Generalized Spectral Decomposition Approach to a Stochastic Finite Integration Technique Electrokinetic Formulation

Authors

  • Lorenzo Codecasa Dipartimento di Elettronica, Informazione e Bioingegneria Politecnico di Milano, Milano, I-20133, Italy
  • Luca Di Rienzo Dipartimento di Elettronica, Informazione e Bioingegneria Politecnico di Milano, Milano, I-20133, Italy

Keywords:

Electrokinetics, finite integration technique, polynomial chaos expansion, resistance welding, uncertainty cuantification

Abstract

In order to efficiently solve the stochastic finite integration technique formulation for electrokinetics, a recently proposed generalized spectral decomposition approach is applied. Compared to the standard approach, the proposed method drastically reduces the computational burden. The results are validated by comparison with those obtained with high order polynomial chaos expansion, taken as the reference solution.

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References

D. Xiu, Numerical Methods for Stochastic Computations: A Spectral Method Approach, Princeton University Press, 2010.

S. Clenet and N. Ida, “Error estimation in a stochastic finite element method in electrokinetics,” International Journal for Numerical Methods in Engineering, vol. 81, no. 11, pp. 1417-1438, 2010.

L. Codecasa and L. Di Rienzo, “Stochastic finite integration technique formulation for electrokinetics,” IEEE Trans. on Magn., vol. 50, no. 2, pp. 573-576, 2014.

A. Nouy, “A generalized spectral decomposition technique to solve a class of linear stochastic partial differential equations,” Comput. Methods Appl. Mech. Eng., vol. 196, pp. 4521-4537, 2007.

L. Codecasa, “Refoundation of the cell method by means of augmented dual grids,” IEEE Trans. on Magn., vol. 50, no. 2, 2014.

L. Codecasa, V. Minerva, and M. Politi, “Use of barycentric dual grids for the solution of frequency domain problems by FIT,'” IEEE Trans. on Magn., vol. 40, no. 2, pp. 1414-1419, 2004.

L. Codecasa, R. Specogna, and F. Trevisan, “A new set of basis functions for the discrete geometric approach,'” Journal of Computational Physics, vol. 229, no. 19, pp. 7401-7410, 2010.

J. R. Magnus and Heinz Neudecker, Matrix Differential Calculus with Applications in Statistics and Econometrics, 2nd Ed., Wiley, 1999.

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Published

2021-08-18

How to Cite

[1]
L. . Codecasa and L. D. . Rienzo, “Generalized Spectral Decomposition Approach to a Stochastic Finite Integration Technique Electrokinetic Formulation”, ACES Journal, vol. 31, no. 07, pp. 771–776, Aug. 2021.

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