A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media
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| 024 | 7 | 0 | |a 10.1007/s10543-014-0499-8 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s10543-014-0499-8 | ||
| 245 | 0 | 2 | |a A spectrally accurate direct solution technique for frequency-domain scattering problems with variable media |h [Elektronische Daten] |c [Adrianna Gillman, Alex Barnett, Per-Gunnar Martinsson] |
| 520 | 3 | |a 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. | |
| 540 | |a Springer Science+Business Media Dordrecht, 2014 | ||
| 690 | 7 | |a Scattering |2 nationallicence | |
| 690 | 7 | |a Multidomain spectral method |2 nationallicence | |
| 690 | 7 | |a Direct solver |2 nationallicence | |
| 690 | 7 | |a High-order discretization |2 nationallicence | |
| 690 | 7 | |a Second kind Fredholm equation |2 nationallicence | |
| 690 | 7 | |a Boundary integral equation |2 nationallicence | |
| 690 | 7 | |a Nyström discretization |2 nationallicence | |
| 690 | 7 | |a Impedance-to-Impedance map |2 nationallicence | |
| 700 | 1 | |a Gillman |D Adrianna |u Department of Mathematics, Dartmouth College, Hanover, USA |4 aut | |
| 700 | 1 | |a Barnett |D Alex |u Department of Mathematics, Dartmouth College, Hanover, USA |4 aut | |
| 700 | 1 | |a Martinsson |D Per-Gunnar |u Department of Applied Mathematics, University of Colorado, Boulder, USA |4 aut | |
| 773 | 0 | |t BIT Numerical Mathematics |d Springer Netherlands |g 55/1(2015-03-01), 141-170 |x 0006-3835 |q 55:1<141 |1 2015 |2 55 |o 10543 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s10543-014-0499-8 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s10543-014-0499-8 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Gillman |D Adrianna |u Department of Mathematics, Dartmouth College, Hanover, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Barnett |D Alex |u Department of Mathematics, Dartmouth College, Hanover, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Martinsson |D Per-Gunnar |u Department of Applied Mathematics, University of Colorado, Boulder, USA |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t BIT Numerical Mathematics |d Springer Netherlands |g 55/1(2015-03-01), 141-170 |x 0006-3835 |q 55:1<141 |1 2015 |2 55 |o 10543 | ||