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Analysis of Algorithm Efficiency for Heat Diffusion at Nanoscale Based on a MEMS Structure Investigation

Author

Listed:
  • Tomasz Raszkowski

    (Department of Microelectronics and Computer Science, Lodz University of Technology, 90-924 Lodz, Poland)

  • Mariusz Zubert

    (Department of Microelectronics and Computer Science, Lodz University of Technology, 90-924 Lodz, Poland)

Abstract

This paper presents an analysis of the time complexity of algorithms prepared for solving heat transfer problems at nanoscale. The first algorithm uses the classic Dual-Phase-Lag model, whereas the second algorithm employs a reduced version of the model obtained using a Krylov subspace method. This manuscript includes a description of the finite difference method approximation prepared for analysis of the real microelectromechanical system (MEMS) structure manufactured by the Polish Institute of Electron Technology. In addition, an approximation scheme of the model, as well as the Krylov subspace-based model order reduction technique are also described. The paper considers simulation results obtained using both investigated versions of the Dual-Phase-Lag model. Moreover, the relative error generated by the reduced model, as well as the computational complexity of both algorithms, and a convergence of the proposed approach are analyzed. Finally, all analyses are discussed in detail.

Suggested Citation

  • Tomasz Raszkowski & Mariusz Zubert, 2020. "Analysis of Algorithm Efficiency for Heat Diffusion at Nanoscale Based on a MEMS Structure Investigation," Energies, MDPI, vol. 13(10), pages 1-15, May.
  • Handle: RePEc:gam:jeners:v:13:y:2020:i:10:p:2520-:d:358855
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    References listed on IDEAS

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    1. Tomasz Raszkowski & Mariusz Zubert, 2020. "Investigation of Heat Diffusion at Nanoscale Based on Thermal Analysis of Real Test Structure," Energies, MDPI, vol. 13(9), pages 1-18, May.
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    Cited by:

    1. Krzysztof Górecki & Krzysztof Posobkiewicz, 2022. "Cooling Systems of Power Semiconductor Devices—A Review," Energies, MDPI, vol. 15(13), pages 1-29, June.
    2. Mariusz Zubert & Zbigniew Kulesza & Mariusz Jankowski & Andrzej Napieralski, 2021. "Application of Scattering Parameters to DPL Time-Lag Parameter Estimation at Nanoscale in Modern Integration Circuit Structures," Energies, MDPI, vol. 14(15), pages 1-14, July.

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    1. Krzysztof Górecki & Krzysztof Posobkiewicz, 2022. "Cooling Systems of Power Semiconductor Devices—A Review," Energies, MDPI, vol. 15(13), pages 1-29, June.
    2. Mariusz Zubert & Zbigniew Kulesza & Mariusz Jankowski & Andrzej Napieralski, 2021. "Application of Scattering Parameters to DPL Time-Lag Parameter Estimation at Nanoscale in Modern Integration Circuit Structures," Energies, MDPI, vol. 14(15), pages 1-14, July.

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