Line search algorithms with guaranteed sufficient decrease
ACM Transactions on Mathematical Software (TOMS)
An introduction to the mathematical theory of inverse problems
An introduction to the mathematical theory of inverse problems
Parallel programming with MPI
Waveform Inversion of Reflection Seismic Data for Kinematic Parameters by Local Optimization
SIAM Journal on Scientific Computing
Shape identification for natural convection problems using the adjoint variable method
Journal of Computational Physics
Journal of Computational Physics
Inverse Problem Theory and Methods for Model Parameter Estimation
Inverse Problem Theory and Methods for Model Parameter Estimation
Journal of Computational Physics
Evaluating the volume of a hidden inclusion in an elastic body
Journal of Computational and Applied Mathematics - Special issue: Applied computational inverse problems
Inverse scattering by a continuation method with initial guesses from a direct imaging algorithm
Journal of Computational Physics
Shape determination for deformed electromagnetic cavities
Journal of Computational Physics
Hi-index | 31.45 |
This study deals with elastic-wave identification of discrete heterogeneities (inclusions) in an otherwise homogeneous ''reference'' solid from limited-aperture waveform measurements taken on its surface. On adopting the boundary integral equation (BIE) framework for elastodynamic scattering, the inverse query is cast as a minimization problem involving experimental observations and their simulations for a trial inclusion that is defined through its boundary, elastic moduli, and mass density. For an optimal performance of the gradient-based search methods suited to solve the problem, explicit expressions for the shape (i.e. boundary) and material sensitivities of the misfit functional are obtained via the adjoint field approach and direct differentiation of the governing BIEs. Making use of the message-passing interface, the proposed sensitivity formulas are implemented in a data-parallel code and integrated into a nonlinear optimization framework based on the direct BIE method and an augmented Lagrangian whose inequality constraints are employed to avoid solving forward scattering problems for physically inadmissible (or overly distorted) trial inclusion configurations. Numerical results for the reconstruction of an ellipsoidal defect in a semi-infinite solid show the effectiveness of the proposed shape-material sensitivity formulation, which constitutes an essential computational component of the defect identification algorithm.