Perfectly matched layers as nonlinear coordinate transforms: a generalized formalization
Related Experiment Videos
Jean Paul Hugonin1, Philippe Lalanne
1Laboratoire Charles Fabry de l'Institut d'Optique, Centre National de la Recherche Scientifique, F-91403 Orsay cedex, France. Jean-Paul.Hugonin@iota.u-psud.fr
Abstract:
A modified formulation of Maxwell's equations is presented that includes a complex and nonlinear coordinate transform along one or two Cartesian coordinates. The added degrees of freedom in the modified Maxwell's equations allow one to map an infinite space to a finite space and to specify graded perfectly matched absorbing boundaries that allow the outgoing wave condition to be satisfied. The approach is validated by numerical results obtained by using Fourier-modal methods and shows enhanced convergence rate and accuracy.
Related Concept Videos
Linear Approximation in Frequency Domain
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.
Linearization and Approximation
Transformations of Functions II
Vector Transformation in Rotating Coordinate Systems
Linear Approximations
Linear Approximation in Time Domain
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length, the...