In this lecture, we will discuss asymptotically consistent discretizations of the Lippmann–Schwinger equations. In other words, we won't enforce exact evaluation of the continuous variational problem over the discretization space. This additional flexibility will allow to derive more efficient numerical schemes.

The following topics will be discussed

• Discussion of the consistent discretization
• On asymptotically consistent discretizations
• Asymptotically consistent discretizations of the microstructure
• Asymptotically consistent discretizations of the Green operator
• Comparison of some discretizations