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Keywords = discontinuous Galerkin method (DGM)

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18 pages, 5103 KiB  
Article
Elastic Wave Propagation Through Cylinders with Fluid-Filled Fractures Using the Discontinuous Galerkin Method
by Ana L. Ramos-Barreto, Jonas D. De Basabe and Raul U. Silva-Avalos
Mathematics 2025, 13(10), 1572; https://doi.org/10.3390/math13101572 - 10 May 2025
Viewed by 388
Abstract
Accurately modeling fractures in wave-propagation simulations is challenging due to their small scale relative to other features. While equivalent-media models can approximate fracture-induced anisotropy, they fail to capture their discrete influence on wave propagation. To address this limitation, the Interior-Penalty Discontinuous Galerkin Method [...] Read more.
Accurately modeling fractures in wave-propagation simulations is challenging due to their small scale relative to other features. While equivalent-media models can approximate fracture-induced anisotropy, they fail to capture their discrete influence on wave propagation. To address this limitation, the Interior-Penalty Discontinuous Galerkin Method (IP-DGM) can be adapted to incorporate the Linear-Slip Model (LSM) to represent fractures explicitly. In this study, we apply IP-DGM to elastic wave propagation in fractured cylindrical domains using realistic fracture compliances obtained from laboratory experiments (using ultrasonic-pulse transmission) to simulate the effects of fluid-filled fractures. We analyze how fracture spacing and fluid type influence P- and S-wave behavior, focusing on amplitude attenuation and wave-front delays. Our numerical results align with experimental and theoretical predictions, demonstrating that higher-density fluids enhance wave transmission, reducing the impedance contrast and improving coupling across fracture surfaces. These findings highlight the capability of IP-DGM to accurately model wave propagation in realistic fractured and saturated media, providing a valuable tool for seismic monitoring in fractured reservoirs and other applications where fluid-filled fractures are prevalent. Full article
(This article belongs to the Special Issue Analysis and Applications of Numerical Methods for Wave-Propagation Problems)
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22 pages, 892 KiB  
Article
Novel Stopping Criteria for Optimization-Based Microwave Breast Imaging Algorithms
by Cameron Kaye, Ian Jeffrey and Joe LoVetri
J. Imaging 2019, 5(5), 55; https://doi.org/10.3390/jimaging5050055 - 22 May 2019
Cited by 5 | Viewed by 5229
Abstract
A discontinuous Galerkin formulation of the Contrast Source Inversion algorithm (DGM-CSI) for microwave breast imaging employing a frequency-cycling reconstruction technique has been modified here to include a set of automated stopping criteria that determine a suitable time to shift imaging frequencies and to [...] Read more.
A discontinuous Galerkin formulation of the Contrast Source Inversion algorithm (DGM-CSI) for microwave breast imaging employing a frequency-cycling reconstruction technique has been modified here to include a set of automated stopping criteria that determine a suitable time to shift imaging frequencies and to globally terminate the reconstruction. Recent studies have explored the use of tissue-dependent geometrical mapping of the well-reconstructed real part to its imaginary part as initial guesses during consecutive frequency hops. This practice was shown to improve resulting 2D images of the dielectric properties of synthetic breast models, but a fixed number of iterations was used to halt DGM-CSI inversions arbitrarily. Herein, a new set of stopping conditions is introduced based on an intelligent statistical analysis of a window of past iterations of data error using the two-sample Kolmogorov-Smirnov (K-S) test. This non-parametric goodness-of-fit test establishes a pattern in the data error distribution, indicating an appropriate time to shift frequencies, or terminate the algorithm. The proposed stopping criteria are shown to improve the efficiency of DGM-CSI while yielding images of equivalent quality to assigning an often liberally overestimated number of iterations per reconstruction. Full article
(This article belongs to the Special Issue Microwave Imaging and Electromagnetic Inverse Scattering Problems)
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