A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals

TL;DR

This paper introduces a multiscale continuous Galerkin method that significantly speeds up and improves the accuracy of stochastic simulations and robust design processes for photonic crystals, leveraging geometric patterns and variance reduction techniques.

Contribution

The paper presents a novel MSCG method combining reduced basis, gradient computation, and variance reduction for efficient stochastic simulation and design of photonic crystals.

Findings

Reduces computational cost for stochastic simulations.

Demonstrates improved accuracy and efficiency in photonic crystal design.

Provides convergence and cost analysis of the proposed method.

Abstract

We present a multiscale continuous Galerkin (MSCG) method for the fast and accurate stochastic simulation and optimization of time-harmonic wave propagation through photonic crystals. The MSCG method exploits repeated patterns in the geometry to drastically decrease computational cost and incorporates the following ingredients: (1) a reference domain formulation that allows us to treat geometric variability resulting from manufacturing uncertainties; (2) a reduced basis approximation to solve the parametrized local subproblems; (3) a gradient computation of the objective function; and (4) a model and variance reduction technique that enables the accelerated computation of statistical outputs by exploiting the statistical correlation between the MSCG solution and the reduced basis approximation. The proposed method is thus well suited for both deterministic and stochastic simulations, as well as robust design of photonic crystals. We provide convergence and cost analysis of the MSCG method, as well as a simulation results for a waveguide T-splitter and a Z-bend to illustrate its advantages for stochastic simulation and robust design.