Shape identification of scatterers via peridynamics-based parameterization

A shape identification, which is an inverse problem finding the configuration of scatterers using discrepancy or an error functional between real wave data with scatterers and estimated wave data, is investigated employing peridynamic theory and gradient-based optimization in plane elastic medium. The particle-based and non-local characteristics of the peridynamic theory enable the direct modeling of interface between scatterers and medium, avoiding remeshing difficulty when employing domain-based methods. The boundary of scatterers is parame-terized using B-spline surfaces and determined by bond parameters in peridynamics material. The required design sensitivity of the error functional is obtained by an efficient adjoint variable method. The peridynamic adjoint sensitivity involving history-dependent variables in transient peridynamics is accurately obtained by using an identical path in both adjoint and response analyses. Numerical examples of various geometry are demonstrated to verify the accuracy and efficiency of the proposed method.

Automated summary

This paper investigates shape identification using peridynamic theory and gradient-based optimization. The particle-based and non-local characteristics of peridynamics allow for direct interface modeling, avoiding remeshing difficulties. The boundary of scatterers is parameterized using B-spline surfaces, and design sensitivity is obtained using an efficient adjoint variable method. The accuracy and efficiency of the proposed method are verified through numerical examples.