Mechanical Engineering Commons^™

The Solution Of Hypersingular Integral Equations With Applications In Acoustics And Fracture Mechanics, Richard S. St. John

Mathematics & Statistics Theses & Dissertations

The numerical solution of two classes of hypersingular integral equations is addressed. Both classes are integral equations of the first kind, and are hypersingular due to a kernel containing a Hadamard singularity. The convergence of a Galerkin method and a collocation method is discussed and computationally efficient algorithms are developed for each class of hypersingular integral equation.

Interest in these classes of hypersingular integral equations is due to their occurrence in many physical applications. In particular, investigations into the scattering of acoustic waves by moving objects and the study of dynamic Griffith crack problems has necessitated a computationally efficient technique …