Singularity-free High Order Boundary Methods for Heterogeneous Wave Problems
Abstract
The overall objective of the project is to develop high order accurate methods for the numerical simulation of time-harmonic waves in heterogeneous media with no accuracy loss due to material interfaces. Our approach exploits Calderon s operators and the method of difference potentials combined with compact finite difference schemes. During the performance period (five years), all the specific research goals have been met. The algorithm handles general scattering shapes on regular structured grids (e.g., Cartesian or polar) with high order accuracy that is unaffected by non-conforming boundaries. It applies to both the pure scattering and transmission-scattering problems, including those with variable coefficients. It can also solve multiple similar problems at a very low individual cost per problem (e.g., same geometry but different boundary conditions and/or the right-hand side). Moreover, it efficiently computes the solutions with singularities due to the discontinuous boundary data. During the last year of performance, we have addressed the two remaining goals. Namely, we have extended the capability to compute singular solutions to the case of singularities due to irregular geometry (e.g., re-entrant corners). We have also added the capability of computing the solutions that involve multiple scattering
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jun 25, 2021
- Source ID
- W911NF1110384
Entities
People
- Semyon Tsynkov
Organizations
- Army Contracting Command
- North Carolina State University
- United States Army