Compatible Product Angular Quadrature for Neutron Transport in x-y Geometry

A second order radiative transfer equation and its solution by meshless method with application to strongly inhomogeneous media

“…It is noted that there are some other principles on the design of angular quadrature schemes, such as requiring the quadrature scheme to be conservative such that the scattering integral being accurate [53,54].…”

“…D are the one-dimensional first-and second-order discrete differentiation matrices defined similar to those defined in Eq (53)…”

Cost-optimized Automated Variance Reduction for Highly Angle-dependent Radiation Transport Analyses [Dissertation]

“…Ultimately, the Triangular Gauss-Chebyshev quadrature was selected. However, one quadrature known to be generally well behaved but not explored beyond a cursory investigation is the quadruple range quadrature [98,99]. A brief investigation was made but because of the combinatoric nature of the quadrature set a thorough investigation would have taken unreasonably long versus the potential benefit versus the Triangular Gauss-Chebyshev quadrature used.…”

“…The two quadrature sets used in this work for 1-D and 2-D calculations are the Gauss-Legendre and Triangular Gauss-Chebyshev quadrature sets, respectively. More information on these quadrature sets is available in Appendix C. Other quadrature sets explored in this work, but ultimately not used, are Jarrell's linear-discontinuous finite element (LDFE) quadrature set [96,97] and Abu-Shamay's quadruple-range (QR) quadrature set [98,99]. The 1-D Gauss-Legendre S 32 quadrature points used in this work are illustrated in Fig.…”