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Abstract. This paper presents a time-domain technique to compute the electromagnetic fields and to reconstruct the permittivity profile within a one-dimensional medium of finite length. The medium is characterized by a permittivity as well as conductivity profile which vary only with depth. The discussed scattering problem is thus one-dimensional. The modeling tool is divided into two different schemes which are named as the forward solver and the inverse solver. The task of the forward solver is to compute the internal fields of the specimen which is performed by Green’s function approach. When a known electromagnetic wave is incident normally on the media, the resulting electromagnetic field within the media can be calculated by constructing a Green’s operator. This operator maps the incident field on either side of the medium to the field at an arbitrary observation point. It is nothing but a matrix of integral operators with kernels satisfying known partial differential equations. The reflection and transmission behavior of the medium is also determined from the boundary values of the Green's operator. The inverse solver is responsible for solving an inverse scattering problem by reconstructing the permittivity profile of the medium. Though it is possible to use several algorithms to solve this problem, the invariant embedding method, also known as the layer-stripping method, has been implemented here due to the advantage that it requires a finite time trace of reflection data. Here only one round trip of reflection data is used, where one round trip is defined by the time required by the pulse to propagate through the medium and back again. The inversion process begins by retrieving the reflection kernel from the reflected wave data by simply using a deconvolution technique. The rest of the task can easily be performed by applying a numerical approach to determine different profile parameters. Both the solvers have been found to have the ability to deal with different types of slabs and incident electromagnetic pulses. Slabs having continuous and discontinuous relative permittivity have already been tested successfully. The tested electromagnetic pulses are a Dirac, Gaussian and sinusoidal pulse. Due to sampling, the resolution of the system also plays a significant role in obtaining better outputs from this scheme.

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Ultrasonic examination of anisotropic inhomogeneous austenitic welds is challenging, because of the columnar grain structure of the weld leads to beam skewing and splitting. Modeling tools play an important role in understanding the ultrasound field propagation and optimization of experimental parameters during the ultrasonic testing of austenitic welds as well as the interpretation of the test results. In this contribution, an efficient theoretical model based on the ray tracing concepts is developed to calculate the ultrasonic fields in inhomogeneous austenitic welds quantitatively. The developed model determines the ultrasound fields by taking into account the directivity of the ray source, the inhomogenity of the weld as well as ray transmission coefficients. Directivity of the ray source in columnar grained austenitic materials (including layback orientation) is obtained in three dimensions based on Lamb's reciprocity theorem. Ray energy reflection and transmission coefficients at an interface between two general columnar grained austenitic materials are calculated in three dimensions. The ray tracing model predictions on inhomogeneous austenitic weld material are compared against those from CIVA, a commercial non-destructive modeling and simulation tool. The ultrasonic modeling tools in CIVA are based on semi-analytical solutions. For beam propagation simulation, a so-called "pencil method" is used, which involves modeling the probe as a set of individual source points, each radiating "a bundle" of diverging rays into the medium and integrating those elementary contributions. Inhomogenity in the weld region is approximated by mapping the grain orientations on weld macrograph. Simulation results for ultrasonic field profiles for an austenitic weld are shown to be in good agreement with the corresponding experimental results.