对于具有异质声音速度和密度的声学赫尔姆霍尔茨方程的Iterative Born解答器
Antonio Stanziola1, Simon R Arridge2, Bradley E Treeby1
1Department of Medical Physics and Biomedical Engineering, University College London, London WC1E 6BT, United Kingdom.
The Journal of the Acoustical Society of America
|February 13, 2026
概括
一个新的代溶解器在复杂的介质中有效地解决了声学赫尔姆霍尔茨方程,从而实现了先进的生物医学和地震成像应用. 这种方法处理密度变化而不需要昂贵的计算.
科学领域:
- 计算物理学的计算物理.
- 声学 声学 在声学方面
- 数字分析 数字分析
背景情况:
- 在异质介质中解决声学海尔姆霍尔茨方程在计算上具有挑战性.
- 现有的方法与涉及空间密度变化的大规模问题作斗争,限制了生物医学声学和地震成像中的应用.
研究的目的:
- 介绍一个快速代解法器,扩展汇波恩数列方法.
- 为了同时处理声音速度,密度和吸收的任意变化.
- 为大规模的三维异质声学问题提供高效的解决方案.
主要方法:
- 重构赫尔姆霍尔茨方程作为一个第一阶系统.
- 应用了一个具有快速富里埃变换的通用分割先决条件,用于无矩阵算法.
- 扩展了融合波恩序列方法,以适应异质密度,而无需昂贵的预处理.
主要成果:
- 解决器有效地处理声音速度,密度和吸收的任意变化.
- 它实现了强散射场景的融合,并且内存开销最小.
- 提供了前向和相邻的解决方案,适合逆向问题.
结论:
- 开发的解决器为异质介质中的声学赫尔姆霍尔茨方程解决方案提供了一个计算效率高的替代方案.
- 它适用于大规模的3D问题,具有最小的内存要求.
- 在跨膜超声波模拟和地震勘探中表现出实际实用性.
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