A Two-Dimensional Acoustic Tangential Derivative Boundary Element Method Including Viscous and Thermal Losses

In recent years, the boundary element method has shown to be an interesting alternative to the finite element method for modeling of viscous and thermal acoustic losses. Current implementations rely on finite-difference tangential pressure derivatives for the coupling of the fundamental equations, which can be a shortcoming of the method. This finite-difference coupling method is removed here and replaced by an extra set of tangential derivative boundary element equations. Increased stability and error reduction is demonstrated by numerical experiments.

Nonconstant Continuous Functions whose Tangential Derivative Vanishes along a Smooth Curve

We provide a simple example showing that the tangential derivative of a continuous function ϕ can vanish everywhere along a curve while the variation of ϕ along this curve is nonzero. We give additional regularity conditions on the curve and/or the function that prevent this from happening.

Novel Boundary Integral Equations for Two-Dimensional Isotropic Elasticity: An Application to Evaluation of the In-Boundary Stress

A new nonsingular system of boundary integral equations (BIEs) of the second kind for two-dimensional isotropic elasticity is deduced following a recently introduced procedure by Wu (J. Appl. Mech., 67, pp. 618–621, 2000) originally applied for anisotropic elasticity. The physical interpretation of the new integral kernels appearing in these BIEs is studied. An advantageous application of one of these BIEs as a boundary integral representation (BIR) of tangential derivative of boundary displacements on smooth parts of the boundary, and subsequently as a BIR of the in-boundary stress, is presented and analyzed in numerical examples. An equivalent BIR obtained by an integration by parts of the integral including tangential derivative of displacements in the former BIR is presented and analyzed as well. The resulting integral is only apparently hypersingular, being in fact a regular integral on smooth parts of the boundary.