基于Cython混合编程的电阻率法正演优化

Resistivity Forward Modeling Optimization Based on Cython Hybrid Programming

摘要: 本文以纯Python实现的电阻率法有限元正演算法为研究对象，开展了一套从性能剖析到靶向优化的混合编程实践研究。通过性能剖析发现，在中小规模网格下，矩阵组装耗时占总计算时间的75%以上，是程序的主要性能瓶颈。针对这一瓶颈，对全局刚度矩阵组装(含单元计算)模块进行Cython静态类型重写，显著提升了代码执行效率。实验结果表明，优化后的算法在保证计算精度的前提下，矩阵组装模块获得最高62倍的加速比，将Python解释器在热点函数中的开销降至可忽略水平。在典型测试模型下，矩阵组装模块获得53倍加速比，程序整体执行效率提升约6.4倍。

Abstract: This paper presents a case study of hybrid programming for a pure Python-implemented finite element forward modeling algorithm for the resistivity method, spanning from performance profiling to targeted optimization. Through performance profiling, it was found that for small to medium-scale meshes, the matrix assembly process accounts for over 75% of the total computation time, making it the primary performance bottleneck of the program. To address this, the global stiffness matrix assembly module (including element calculations) was rewritten with Cython static typing, significantly enhancing code execution efficiency. Experimental results demonstrate that the optimized algorithm achieves a speedup of up to 62x for the matrix assembly module while maintaining computational accuracy, reducing the overhead of the Python interpreter in hot functions to negligible levels. Under the typical test model, the matrix assembly module achieves a 53x speedup, and the overall program execution efficiency improves by approximately 6.4x.