The direct interpolation boundary element method and the domain superposition technique applied to piecewise Helmholtz's problems with internal heterogeneity

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.

Automated summary

This study combines the direct interpolation boundary element method (DIBEM) and the domain superposition technique (DST) to solve piecewise inhomogeneous two-dimensional Helmholtz problems. The proposed methodology preserves the main features and advantages of the Boundary Element Method, and numerical evaluations are conducted through three different tests with benchmarks generated from Finite Element Method simulations.