Fast Computational Modeling Based on the Boundary Element Method Towards the Design of an Ultrasonic Biomedical Applicator

The aim of this work is to analyze the usage of the boundary element method (BEM) as a fast computational tool for solving large ultrasonic field problems, i.e. 3D models. A proposed tridimensional radiating surface SR was modeled by means of BEM and the finite element method (FEM). Four time-harmonics models were developed: two containing the entire SR and two considering a symmetrical plane at half-length of the radiator. BEM solutions were validated with FEM models by contours at -3 dB and -6 dB pressure decays, areas within the contours, elliptical shape ratio Er and ellipsoidal focal volume approximations. The average differences in pressure and distance at the focus were 39.875 Pa and 0.4515 mm, respectively; the areas within the contours show differences between 0.6 mm2 and 2.3 mm2. The Er of the focal zone was over 92 %, while the ellipsoidal volume approximation showed differences between 0.0817 mm3 to 1.4632 mm3 at -3 dB, and 1.2354 mm3 to 4.1144 mm3 at -6 dB. Analyzed data suggest the use of BEM to model the ultrasonic beam pattern in a lossless medium during ultrasonic biomedical applicators design, reducing the solution time from 22 h with FEM to 2 min with BEM.