Surface Integral Equation-Domain Decomposition Scheme for Solving Multiscale Nanoparticle Assemblies With Repetitions

Abstract

In this paper, we introduce the use of the multilevel fast multipole algorithm (MLFMA) in synergy with a multilevel nonoverlapping additive Schwarz domain decomposition (DD) preconditioner for the solution of large arrays of nanoparticles presenting multiscale and multiphysics features. The judicious selection of subdomains allows for the isolation of the different scale/physics subproblems, yielding an efficient and effective preconditioner for the surface integral equation matrix system. Furthermore, the MLFMA-method of moments is employed to take advantage of the repetition pattern inherent to these kinds of structures. Numerical experiments solving real-life plasmonic biosensors built up from complicated particle assemblies reveal a great improvement of convergence, testifying to the robustness and versatility of the DD approach.

Keywords

• Domain decomposition
• integral equations
• nanoparticle assemblies
• Raman spectroscopy
• plasmonics.