In this course, we will discuss spatial discretization of the Lippmann–Schwinger using a Galerkin technique. The resulting discretization is consistent, because the linear and bilinear forms of the weak form of the Lippmann–Schwinger equation are evaluated exactly. The derivation of the discrete Green operator will clarify how “FFT-based homogenization methods” rely on... the FFT.

The following topics will be discussed

• Weak form of the LS equation
• Galerkin discretization of the LS equation
• The discretized operators
• Applying the discrete Green operator
• Towards linear LS solvers