zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The perfectly matched layer in curvilinear coordinates. (English) Zbl 0940.78011
A Maxwell system in two space dimensions is considered. Change of variable technique is used to construct Berenger’s perfectly matched layer (PML) model in curvilinear coordinates. For the time harmonic scattering problem the existence of a unique solution is proved for the obtained model with infinite layer. Then two truncation procedures are considered using, respectively Dirichlet condition and Sommerfeld radiation condition on the outer boundary. Except for a finite set of exceptional frequencies the existence of a unique solution of the truncated problems is proved. The models obtained are suitable to be solved numerically by the finite element method. Berenger’s PML for a time dependent Maxwell system is developed as well. Several test problems are considered. The numerical results show high accuracy of the developed approach.

MSC:
78M10Finite element methods (optics)
78A45Diffraction, scattering (optics)
65N30Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (BVP of PDE)
65M60Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods (IVP of PDE)
35Q60PDEs in connection with optics and electromagnetic theory