{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T22:06:12Z","timestamp":1764194772481,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2023,5,13]],"date-time":"2023-05-13T00:00:00Z","timestamp":1683936000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at Umm Al-Qura University","award":["22UQU4340548DSR16"],"award-info":[{"award-number":["22UQU4340548DSR16"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The main goal of this work is to develop a novel boundary element method (BEM) model for analyzing ultrasonic wave propagation in three-temperature anisotropic viscoelastic porous media. Due to the problems of the strong nonlinearity of ultrasonic wave propagation in three-temperature porous media, the analytical or numerical solutions to the problems under consideration are always challenging, necessitating the development of new computational techniques. As a result, we use a new BEM model to solve such problems. A time-stepping procedure based on the linear multistep method is obtained after solving the discretized boundary integral equation with the quadrature rule. The calculation of a double integral is required to obtain fundamental solutions, but this increases the total BEM computation time. Our proposed BEM technique is used to solve the current problem and improve the formulation efficiency. The numerical results are graphed to demonstrate the effects of viscosity and anisotropy on the nonlinear ultrasonic stress waves in three-temperature porous media. The validity, accuracy, and efficiency of the proposed methodology are demonstrated by comparing the obtained results to a corresponding solution obtained from the finite difference method (FDM).<\/jats:p>","DOI":"10.3390\/axioms12050473","type":"journal-article","created":{"date-parts":[[2023,5,15]],"date-time":"2023-05-15T08:33:01Z","timestamp":1684139581000},"page":"473","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Three-Temperature Boundary Element Modeling of Ultrasound Wave Propagation in Anisotropic Viscoelastic Porous Media"],"prefix":"10.3390","volume":"12","author":[{"given":"Mohamed Abdelsabour","family":"Fahmy","sequence":"first","affiliation":[{"name":"Department of Basic Sciences, Adham University College, Umm Al-Qura University, Makkah 28653, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohammed O.","family":"Alsulami","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 24381, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ahmed E.","family":"Abouelregal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science and Arts, Jouf University, Al-Qurayyat 72388, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1087","DOI":"10.1016\/j.ijheatmasstransfer.2014.08.057","article-title":"Steady MHD flow and heat transfer of a third grade fluid in wire coating analysis with temperature dependent viscosity","volume":"79","author":"Nayak","year":"2014","journal-title":"Int. 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