Abstract

The homogeneous version of the B₁ leakage model is a non-linear eigenvalue problem which is generally solved iteratively by a root-finding algorithm, combined to the supplementary eigenvalue problem of the multiplication factor. This problem is widely used for ordinary cross section preparation in reactor analysis. Our work approximates this problem with a polynomial eigenvalue problem, which can be easily transformed into an ordinary linear generalized eigenproblem of size equal to the initial one multiplied by the polynomial degree used for the approximation of a transcendental function. This procedure avoids recurring to numerical root-finding methods supported by extra eigenvalue problems. The solution of the fundamental buckling with increasing approximation order is compared to the reference value obtained by inverse iterations.

摘要

B ₁的同质版本泄漏模型是一个非线性特征值问题，通常通过寻根算法迭代求解，并结合乘法因子的补充特征值问题。这个问题广泛用于反应器分析中的普通横截面制备。我们的工作用多项式特征值问题来近似这个问题，它可以很容易地转化为一个普通的线性广义特征问题，其大小等于初始值乘以用于逼近超越函数的多项式次数。此过程避免重复使用由额外特征值问题支持的数值求根方法。将近似阶次增加的基本屈曲的解与通过逆迭代获得的参考值进行比较。