Report: Computational complexity and cost of an approximate hybrid method for electromagnetic scattering from an underground target
Recently, a novel hybrid method for modeling marine controlled source electromagnetics (CSEM), simplified integral equation (SIE) modeling, has shown very promising results in a simplistic 2D setting (Bakr and Mannseth 2009). SIE replaces the computationally intensive part of rigorous integral equation (IE) modeling by an approximate method.
Many 3D CSEM applications are characterized by use of a large number of grid cells in the discretized model of the target. This puts extra emphasis on computational cost and complexity. With finite difference methods the computational domain is larger than the target itself. An advantage, however, is that the corresponding coefficient matrix is sparse. With integral equation (IE) methods only the target needs to be discretized. A disadvantage is that the corresponding coefficient matrix is dense.
We assess the computational cost and complexity of SIE modeling and compare its computational performance to IE modeling for a typical CSEM application in two ways. Firstly, we quantify the theoretical computational performance by analyzing the algorithms and subsequently calculating the number of floating point operations per iteration. Secondly, we observe the number of iterations required to numerically solve a sample of representative problems, and the corresponding CPU times.
It is shown that the theoretical number of floating point operations per iteration with SIE modeling is orders of magnitude smaller than that with IE modeling. A similar computational advantage of SIE over IE is found from the numerical simulations.
