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For the interest of readers who do not need to deal with detailed mathematics, a succinct summary of the newly developed GSP N theory ( Chao, 2017 ) is given in this technical note. A streamlined presentation of the idea, concept, logic, formulation and the physics of the theory is given here such that the readers can more easily comprehend the overall picture and the explicit resulting equations to be used in implementation. The mathematical details are referred to the previous papers (Chao, 2016, 2017). All the relevant equations for the P 3 equivalent GSP 3 ( 3 ) theory are explicitly given. Issues of numerical implementation of the theory are discussed, and potentially viable methods are suggested and conceptually described. [ABSTRACT FROM AUTHOR]

Abstract: The accuracy of the point-kernel method, which is a widely used practical tool for γ-ray shielding calculations, strongly depends on the quality and accuracy of buildup factors used in the calculations. Although, buildup factors for single-layer shields comprised of a single material are well known, calculation of buildup factors for stratified shields, each layer comprised of different material or a combination of materials, represent a complex physical problem. Recently, a new compact mathematical model for multi-layer shield buildup factor representation has been suggested for embedding into point-kernel codes thus replacing traditionally generated complex mathematical expressions. The new regression model is based on support vector machines learning technique, which is an extension of Statistical Learning Theory. The paper gives complete description of the novel methodology with results pertaining to realistic engineering multi-layer shielding geometries. The results based on support vector regression machine learning confirm that this approach provides a framework for general, accurate and computationally acceptable multi-layer buildup factor model. [Copyright &y& Elsevier]

Abstract: The Generalized Minimal RESidual (GMRES) method, using a Krylov subspace projection, is adapted and implemented to accelerate a 3D iterative transport solver based on the characteristics method. Another acceleration technique called the self-collision rebalancing technique (SCR) can also be used to accelerate the solution or as a left preconditioner for GMRES. The GMRES method is usually used to solve a linear algebraic system . It uses as projection subspace and for the orthogonalization of the residual. This paper compares the performance of these two combined methods on various problems. To implement the GMRES iterative method, the characteristics equations are derived in linear algebra formalism by using the equivalence between the method of characteristics and the method of collision probability to end up with a linear algebraic system involving fluxes and currents. Numerical results show good performance of the GMRES technique especially for the cases presenting large material heterogeneity with a scattering ratio close to 1. Similarly, the SCR preconditioning slightly increases the GMRES efficiency. [Copyright &y& Elsevier]