Author: Youssef F. Rashed, Dept. of Structural Engineering, Cairo University, Giza Egypt
In this tutorial, we will continue the discussion, started in the tutorial 4, about the derivation of the fundamental solutions. In the former tutorial, we presented techniques for setting up the fundamental solution for simple and compound operators. Herein, we will discuss the use of operator decoupling technique to breakdown matrix operators to simple or compound scalar ones. This method is due to Lars Hörmander  and it was introduced to the setting up of fundamental solutions within the context of boundary element method by Kitahara ( cf. Ref. ) and Tosaka (cf. Ref. ).
We will present two examples: elasticity and plate bending problems, to demonstrate the usage of such technique.