Application of Block Krylov Subspace Spectral Methods to Maxwell’s Equations

2009 ◽  
Author(s):  
James V. Lambers ◽  
Sio-Iong Ao ◽  
Alan Hoi-Shou Chan ◽  
Hideki Katagiri ◽  
Li Xu
Keyword(s):  
Spectral Methods ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Krylov Subspace ◽  
Krylov Subspace Spectral Methods

Krylov Subspace Spectral Methods for Systems of Variable-Coefficient PDE

2007 ◽  
Author(s):  
James V. Lambers ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Spectral Methods ◽  
Variable Coefficient ◽  
Krylov Subspace ◽  
Krylov Subspace Spectral Methods

scholarly journals Recent advances in Krylov subspace spectral methods

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2020143-2020144
Author(s):  
James V. Lambers
Keyword(s):  
Spectral Methods ◽  
Krylov Subspace ◽  
Recent Advances ◽  
Krylov Subspace Spectral Methods

scholarly journals Data-driven acceleration of photonic simulations

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Rahul Trivedi ◽  
Logan Su ◽  
Jesse Lu ◽  
Martin F. Schubert ◽  
Jelena Vuckovic
Keyword(s):  
Frequency Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Krylov Subspace ◽  
Principal Component ◽  
Optimization Procedure ◽  
Data Driven ◽  
Electromagnetic Simulations ◽  
Order Of Magnitude ◽  
Gradient Based

AbstractDesigning modern photonic devices often involves traversing a large parameter space via an optimization procedure, gradient based or otherwise, and typically results in the designer performing electromagnetic simulations of a large number of correlated devices. In this paper, we investigate the possibility of accelerating electromagnetic simulations using the data collected from such correlated simulations. In particular, we present an approach to accelerate the Generalized Minimal Residual (GMRES) algorithm for the solution of frequency-domain Maxwell’s equations using two machine learning models (principal component analysis and a convolutional neural network). These data-driven models are trained to predict a subspace within which the solution of the frequency-domain Maxwell’s equations approximately lies. This subspace is then used for augmenting the Krylov subspace generated during the GMRES iterations, thus effectively reducing the size of the Krylov subspace and hence the number of iterations needed for solving Maxwell’s equations. By training the proposed models on a dataset of wavelength-splitting gratings, we show an order of magnitude reduction (~10–50) in the number of GMRES iterations required for solving frequency-domain Maxwell’s equations.

Sign in / Sign up

Export Citation Format

Share Document