Perfectly matched layer

A perfectly matched layer (PML) is an artificial absorbing layer for <a href="/facts/Wave_equation/J2ksD2Az">wave equations</a>, commonly used to truncate computational regions in <a href="/facts/Numerical_method/MrQIMSIY">numerical methods</a> to simulate problems with open boundaries, especially in the <a href="/facts/Finite-difference_time-domain_method/PvvfRVJo">FDTD</a> and <a href="/facts/Finite_element_method/eUcfP1vn">FE</a> methods. The key property of a PML that distinguishes it from an ordinary absorbing material is that it is designed so that waves incident upon the PML from a non-PML medium do not reflect at the interface—this property allows the PML to strongly absorb outgoing waves from the interior of a computational region without reflecting them back into the interior.
PML was originally formulated by Berenger in 1994 for use with <a href="/facts/Maxwell%2527s_equations/LfJ1drHS">Maxwell's equations</a>, and since that time there have been several related reformulations of PML for both Maxwell's equations and for other wave-type equations, such as elastodynamics, the linearized Euler equations, Helmholtz equations, and poroelasticity. Berenger's original formulation is called a split-field PML, because it splits the <a href="/facts/Electromagnetic_field/MacraS8y">electromagnetic fields</a> into two unphysical fields in the PML region. A later formulation that has become more popular because of its simplicity and efficiency is called uniaxial PML or UPML, in which the PML is described as an artificial <a href="/facts/Birefringence/J4lLuR3a">anisotropic</a> absorbing material. Although both Berenger's formulation and UPML were initially derived by manually constructing the conditions under which incident <a href="/facts/Plane_wave/0aDUbNhQ">plane waves</a> do not reflect from the PML interface from a homogeneous medium, both formulations were later shown to be equivalent to a much more elegant and general approach: stretched-coordinate PML. In particular, PMLs were shown to correspond to a <a href="/facts/Coordinate_transformation/Mtd0q4SP">coordinate transformation</a> in which one (or more) coordinates are mapped to <a href="/facts/Complex_number/2w7mqI7e">complex numbers</a>; more technically, this is actually an <a href="/facts/Analytic_continuation/aBCuEgvt">analytic continuation</a> of the wave equation into complex coordinates, replacing propagating (oscillating) waves by <a href="/facts/Exponentially_decaying/wLB1zYDP">exponentially decaying</a> waves. This viewpoint allows PMLs to be derived for inhomogeneous media such as <a href="/facts/Waveguide/tJS9Y0GH">waveguides</a>, as well as for other <a href="/facts/Coordinate_system/Mtd0q4SP">coordinate systems</a> and wave equations.

Perfectly matched layer open-in-new

Perfectly matched layer