@inbook{3c76fa7fccd74391b8da8fba75dd14f8,
title = "High order Nystr{\"o}m methods for transmission problems for Helmholtz equation",
abstract = "We present super-algebraic compatible Nystr{\"o}m discretizations for the four Helmholtz boundary operators of Calder{\'o}n{\textquoteright}s calculus on smooth closed curves in 2D. These discretizations are based on appropriate splitting of the kernels combined with very accurate product-quadrature rules for the different singularities that such kernels present. A Fourier based analysis shows that the four discrete operators converge to the continuous ones in appropriate Sobolev norms. This proves that Nystr{\"o}m discretizations of many popular integral equation formulations for Helmholtz equations are stable and convergent. The convergence is actually super-algebraic for smooth solutions.",
author = "V{\'i}ctor Dom{\'i}nguez and Catalin Turc",
note = "Funding Information: This research was partially supported by Spanish MINECO grants MTM2011-22741 and MTM2014-54388. Funding Information: Acknowledgements Catalin Turc gratefully acknowledge support from NSF through contract DMS-1312169. V{\'i}ctor Dom{\'i}nguez is partially supported by Ministerio de Econom{\'i}a y Compet-itividad, through the grant MTM2014-52859. Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.",
year = "2016",
doi = "10.1007/978-3-319-32013-7_15",
language = "English (US)",
series = "SEMA SIMAI Springer Series",
publisher = "Springer International Publishing",
pages = "261--285",
booktitle = "SEMA SIMAI Springer Series",
}