zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Indirect methods with Brakhage-Werner potentials for Helmholtz transmission problems. (English) Zbl 1119.65414
Bermúdez de Castro, Alfredo (ed.) et al., Numerical mathematics and advanced applications. Proceedings of ENUMATH 2005, the 6th European conference on numerical mathematics and advanced applications, Santiago de Compostela, Spain, July 18–22, 2005. Berlin: Springer (ISBN 3-540-34287-7/hbk). 1146-1154 (2006).
Summary: We propose and analyse numerical methods for Helmholtz transmission problems in two and three dimensions. The methods we analyse use combined single and double layer potentials to represent the interior and exterior solution of the transmission problem. The corresponding boundary integral system includes weakly singular and hypersingular boundary integral operators on the interface. Its invertibility is equivalent to the unique solvability of the transmission problem, since the use of the above mentioned potentials does not introduce spurious eigenmodes in the formulation. We give necessary and sufficient conditions for the convergence of general Petrov-Galerkin schemes for solving the resulting system, providing some concrete methods for the two-dimensional case. Some numerical experiments are shown.
65N38Boundary element methods (BVP of PDE)
35J05Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation
65N12Stability and convergence of numerical methods (BVP of PDE)