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This manuscript is the second in a series presenting fast direct solutiontechniques for solving two-dimensional wave scattering problems fromquasi-periodic multilayered structures. The fast direct solvers presented inthe series are for the linear system that results from the discretization of arobust integral formulation. The fast direct solver presented in thismanuscript has a computational cost that scales linearly with respect to thenumber of discretization points on the interfaces and the number of layers. Thelatter is an improvement over the previous solver and makes the new solver moreefficient especially for problems involving multiple incident angles andchanges to the layered media. Numerical results illustrate the improvedperformance of the new solver over the previous one.

A fast direct solver for two dimensional quasi-periodic multilayered media scattering problems, Part II