Zooming into the near field: Erroneous assumption of superluminal speeds in Green´s function theory as the origin of singularities

The combined FEM-BEM analysis technique, introduced nearly two decades ago, has been widely accepted as a powerful technique in SAW and BAW community for modelling the masslaoding effect. It is also widely acknowledged that simulations based on exclusive usage of BEM produce the most accurate and reliable numerical predictions, which hardly can be surpassed by competing techniques. On the other hand, it is also common knowledge that the singularities occurring in Green´s functions, and in their spatial derivatives, severely limit the applicability, implementation, accuracy, and the versatility of the BEM. This presentation introduces a method for diagnosing the root of the singularities in Green´s functions. The singularities of Green´s functions originate in a physically inadequate assumption of superluminal speed of electrostatic- and elastostatic interaction propagation in pieozoeletric media, which is implicitly embedded in conventionally constructed Green´s functions. Based on a fundamental insight it is shown that the analytical and numerical difficulties arising in the application of BEM can be avoided systematically by applying an easy-to-use (iterative matrix) method which will be presented for the first time.