a transient part. Static condensation is performed to obtain the global basis for the steady-state response and an eigenvalue problem is solved to obtain a global basis for the transient response. The macroscopic quantities are then extracted by averaging and expressed in terms of the coefficients of the reduced basis. Proof-of-principle simulations are conducted with materials exhibiting high contrast material properties. The proposed homogenization method is compared with the conventional steady-state homogenization and transient computational homogenization methods. Within its applicability limits, the proposedhomogenization method is able to accurately capture the microscopic thermal inertial effects with significant computational efficiency.

AB - This paper presents a computationally efficient homogenization method for transient heat conduction problems. The notion of relaxed separation of scales is introduced and the homogenization framework is derived. Under the assumptions of linearity and relaxed separation of scales, the microscopic solution is decomposed into a steady-state and a transient part. Static condensation is performed to obtain the global basis for the steady-state response and an eigenvalue problem is solved to obtain a global basis for the transient response. The macroscopic quantities are then extracted by averaging and expressed in terms of the coefficients of the reduced basis. Proof-of-principle simulations are conducted with materials exhibiting high contrast material properties. The proposed homogenization method is compared with the conventional steady-state homogenization and transient computational homogenization methods. Within its applicability limits, the proposedhomogenization method is able to accurately capture the microscopic thermal inertial effects with significant computational efficiency.

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