Fundamental Solutions: I-simple and Compound Operators

In the tutorial 3, we presented other examples on the derivation of the boundary integral equation in the direct form. Mainly, elasticity and plate in bending problems were discussed. In this tutorial, we will discuss the definitions and the methods of derivation of fundamental solutions. The use of such solution within the boundary element method was discussed in the former tutorial. A table presents the commonly used forms of fundamental solution is given. Also a method based on simple analogy to the algebraic partial fraction is discussed to decompose compound differential operators. In the next tutorial, we will continue discussing how to set up the fundamental solutions for complex matrix operators.