This work presents the combination of the direct interpolation boundary element method (DIBEM) and the domain superposition technique (DST) to address piecewise inhomogeneous two dimensional Helmholtz problems, in which the internal constitutive property in each sector varies smoothly according to a known function. The domain integrals generated by the medium's heterogeneity are transformed into boundary integrals according to the DIBEM strategy where radial basis functions are used. The DST is applied to generate the influence coefficients related to the several sectors and compute them in the final matrix system. Thus, the proposed methodology preserves the main features and advantages of the Boundary Element Method. Concerning the evaluation of the numerical results, three different tests are performed, considering regular and irregular domains. For each example, benchmarks are generated by correlate simulations using the Finite Element Method.

这项工作提出了直接插值边界元方法 (DIBEM) 和域叠加技术 (DST) 的组合，以解决分段非齐次二维亥姆霍兹问题，其中每个扇区的内部本构属性根据已知函数平滑变化。根据使用径向基函数的 DIBEM 策略，由介质的异质性生成的域积分被转换为边界积分。应用 DST 生成与多个部门相关的影响系数，并在最终矩阵系统中计算它们。因此，所提出的方法保留了边界元方法的主要特征和优点。关于数值结果的评估，进行了三种不同的测试，考虑规则域和不规则域。对于每个示例，基准是通过使用有限元方法的相关模拟生成的。