P1 synthetic acceleration and convergence analysis for the solution of the one-speed nonclassical spectral SN equations in slab geometry

Ph.D. thesis

Alan S. da Silva
Ricardo C. Barros (Advisor), Richard Vasques (Co-Advisor), D.Sc. in Computational Modeling, Rio de Janeiro State University, Brazil, 2025 Dec

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Cite

APA Click to copy
da Silva, A. S. (2025, December). P1 synthetic acceleration and convergence analysis for the solution of the one-speed nonclassical spectral SN equations in slab geometry (PhD thesis). (R. C. B. (Advisor) & R. V. (Co-Advisor), Eds.), D.Sc. in Computational Modeling. Rio de Janeiro State University, Brazil.

Chicago/Turabian Click to copy
Silva, Alan S. da. “P1 Synthetic Acceleration and Convergence Analysis for the Solution of the One-Speed Nonclassical Spectral SN Equations in Slab Geometry .” Edited by Ricardo C. Barros (Advisor) and Richard Vasques (Co-Advisor). D.Sc. in Computational Modeling. PhD thesis, Rio de Janeiro State University, 2025.

MLA Click to copy
da Silva, Alan S. “P1 Synthetic Acceleration and Convergence Analysis for the Solution of the One-Speed Nonclassical Spectral SN Equations in Slab Geometry .” D.Sc. in Computational Modeling, edited by Ricardo C. Barros (Advisor) and Richard Vasques (Co-Advisor), Rio de Janeiro State University, Dec. 2025.

BibTeX Click to copy

@phdthesis{alan2025a,
  title = {P1 synthetic acceleration and convergence analysis for the solution of the one-speed nonclassical spectral SN equations in slab geometry },
  year = {2025},
  month = dec,
  address = {Brazil},
  journal = {D.Sc. in Computational Modeling},
  school = {Rio de Janeiro State University},
  author = {da Silva, Alan S.},
  editor = {(Advisor), Ricardo C. Barros and (Co-Advisor), Richard Vasques},
  month_numeric = {12}
}

Dr. Alan da Silva

ABSTRACT: The linear Boltzmann transport equation is a fundamental equation that models neutral particle transport processes. In some applications, the flux of particles does not attenuate as an exponential function of the particle’s free-path. Boltzmann equation which models these applications are referred to as the non-classical transport equation. Recently, a spectral approach has been developed in order to solve a simplified version of this non-classical transport equation. This approach is based on the fact that the non-classical angular flux can be represented in terms of a series of Laguerre polynomials in the free-path variable s. This allows the non-classical transport equation to be written in the form of a classical transport equation. In this work, we use a synthetic acceleration scheme to speed up the iterative algorithm for the solution of this non-classical transport equation. The results of our numerical experiments indicate that the synthetic acceleration scheme is effective in reducing the number of iterations and the CPU execution time needed to obtain an accurate solution. Besides, a Fourier convergence analysis has been developed to calculate the spectral radius of the synthetic acceleration schemes developed. By estimating the spectral radius, we can obtain information about the performance of a synthetic acceleration scheme.