Complex coordinate system as a generalized absorbing boundary condition

W. C. Chew, J. M. Jin, E. Michielssen

Research output: Contribution to journalConference articlepeer-review


The perfectly matched layer (PML) in Cartesian coordinates is equivalent to solving the wave equation or Maxwell's equations in a complex coordinate system. A closed form solutions that exist in the real coordinate system map to solutions in the complex coordinate system. In the complex coordinate system, the boundaries exist in a complex space, providing absorbing boundary conditions. Hence, this transformation provides a new view of PML in the Cartesian coordinates, clearly showing that a mapping to a complex coordinate system does not induce reflections, explaining why PML works near the corner of a simulation region, and when a dielectric interface, or a metallic surface, extends to the edge of a simulation region.

Original languageEnglish (US)
Pages (from-to)2060-2063
Number of pages4
JournalIEEE Antennas and Propagation Society, AP-S International Symposium (Digest)
StatePublished - 1997
EventProceedings of the 1997 IEEE Antennas and Propagation Society International Symposium. Part 1 (of 4) - Montreal, Can
Duration: Jul 13 1997Jul 18 1997

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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