Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Anistratov, Dmitriy Y.; Azmy, Yousry Y.

doi:10.1016/j.jcp.2015.05.033

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

Journal Article · Thu May 28 00:00:00 EDT 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2015.05.033· OSTI ID:1437429

Anistratov, Dmitriy Y. ^[1]; Azmy, Yousry Y. ^[2]

North Carolina State University, Raleigh, NC (United States); CNEC/NC State
North Carolina State University, Raleigh, NC (United States)

Here, we study convergence of the integral transport matrix method (ITMM) based on a parallel block Jacobi (PBJ) iterative strategy for solving particle transport problems. The ITMM is a spatial domain decomposition method proposed for massively parallel computations. AFourier analysis of the PBJ-based iterations applied to SN diamond-difference equations in 1D slab and 2D Cartesian geometries is performed. It is carried out for infinite-medium problems with homogeneous material properties. To analyze the performance of the ITMM with the PBJ algorithm and evaluate its potential in scalability we consider a limiting case of one spatial cell per subdomain. The analysis shows that in such limit the spectral radius of the iteration method is one without regard to values of the scattering ratio and optical thickness of the spatial cells. This implies lack of convergence in infinite medium. Numerical results of finite-medium problems are presented. They demonstrate effects of finite size of spatial domain on the performance of the iteration algorithm as well as its asymptotic behavior when the extent of the spatial domain increases. Finally, these numerical experiments also show that for finite domains iterative convergence to a finite criterion is achievable in a multiple of the sum of number of cells in each dimension.

Research Organization:: North Carolina State University, Raleigh, NC (United States)

Sponsoring Organization:: USDOE; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC07-05ID14517; NA0002576

OSTI ID:: 1437429

Alternate ID(s):: OSTI ID: 1249985

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 297; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICS AND COMPUTING
Fourier analysis
domain decomposition
iterative methods
particle transport equation
radiative transfer equation

Iterative stability analysis of spatial domain decomposition based on block Jacobi algorithm for the diamond-difference scheme

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