The selection of fixed-order quadratures in point-kernel shielding calculations

Trapezoidal rule and Gauss-Legendre quadratures are representative of the numeric techniques used in integrating over radiation source regions in point-kernel shielding programs. The orders of quadrature selected for such integrations are important since a sparse quadrature may calculate inaccurate results while unnecessarily large orders of quadrature waste computer time. Rules are given for choosing trapezoidal and Gauss quadrature orders for linear, radial, and azimuthal intervals of integrate, based on problem geometry and source attenuation. These rules show that for like accuracy, a trapezoidal rule quadrature of order N may be replaced by a Gauss quadrature with order between the square root of N and N/2. Replacing trapezoidal-scale quadratures by lesser order Gauss quadratures can save large amounts of computer time. Gauss quadratures, on the other hand, ideally should be set up individually for detector points in different locations