TY - JOUR
T1 - High-order discretization of a stable time-domain integral equation for 3D acoustic scattering
AU - Barnett, Alex
AU - Greengard, Leslie
AU - Hagstrom, Thomas
N1 - Funding Information:
Funding: Supported in part by NSF Grant DMS-1418871 and the U.S. Department of Energy ASCR Applied Mathematics program. Any conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF or DOE.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation. The spatial discretization, of Nyström type, uses Gaussian quadrature on panels combined with a special treatment of the weakly singular kernels arising in near-neighbor interactions. In time, a new class of convolution splines is used in a predictor-corrector algorithm. Experiments on a torus and a perturbed torus are used to explore the stability and accuracy of the proposed scheme. This involved around one thousand solver runs, at up to 8th order and up to around 20,000 spatial unknowns, demonstrating 5–9 digits of accuracy. In addition we show that parameters in the combined field formulation, chosen on the basis of analysis for the sphere and other convex scatterers, work well in these cases.
AB - We develop a high-order, explicit method for acoustic scattering in three space dimensions based on a combined-field time-domain integral equation. The spatial discretization, of Nyström type, uses Gaussian quadrature on panels combined with a special treatment of the weakly singular kernels arising in near-neighbor interactions. In time, a new class of convolution splines is used in a predictor-corrector algorithm. Experiments on a torus and a perturbed torus are used to explore the stability and accuracy of the proposed scheme. This involved around one thousand solver runs, at up to 8th order and up to around 20,000 spatial unknowns, demonstrating 5–9 digits of accuracy. In addition we show that parameters in the combined field formulation, chosen on the basis of analysis for the sphere and other convex scatterers, work well in these cases.
KW - Acoustic scattering
KW - High-order methods
KW - Time-domain integral equations
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U2 - 10.1016/j.jcp.2019.109047
DO - 10.1016/j.jcp.2019.109047
M3 - Article
AN - SCOPUS:85074895909
VL - 402
JO - Journal of Computational Physics
JF - Journal of Computational Physics
SN - 0021-9991
M1 - 109047
ER -