基于重启多项式Krylov子空间模型降阶的全波形瞬变电磁三维正演

Three-dimensional full-time transient electromagnetic modeling using restarting polynomial Krylov subspace model order reduction method

瞬变电磁三维正演在内存占用和求解时间上都是大的挑战.瞬变电磁响应受到发射波形的影响,正演计算中还需考虑发射波形.基于重启多项式Krylov子空间模型降阶方法,本文实现了一种新的全波形瞬变电磁三维正演算法.采用规则六面体网格的拟态有限体积方法对全波形控制方程进行空间离散,引入一阶φ函数推导得到全时段响应的统一表达式,利用重启多项式Krylov子空间算法求解φ函数表达式,对于给定的重启子空间维度,基于残差公式得到满足给定精度的任意时刻的正演响应.该算法内存占用小,不需要求解大型线性方程组,内存占用主要由空间离散网格数量和重启子空间维度决定.数值模型正演结果验证了本文算法的有效性.

Transient electromagnetic(TEM)modeling is a challenge in terms of memory and computing time.TEM responses are affected by the full transmitting-current waveforms and needs to be considered in the forward calculation.In this paper,we present a restarting polynomial Krylov method for modeling three-dimensional full-time TEM responses.The mimetic finite volume method is carried out for spatial discretization.The full-time TEM response then can be expressed as a matrixφfunction.The restarting polynomial Krylov method is used to solve the matrixφfunction.For a given restart subspace dimension,the residual is used to obtain the forward response at any time that meet the given accuracy.This method does not need to solve large-scale linear equations.Furthermore,the memory usage is mainly determined by the number of spatial discrete grids and the restart subspace order.The numerical experiments demonstrated that the method is accurate and memory efficient.