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

TL;DR

This paper introduces a fast direct solver for 2D wave scattering in quasi-periodic multilayered media, significantly reducing computation time for complex geometries and reusing precomputed data for multiple incident waves.

Contribution

The novel solver efficiently handles complex multilayered structures with reusability, reducing computational costs for multiple scattering problems and updates.

Findings

Solver handles over 200 problems 100 times faster than building from scratch.

Precomputation is reusable for different incident waves.

Updating the solver for new geometries is inexpensive.

Abstract

This manuscript presents a fast direct solution technique for solving two dimensional wave scattering problems from quasi-periodic multilayered structures. When the interface geometries are complex, the dominant term in the computational cost of creating the direct solver scales $O(NI)$ where $N$ is the number of discretization points on each interface and $I$ is the number of interfaces. The bulk of the precomputation can be re-used for any choice of incident wave. As a result, the direct solver can solve over 200 scattering problems involving an eleven layer geometry with complex interfaces 100 times faster than building a new fast direct solver from scratch for each new set of boundary data. An added benefit of the presented solver is that building an updated solver for a new geometry involving a replaced interface or a change in material property in one layer is inexpensive compared to building a new fast direct solver from scratch.