TY - JOUR
T1 - High-order numerical solutions in frequency-independent computational times for scattering applications associated with surfaces with composite roughness
AU - Reitich, Fernando
AU - Turc, Catalin
N1 - Funding Information:
Effort sponsored by the Air Force Office of Scientific Research, Air Force Materials Command, USAF, under grant number FA9550-05-1-0019, and by AHPCRC under the auspices of the Department of the Army, Army Research Laboratory cooperative agreement number DAAD19-01-2-0014. The US Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the author and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Research, the Army Research Laboratory or the US Government.
Funding Information:
Fernando Reitich gratefully acknowledges support from AFOSR through contract No. FA9550-05-1-0019, from NSF through grant No. DMS–0311763, and from the Army High Performance Computing Research Center (AHPCRC) under Army Research Laboratory cooperative agreement number DAAD19-01-2-0014.
PY - 2008
Y1 - 2008
N2 - We introduce a new numerical scheme capable of producing, in frequency independent computational times, high-order solutions to scattering problems associated with surfaces with composite roughness. The procedure can be interpreted as providing a high-order version of the classical (low-order) two-scale method and, as such, it can produce solutions of significantly higher quality with comparable computational effort. The basic strategy consists of a suitable combination of (1) a high-order boundary perturbation treatment that views the highly oscillatory components of the surface as a (possibly large) deformation of the slowly varying portion; and (2) an accurate solution method applicable to single-scattering configurations for the sequence of high-frequency scattering problems that results from (1), which entails a fixed, frequency-independent computational cost. More precisely, the boundary variation procedure in (1) allows for the representation of the fields as a convergent sum of terms which are recursively defined as solutions to scattering problems on the slowly varying portion of the surface, with high-frequency incidences that are derived from its highly oscillatory components.
AB - We introduce a new numerical scheme capable of producing, in frequency independent computational times, high-order solutions to scattering problems associated with surfaces with composite roughness. The procedure can be interpreted as providing a high-order version of the classical (low-order) two-scale method and, as such, it can produce solutions of significantly higher quality with comparable computational effort. The basic strategy consists of a suitable combination of (1) a high-order boundary perturbation treatment that views the highly oscillatory components of the surface as a (possibly large) deformation of the slowly varying portion; and (2) an accurate solution method applicable to single-scattering configurations for the sequence of high-frequency scattering problems that results from (1), which entails a fixed, frequency-independent computational cost. More precisely, the boundary variation procedure in (1) allows for the representation of the fields as a convergent sum of terms which are recursively defined as solutions to scattering problems on the slowly varying portion of the surface, with high-frequency incidences that are derived from its highly oscillatory components.
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U2 - 10.1080/17455030802360736
DO - 10.1080/17455030802360736
M3 - Article
AN - SCOPUS:54349097096
SN - 1745-5030
VL - 18
SP - 693
EP - 720
JO - Waves in Random and Complex Media
JF - Waves in Random and Complex Media
IS - 4
ER -