Mathematical Foundations of Computational Electromagnetism by Franck Assous Patrick Ciarlet & Simon Labrunie

Author:Franck Assous, Patrick Ciarlet & Simon Labrunie
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

5.2.4.1 Homogeneous Absorbing Boundary Condition

We scale the unknowns, as in Sect. 5.2.2: and . The homogeneous ABC then writes

To fit within the framework of first-order problems, we introduce (with a superscript e )

The operator A e is an unbounded operator of V e  = L 2(Ω) ×L 2(Ω), and we define its domain by

As V e  = V h , we use the definitions and notations of Sect. 5.2.1 (replace h with e ) for its scalar product and norm.

Proposition 5.2.8

The operator A e is maximal monotone.

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