Analysis and Applications of Numerical Methods for Wave-Propagation Problems

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 10 October 2025 | Viewed by 412

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Centro de Investigación Científica y de Educación Superior de Ensenada (CICESE), Baja California, 22860 Ensenada, Mexico
Interests: numerical analysis; elastic wave propagation; seismology, geophysics; fractured media
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Guest Editor
Department of Mathematics and Statistics, Texas A&M University-Corpus Christi, Corpus Christi, TX 78412, USA
Interests: numerical analysis; elastic wave propagation; geophysics; fractured media; multiscale methods
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Wave-propagation problems are found in every field of science and engineering, including geophysics, oceanology, civil engineering, aerospace engineering, medicine, and many others. This Special Issue covers all areas of the analysis and application of numerical methods for wave-propagation problems, including acoustic, elastic, seismic, viscoelastic, poroelastic and electromagnetic waves. We encourage the submission of papers that consider pseudospectral, finite volume, finite difference, finite element, spectral element, discontinuous Galerkin, or enriched Galerkin methods. Papers dealing with other methods applicable to wave phenomena will also be considered.

Prof. Dr. Jonas D. De Basabe
Dr. Maria Vasilyeva
Guest Editors

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Keywords

  • discontinuous Galerkin
  • wave equation
  • numerical analysis
  • finite elements
  • hyperbolic equations
  • wave propagation
  • finite difference method
  • finite volume method
  • spectral element method
  • enriched Galerkin method
  • mixed finite element method
  • multiscale methods
  • upscaling/homogeneization

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Published Papers (1 paper)

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Research

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 259
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
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