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The perfectly matched layer is very important for the elastic wave problem inthe frequency domain. Generally, the formulas of the elasticity tensor in theperfectly matched layers are derived from the transformed momentum equation. Inthis note, we proved that the transformed elasticity tensor derived in this waylost its symmetry. Therefore, these formulas are inconsistency in theory andit's hard to explain its numerical performance. We present a new symmetricalformula of elasticity tensor from the weak form. So the theory of elasticity isstill applicable in the perfectly matched layers.

A symmetric formula of transformed elasticity tensor in PML domain for elastic wave problem