Abstract

The multidual differentiation method has been implemented in a ray-tracing transport simulation for the purpose of calculating arbitrary-order sensitivities of the uncollided particle leakage. This method extends dual number differentiation by perturbing variables along multiple nonreal axes to calculate arbitrary-order derivatives. Numerical results of first-through third-order multidual sensitivities of the uncollided particle leakage with respect to isotope densities, microscopic cross sections, source emission rates, and material interface locations (including the outer boundary) are shown for a two-region sphere. The relative error of first and second partial derivatives with respect to isotopic parameters and first partial derivatives of the leakage with respect to interface locations are within 9.8E−10% of existing adjoint-based sensitivities. Higher-order multidual-based derivatives that are not available with the adjoint method are in excellent agreement with central difference approximations.

摘要

为了计算未碰撞粒子泄漏的任意阶灵敏度，已在射线追踪传输模拟中实施了多重微分方法。该方法通过沿多个非实轴扰动变量来计算任意阶导数，从而扩展了对偶数微分。显示了两区域球体的未碰撞粒子泄漏在同位素密度、微观截面、源发射率和材料界面位置（包括外边界）方面的一到三阶多重敏感性的数值结果。同位素参数的一阶和二阶偏导数的相对误差以及泄漏的界面位置的一阶偏导数的相对误差在 9 以内。现有基于伴随的灵敏度的 8E-10%。伴随方法不可用的高阶多重对偶导数与中心差分近似非常吻合。