Memory-friendly fixed-point iteration method for nonlinear surface mode oscillations of acoustically driven bubbles: from the perspective of high-performance GPU programming

• Published in: Ultrasonics sonochemistry 2023-10, Vol.99, p.106546-106546, Article 106546
• Main Authors: Kalmár, Péter, Hegedűs, Ferenc, Nagy, Dániel, Sándor, Levente, Klapcsik, Kálmán
• Format: Article
• Language: English
• Subjects: Acoustic cavitation; Bubble dynamics; Fixed-point iteration; High-performance computing; Implicit dynamical system; Original
• ISSN: 1350-4177; 1873-2828
• DOI: 10.1016/j.ultsonch.2023.106546

•Nonlinear spherical stability analysis of acoustic bubbles.•Fixed-point iteration technique to handle implicit nature.•Theoretical comparison with Gauss elimination.•The role of GPU programming.•Analysis of arithmetic operation counts.•Analysis of memory bandwidth limitations. A fixed-point iteration technique is presented to handle the implicit nature of the governing equations of nonlinear surface mode oscillations of acoustically excited microbubbles. The model is adopted from the theoretical work of Shaw [1], where the dynamics of the mean bubble radius and the surface modes are bi-directionally coupled via nonlinear terms. The model comprises a set of second-order ordinary differential equations. It extends the classic Keller–Miksis equation and the linearized dynamical equations for each surface mode. Only the implicit parts (containing the second derivatives) are reevaluated during the iteration process. The performance of the technique is tested at various parameter combinations. The majority of the test cases needs only a single reevaluation to achieve 10-9 error. Although the arithmetic operation count is higher than the Gauss elimination, due to its memory-friendly matrix-free nature, it is a viable alternative for high-performance GPU computations of massive parameter studies.