使用可混合的不连续的加勒金方法,高精度计算电场用于跨磁刺激
1Dept. of Electrical Engineering, Tsinghua University, Beijing, 100084, China.
Scientific reports
|December 2, 2024
概括
混合顺序的混合化不连续的加勒金有限元素方法 (HDG-FEM) 提供了超级电场计算,用于跨磁刺激 (TMS). 与传统方法相比,HDG-FEM在薄层计算中实现了更高的准确性和更低的误差.
科学领域:
- 计算电磁学的计算.
- 数字分析 数字分析
- 生物医学工程 生物医学工程
背景情况:
- 精确的电场计算对于跨磁刺激 (TMS) 是至关重要的.
- 传统的方法,如传统的有限元素方法 (CG-FEM),在处理具有参数变化的薄层时面临挑战.
- 薄层的梯度计算是TMS电场计算中的一个关键难点.
研究的目的:
- 引入和验证TMS电场计算的混合顺序混合化不连续的Galerkin有限元素方法 (HDG-FEM).
- 为了证明HDG-FEM在精度,错误减少和计算效率方面比CG-FEM更优越.
- 分析HDG-FEM在头部模型薄层区域中的性能.
主要方法:
- 导出HDG-FEM的离散格式与TMS的混合订单.
- HDG-FEM与CG-FEM在修改后和现实的头部模型上的比较.
- 评估计算错误 (L∞和L2规范),混合订单利用率和计算成本.
- 将 3D TMS 问题转换为 2D 问题以减少计算复杂性.
主要成果:
- HDG-FEM显示了与具有相同网格的二级CG-FEM相似的L∞规范误差.
- HDG-FEM比同序CG-FEM实现较小的L2规范误差.
- 在HDG-FEM中,混合订单显著减少了薄层错误,而不会大幅增加成本.
- 通过将3D问题转换为2D,计算复杂性从O (p3) 降低到O (p2).
结论:
- HDG-FEM是TMS电场计算的高度准确和高效的方法,特别是在薄层区域.
- 在HDG-FEM中混合订单的灵活性为模拟复杂的头部几何形状提供了显著的优势.
- HDG-FEM为TMS计算提供了一个有希望的新替代方案,其性能优于传统方法.
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