An Advanced Algorithm for Construction of Integral Transport Matrix Method Operators Using Accumulation of Single Cell Coupling Factors

Brian Powell, North Carolina State University

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The Integral Transport Matrix Method (ITMM) has been shown to be an effective method for solving the neutron transport equation in large domains on massively parallel architectures. The speed of the algorithm and its suitability for unstructured meshes, i.e. other than an ordered Cartesian grid, is limited by the construction of four matrix operators required for obtaining the solution in each subdomain. The existing algorithm used for construction of these matrix operators, termed the differential mesh sweep, is computationally expensive and was developed for a structured grid. This work proposes the use of a new algorithm for construction of these operators based on the construction of a single, fundamental matrix representing the transport of a particle along every possible path throughout the sub-domain mesh. Each of the operators is constructed by multiplying an element of this fundamental matrix by two factors dependent only upon the operator being constructed and on properties of the emitting and incident cells. The ITMM matrix operator construction time for the new algorithm is demonstrated to be shorter than the existing algorithm in all tested cases with both isotropic and anisotropic scattering considered. While also being a more efficient algorithm on a structured Cartesian grid, the new algorithm is promising in its geometric robustness and potential for application to an unstructured mesh, with the ultimate goal of application to an unstructured tetrahedral mesh on a massively parallel architecture.

Abstract Author(s): Brian P. Powell