The scaled boundary finite element method (SBFEM) is known for its inherent ability to simulate unbounded domains and singular fields, and its flexibility in the meshing procedure. Keeping the analytical form of the field variables along one coordinate intact, it transforms the governing partial differential equations of the problem into a system of one-dimensional (initial–)boundary value problems. However, closed-form solution of the said system is not available for most cases (e.g. transient heat transfer, acoustics, ultrasonics, etc.) since the system cannot be diagonalized in general. This paper aims to establish a numerical tool within the context of the shooting technique to evaluate the coefficient matrices of the subdomains without a priori knowledge of the analytical solution of the semi-discretized system. With proper choice of boundary conditions, the technique uses the strong form of the scaled boundary finite element equations to pass the required information and with the desired accuracy from one boundary to another. Due to generality of the technique, its procedure can be adjusted for any field equations. Since this technique is presented here for the first time, linear elastostatics, for which the closed-form solution is well-established, is formulated to provide valid comparisons. In addition, any direct solution method can be used for integrating the scaled boundary equations. Thus, without loss of generality, a Nyström extension of the classical fourth-order Runge–Kutta method is employed. A quantitative sensitivity analysis is also conducted, and efficiency of the classical and proposed solution techniques is compared in terms of computational time. Finally, some numerical examples, including bounded and unbounded domains, as well as singular stress fields are simulated based on the classical and proposed solution techniques.

缩放边界有限元方法 (SBFEM) 以其固有的模拟无界域和奇异场的能力以及网格划分过程的灵活性而闻名。保持场变量沿一个坐标的解析形式不变，它将问题的控制偏微分方程转化为一维（初）边值问题系统。然而，由于系统一般不能对角化，因此对于大多数情况（例如瞬态传热、声学、超声波等），所述系统的封闭形式解是不可用的。本文旨在在射击技术的背景下建立一个数值工具来评估子域的系数矩阵，而无需先验了解半离散系统的解析解。通过正确选择边界条件，该技术使用缩放边界有限元方程的强形式来传递所需信息，并且从一个边界到另一个边界的所需精度。由于该技术的通用性，其程序可以针对任何场方程进行调整。由于此技术是第一次在此提出，线性弹性静力学，其封闭形式的解决方案已经很好地建立起来，以提供有效的比较。此外，任何直接求解方法都可用于对缩放边界方程进行积分。因此，不失一般性，采用经典四阶龙格-库塔方法的 Nyström 扩展。还进行了定量敏感性分析，并且在计算时间方面比较了经典求解技术和提出的求解技术的效率。最后，一些数值例子，包括有界和无界域，以及奇异应力场是基于经典和建议的求解技术进行模拟。