Obstacle identification using the TRAC algorithm with a second‐order ABC

Abstract

Summary We consider obstacle identification using wave propagation. In such problems, one wants to find the location, shape, and size of an unknown obstacle from given measurements. We propose an algorithm for the identification task based on a time‐reversed absorbing condition (TRAC) technique. Here, we apply the TRAC method to time‐dependent linear acoustics, although our methodology can be applied to other wave‐related problems as well, such as elastodynamics. There are two main contributions of our identification algorithm. The first contribution is the development of a robust and effective method for obstacle identification. While the original paper presented criteria for accepting or rejecting regions that enclose the obstacle, we use these criteria to develop an algorithm that automatically identifies the location of the obstacle. The second contribution is the utilization of an improved absorbing boundary condition (ABC) for the identification. We use the second‐order Engquist‐Majda ABC, and we implement it with a finite element scheme. To our knowledge, this is the first time that the second‐order Engquist‐Majda ABC is employed with the finite element method, as this boundary condition does not naturally fit in finite element schemes in its original form. Numerical experiments for the algorithms are presented.

Scatterer identification in a 2D geophysical medium using an augmented computational time reversal method

“…47. Also, in the TRAC variant of the TR method, 48 the scheme is stable despite the use of a time‐reversed ABC.…”

Dirichlet‐type absorbing boundary conditions for peridynamic scalar waves in two‐dimensional viscous media

“…4 The perfectly matched layer (PML) and the absorbing boundary conditions (ABCs) are the most prominent ABMs, and development of new ABMs is still an ongoing topic of research. [5][6][7][8] Essentially, the idea of ABMs is to limit the computational domain to a region of interest called the near-field, while referring to the area outside that region as the far-field. Provided that appropriate (artificial) boundary conditions are imposed on the boundary of the near-field (referred to as the truncating boundary), the solution of an unbounded problem can be obtained within this region.…”

“…Artificial boundary methods (ABMs) have been developed to address problems on unbounded domains 4 . The perfectly matched layer (PML) and the absorbing boundary conditions (ABCs) are the most prominent ABMs, and development of new ABMs is still an ongoing topic of research 5‐8 . Essentially, the idea of ABMs is to limit the computational domain to a region of interest called the near‐field , while referring to the area outside that region as the far‐field .…”

Perfectly matched layers for peridynamic scalar waves and the numerical discretization on real coordinate space

“…Development of new ABMs is still an ongoing topic of research. [12][13][14] More recently, a number of studies have been conducted on the application of ABCs to nonlocal models. In one dimension (1D), ABCs are considered for the PD scalar wave-type equation in Reference 15 and for the nonlocal Schrödinger equation in References 16 and 17.…”