Notes on Perfectly Matched Layers (PMLs)

Abstract

This note is intended as a brief introduction to the theory and practice of perfectly matched layer (PML) absorbing boundaries for wave equations, originally developed for MIT courses 18.369 and 18.336. It focuses on the complex stretched-coordinate viewpoint, and also discusses the limitations of PML.

References in corpus (1)

• Perturbation theory for anisotropic dielectric interfaces, and application to sub-pixel smoothing of discretized numerical methods

Cited by in corpus (33)

• A rapidly converging domain decomposition method for the Helmholtz equation
• A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equations
• Review and Recent Developments on the Perfectly Matched Layer (PML) Method for the Numerical Modeling and Simulation of Elastic Wave Propagation in Unbounded Domains
• A multigrid method for the Helmholtz equation with optimized coarse grid corrections
• Single-cone real-space finite difference scheme for the time-dependent Dirac equation
• A dispersion minimizing scheme for the 3-D Helmholtz equation based on ray theory
• A Reflectionless Discrete Perfectly Matched Layer
• L-Sweeps: A scalable, parallel preconditioner for the high-frequency Helmholtz equation
• Recursive Sweeping Preconditioner for the 3D Helmholtz Equation
• Sweeping Preconditioner for the Helmholtz Equation: Moving Perfectly Matched Layers
• Unscreening scalarons with a black hole
• A nested hybridizable discontinuous Galerkin method for computing second-harmonic generation in three-dimensional metallic nanostructures
• Pseudospectral methods with PML for nonlinear Klein-Gordon equations in classical and non-relativistic regimes
• A computational method for the Helmholtz equation in unbounded domains based on the minimization of an integral functional
• Sweeping Preconditioner for the Helmholtz Equation: Hierarchical Matrix Representation
• Sparsifying preconditioner for the time-harmonic Maxwell's equations
• A multiscale continuous Galerkin method for stochastic simulation and robust design of photonic crystals
• Domain decomposition for quasi-periodic scattering by layered media via robust boundary-integral equations at all frequencies
• Eliminating artificial boundary conditions in time-dependent density functional theory using Fourier contour deformation
• A matrix-free Discontinuous Galerkin method for the time dependent Maxwell equations in unbounded domains
• Perfectly matched layer for second-order time-domain elastic wave equation: formulation and stability
• A boundary integral approach to linear and nonlinear transient wave scattering
• Sparsify and sweep: an efficient preconditioner for the Lippmann-Schwinger equation
• Effect of Choices of Boundary Conditions on the Numerical Efficiency of Direct Solutions of Finite Difference frequency Domain Systems with Perfectly Matched Layers
• Additive Sweeping Preconditioner for the Helmholtz Equation
• Eigenvalue-accelerated LDOS optimization of high-Q optical resonances
• Damping for fractional wave equations and applications to water waves
• PML and high-accuracy boundary integral equation solver for wave scattering by a locally defected periodic surface
• Efficient and Stable Finite Difference Modelling of Acoustic Wave Propagation in Variable-density Media
• Fractional Buffer Layers: Absorbing Boundary Conditions for Wave Propagation
• An isogeometric boundary element method for three-dimensional doubly-periodic layered structures in electromagnetics
• A Truly Exact and Optimal Perfect Absorbing Layer for Time-harmonic Acoustic Wave Scattering Problems
• A symmetric formula of transformed elasticity tensor in PML domain for elastic wave problem