The perfectly matched layer (PML) is one of the most popular domain truncation techniques used in differential-equation based wave-type equation solvers. Practical implementations of PMLs often use smooth-varying attenuation coefficients to reduce the numerical reflection from PMLs and to reduce the thickness required for reaching a certain level of absorption . In discontinuous Galerkin time-domain (DGTD) methods, assigning smooth-varying coefficients calls for storing individual mass matrices for each mesh element , which significantly increases the memory-cost. This workproposes a memory-efficient implementation of smooth-varying PMLs in DGTD. A weight-adjusted approximation is applied to the mass matricesinvolved in the PML formulation, which yields a low memory-cost algorithm and maintains the high-order accuracy of DGTD. The proposed scheme has the same accuracy as the implementation of storing local mass matricesof each element, and provides a higher mesh flexibility and a smaller reflectionthan using a constant coefficient in each element .
Wrapping a computation domain with a perfectly matched layer (PML) is one of the most effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave equation solvers. Many PML implementations often use a smoothly-increasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to reduce the numerical reflection from the interface between the computation domain and the PML . In discontinuous Galerkin time-domain (DGTD) methods, using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore significantly increases the memory footprint. In this work, this bottleneck is addressed by applying a weight-adjusted approximation to these mass matrices. The resulting DGTD scheme has the same advantages as the scheme that stores individual mass matrices, namely higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer) but it requires significantly less memory .
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The
Wrapping a computation domain with a
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popular domain truncation techniques used in differential-equation based wave-type
effective methods of imitating/approximating the radiation boundary condition in Maxwell and wave
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Practical implementations of PMLs often use smooth-varying attenuation coefficients to
Many PML implementations often use a smoothly-increasing attenuation coefficient to increase the absorption for a given layer thickness, and, at the same time, to
R
PMLs and to reduce the thickness required for reaching a certain level of absorption
the interface between the computation domain and the PML
R
assigning smooth-varying coefficients calls for storing individual mass matrices for each mesh element , which
using a PML coefficient that varies within a mesh element requires a different mass matrix to be stored for every element and therefore
R
memory-cost. This workproposes a memory-efficient implementation of smooth-varying PMLs in DGTD. A
memory footprint. In this work, this bottleneck is addressed by applying a
R
is applied to the mass matricesinvolved in the PML formulation, which yields a low memory-cost algorithm and maintains the high-order accuracy of DGTD. The proposed
to these mass matrices. The resulting DGTD
R
accuracy as the implementation of storing local mass matricesof each element, and provides a higher mesh flexibility and a smaller reflectionthan using a constant coefficient in each element
advantages as the scheme that stores individual mass matrices, namely higher accuracy (due to reduced numerical reflection) and increased meshing flexibility (since the PML does not have to be defined layer by layer) but it requires significantly less memory