Abstract
A gradual long-time growth of the solution in perfectly matched layers (PMLs) has been previously reported in the literature. This undesirable phenomenon may hamper the performance of the layer, which is designed to truncate the computational domain for unsteady wave propagation problems. For unsplit PMLs, prior studies have attributed the growth to the presence of multiple eigenvalues in the amplification matrix of the governing system of differential equations. In the current paper, we analyze the temporal behavior of unsplit PMLs for some commonly used second order explicit finite-difference schemes that approximate the Maxwell's equations. Our conclusion is that on top of having the PML as a potential source of long-time growth, the type of the layer and the choice of the scheme play a major role in how rapidly this growth may manifest itself and whether or not it manifests itself at all.
Original language | English |
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Pages (from-to) | 1-12 |
Number of pages | 12 |
Journal | Journal of Scientific Computing |
Volume | 41 |
Issue number | 1 |
DOIs | |
State | Published - Oct 2009 |
Externally published | Yes |
Bibliographical note
Funding Information:Research supported by the US Air Force, grant number FA9550-07-1-0170, and US NSF, grant number DMS-0509695.
Funding
Research supported by the US Air Force, grant number FA9550-07-1-0170, and US NSF, grant number DMS-0509695.
Funders | Funder number |
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US Air Force | FA9550-07-1-0170 |
National Science Foundation | DMS-0509695 |
Directorate for Mathematical and Physical Sciences | 0509695 |
Keywords
- Central difference/Runge-Kutta scheme
- Lax-Wendroff scheme
- Leap-frog scheme
- Long-time growth
- Maxwell's equations
- Numerical solution
- Perfectly matched layer (PML)
- Second order approximation
- Wave propagation
- Yee scheme
- Yee/Runge-Kutta scheme