3D time-dependent scattering about complex shapes using high order difference potentials

Sergey Petropavlovsky, Semyon Tsynkov*, Eli Turkel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We compute the scattering of unsteady acoustic waves about complex three-dimensional bodies with high order accuracy. The geometry of a scattering body is defined with the help of CAD. Its surface is represented as a collection of non-overlapping patches, each parameterized independently by means of high order splines (NURBS). As a specific example, we consider a submarine-like scatterer constructed using five different patches. The acoustic wave equation on the region exterior to the scatterer is solved by first reducing it to a system of Calderon's boundary operator equations. The latter are obtained using the method of difference potentials coupled with a compact fourth order accurate finite difference scheme. When solving the boundary operator equations, we employ Huygens' principle. It allows us to work on a sliding time window of non-increasing duration rather than keep the entire temporal history of the solution at the boundary. The proposed methodology demonstrates grid-independent computational complexity at the boundary and sub-linear complexity with respect to the grid dimension. It efficiently handles complex non-conforming geometries on Cartesian grids with no penalty for either accuracy or stability due to the cut cells. Its performance does not deteriorate over arbitrarily long simulation times. The exact treatment of artificial outer boundaries is inherently built in. Finally, multiple similar problems can be solved efficiently at a low individual cost per problem. This is important when, for example, the boundary condition on the surface changes but the scattering body stays the same.

Original languageEnglish
Article number111632
JournalJournal of Computational Physics
StatePublished - 15 Dec 2022


FundersFunder number
Bloom's Syndrome Foundation2020128
Bloom's Syndrome Foundation
United States-Israel Binational Science Foundation


    • CAD surface with patched parameterization
    • Calderon's boundary equations
    • High order splines (NURBS)
    • High-order compact schemes on Cartesian grids
    • Huygens' principle
    • Unsteady acoustic waves


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