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Perfectly matched layers for hyperbolic systems: General formulation, well-posedness, and stability. (English) Zbl 1110.35042

Summary: Since its introduction the perfectly matched layer (PML) has proven to be an accurate and robust method for domain truncation in computational electromagnetics. However, the mathematical analysis of PMLs has been limited to special cases. In particular, the basic question of whether or not a stable PML exists for arbitrary wave propagation problems remains unanswered. In this work we develop general tools for constructing PMLs for first order hyperbolic systems. We present a model with many parameters, which is applicable to all hyperbolic systems and which we prove is well-posed and perfectly matched. We also introduce an automatic method for analyzing the stability of the model and establishing energy inequalities. We illustrate our techniques with applications to Maxwell’s equations, the linearized Euler equations, and arbitrary \(2 \times 2\) systems in \((2+1)\) dimensions.

MSC:

35L45 Initial value problems for first-order hyperbolic systems
35B35 Stability in context of PDEs
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