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Finite element discretization of nonlinear models of ultrasound heating

Careaga, Julio; Dörich, Benjamin ORCID iD icon 1; Nikolić, Vanja
1 Institut für Angewandte und Numerische Mathematik (IANM), Karlsruher Institut für Technologie (KIT)

Abstract:

Heating generated by high-intensity focused ultrasound waves is central to many emerging medical applications, including non-invasive cancer therapy and targeted drug delivery. In this study, we aim to gain a fundamental understanding of numerical simulations in this context by analyzing conforming finite element approximations of the underlying nonlinear models that describe ultrasound-heat interactions. These models are based on a coupling of a nonlinear Westervelt–Kuznetsov acoustic wave equation to the heat equation with a pressure-dependent source term. A particular challenging feature of the system is that the acoustic medium parameters may depend on the temperature. The core of our new arguments in the a prior error analysis lies in devising energy estimates for the coupled semi-discrete system that can accommodate the nonlinearities present in the model. To derive them, we exploit the parabolic nature of the system thanks to the strong damping present in the acoustic component. Theoretically obtained optimal convergence rates in the energy norm are confirmed by the numerical experiments. In addition, we conduct a further numerical study of the problem, where we simulate the propagation of acoustic waves in liver tissue for an initially excited profile and under high-frequency sources.

Zugehörige Institution(en) am KIT Institut für Angewandte und Numerische Mathematik (IANM)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 01.2025
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000178566
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 28 S.
Serie CRC 1173 Preprint ; 2025/3
Projektinformation SFB 1173/3 (DFG, DFG KOORD, SFB 1173/3)
Externe Relationen Forschungsdaten/Software
Abstract/Volltext
Schlagwörter Westervelt’s equation, Kuznetsov’s equation, wave-heat coupling, finite element approximation, a priori analysis

Volltext §
DOI: 10.5445/IR/1000178566
Veröffentlicht am 30.01.2025
Seitenaufrufe: 24
seit 30.01.2025
Downloads: 14
seit 31.01.2025
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