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MICROLOCAL DIAGONALIZATION OF STRICTLY HYPERBOLIC PSEUDODIFFERENTIAL SYSTEMS AND APPLICATION TO THE
 

Summary: MICROLOCAL DIAGONALIZATION OF STRICTLY HYPERBOLIC
PSEUDODIFFERENTIAL SYSTEMS AND APPLICATION TO THE
DESIGN OF RADIATION CONDITIONS IN ELECTROMAGNETISM #
XAVIER ANTOINE + AND HELENE BARUCQ #
SIAM J. APPL. MATH. c
# 2001 Society for Industrial and Applied Mathematics
Vol. 61, No. 6, pp. 1877--1905
Abstract. In [Comm. Pure Appl. Math., 28 (1975), pp. 457--478], M. E. Taylor describes a
constructive diagonalization method to investigate the reflection of singularities of the solution to
first­order hyperbolic systems. According to further works initiated by Engquist and Majda, this
approach proved to be well adapted to the construction of artificial boundary conditions. However,
in the case of systems governed by pseudodi#erential operators with variable coe#cients, Taylor's
method involves very elaborate calculations of the symbols of the operators. Hence, a direct approach
may be di#cult when dealing with high­order conditions. This motivates the first part of this
paper, where a recursive explicit formulation of Taylor's method is stated for microlocally strictly
hyperbolic systems. Consequently, it provides an algorithm leading to symbolic calculations which
can be handled by a computer algebra system. In the second part, an application of the method
is investigated for the construction of local radiation boundary conditions on arbitrarily shaped
surfaces for the transverse electric Maxwell system. It is proved that they are of complete order,
provided the introduction of a new symbols class well adapted to the Maxwell system. Next, a

  

Source: Antoine, Xavier - Institut de Mathématiques Élie Cartan, Université Henri Poincaré - Nancy 1

 

Collections: Mathematics