caa a22 4500 605496765 CHVBK 20210128100538.0 cr unu---uuuuu 210128e20150301xx s 000 0 eng 10.1007/s10543-014-0499-8 doi (NATIONALLICENCE)springer-10.1007/s10543-014-0499-8 A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media [Elektronische Daten] [Adrianna Gillman, Alex Barnett, Per-Gunnar Martinsson] This paper presents a direct solution technique for the scattering of time-harmonic waves from a bounded region of the plane in which the wavenumber varies smoothly in space. The method constructs the interior Dirichlet-to-Neumann (DtN) map for the bounded region via bottom-up recursive merges of (discretization of) certain boundary operators on a quadtree of boxes. These operators take the form of impedance-to-impedance (ItI) maps. Since ItI maps are unitary, this formulation is inherently numerically stable, and is immune to problems of artificial internal resonances. The ItI maps on the smallest (leaf) boxes are built by spectral collocation on tensor-product grids of Chebyshev nodes. At the top level the DtN map is recovered from the ItI map and coupled to a boundary integral formulation of the free space exterior problem, to give a provably second kind equation. Numerical results indicate that the scheme can solve challenging problems 70 wavelengths on a side to 9-digit accuracy with 4 million unknowns, in under 5min on a desktop workstation. Each additional solve corresponding to a different incident wave (right-hand side) then requires only 0.04s. Springer Science+Business Media Dordrecht, 2014 Scattering nationallicence Multidomain spectral method nationallicence Direct solver nationallicence High-order discretization nationallicence Second kind Fredholm equation nationallicence Boundary integral equation nationallicence Nyström discretization nationallicence Impedance-to-Impedance map nationallicence Gillman Adrianna Department of Mathematics, Dartmouth College, Hanover, USA aut Barnett Alex Department of Mathematics, Dartmouth College, Hanover, USA aut Martinsson Per-Gunnar Department of Applied Mathematics, University of Colorado, Boulder, USA aut BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 141-170 0006-3835 55:1<141 2015 55 10543 https://doi.org/10.1007/s10543-014-0499-8 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10543-014-0499-8 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Gillman Adrianna Department of Mathematics, Dartmouth College, Hanover, USA aut NATIONALLICENCE 700 1- Barnett Alex Department of Mathematics, Dartmouth College, Hanover, USA aut NATIONALLICENCE 700 1- Martinsson Per-Gunnar Department of Applied Mathematics, University of Colorado, Boulder, USA aut NATIONALLICENCE 773 0- BIT Numerical Mathematics Springer Netherlands 55/1(2015-03-01), 141-170 0006-3835 55:1<141 2015 55 10543