大规模三维频率域电磁积分方程法数值模拟

Large-scale 3D electromagnetic modeling in frequency domain using integration equation method

地电磁学频率域电磁法在地球深部结构探测、油气勘查、环境与工程勘探等领域有着广泛的应用,其数值模拟的精度、速度直接影响资料解释结果。然而,当前频率域电磁三维数值模拟存在着求解精度差、计算时间长、计算规模受限等问题。采用积分方程法和直接解法提高求解精度,采用多层级多粒度混合并行、分布式存储等技术,大幅减少计算时间,扩大计算规模。实现了一种频点间并行、阻抗矩阵并行填充、方程组并行直接求解的快速、高精度、高可扩展性的频率域电磁三维数值模拟。首先,详细介绍了积分方程法理论和并行实现方案。然后,选取典型案例,通过与前人计算结果进行对比验证了程序的正确性。最后,针对1个16频点、16×12495个未知量、861个观测点的大规模算例进行了可扩展性测试,相比于1个节点32个进程,当计算规模达到256个节点8 192个进程时,加速比为69.69,并行效率为27.22%。此大规模并行算法适用于大地电磁和可控源音频大地电磁积分方程法。

Electromagnetic method of geoelectrical frequency domain has a wide range of applications in exploring Earth's deep structure,petroleum exploration,environmental and engineering surveying,and its accuracy and efficiency of numerical simulation directly affect the interpretation results of data.However,there are currently issues with low accuracy and long computation time in three-dimensional numerical simulation of frequency domain electromagnetic fields,as well as limitations in computational scale.This paper proposes to use integral equation method and direct solution method to improve the solution accuracy,and adopt technologies such as hybrid parallel processing at multiple levels and multiple grain sizes,distributed storage,etc.,to greatly reduce the computation time and expand the computational scale.This paper implements a fast,high-precision,and highly scalable three-dimensional numerical simulation method of frequency domain electromagnetic fields,which includes parallel processing between frequency points,parallel filling of impedance matrix,and parallel direct solution of equations.Firstly,the theoretical framework of integral equation method and its parallel implementation solution are introduced in detail.Then,typical cases are selected to verify the correctness of the program by comparing with previous calculation results.Finally,the scalability is tested for a large-scale example with 16 frequencies,16×12495 unknowns,and 861 observation points.Compared to a single node with 32 processes,when the computational scale reaches 256 nodes and 8192 processes,the speedup ratio is 69.69 and the parallel efficiency is 27.22%.This large-scale parallel algorithm is applicable to both geomagnetic and controlled source audio geomagnetic integral equation methods.