Domain Decomposition Methods For Two-dimensional Magnetotelluric Forward Modeling

With the development of the fine exploration and 3D exploration,the forward and inverse calculation of large-scale and massive data is becoming one of the difficult and hot issues.In recent years,the three-dimensional forward and inverse electromagnetic method has made great progress in the aspects of calculation speed,algorithm optimization and parallel acceleration;However,it is still difficult to be widely used in practical exploration because of the limitation of memory space,computational efficiency and forward accuracy.The domain decomposition algorithm(DDM)is a powerful tool to solve large scale and complex numerical problems by transforming the large-scale problem into many small problems with reducing computational scale greatly and saving memory space.Based on this,this paper takes magnetotelluric(MT)two-dimensional forward modeling as an example to carry out the research and comparative analysis of several different domain decomposition algorithms.It provides the reference and basis for the study of 3D fast forward and inverse modeling of large-scale electromagnetic problem.In this paper,we introduce the basic theory of MT two-dimensional finite difference forward modeling firstly,then introduce the partition method and decomposition patterns of the domain decomposition algorithm.On this basis,we put forward four kinds of different domain decomposition algorithm(The Schur compensation algorithm based on the element partition(E_Schur),the hierarchical domain decomposition algorithm(HDD),the Schur compensation algorithm based on vertex partition(V_Schur)and the Schwarz alternating method(Schwarz))and realize MT two-dimensional forward modeling.Finally,the accuracy and feasibility of the proposed algorithm are verified by a typical geoelectric model.It also makes a comprehensive analysis on the calculation efficiency and influence of the domain decomposition algorithm,such as the partition method,the subdomain shape,the subdomain combination,the number of subdomains and subdomain overlap size.The computational efficiency and required memory are evaluated comprehensively.The numerical simulation results show that the CPU computation time of the four domain decomposition algorithms increases and the memory decreases with the increase of the number of subdomains when compared to the traditional whole domain algorithm.Required memory of E_Schur,HDD and V_Schur drops rapidly with the increase of the number of subdomains first,then showed a slow rise,but overall is still less than the whole domain algorithm;The memory required by the Schwarz alternating method decreases with the increase of the number of subdomains,and the overlapping subdomain combination and overlapping size have some influence on the computational efficiency,which need to be optimized.In this paper,HDD algorithm is relatively good computational efficiency,E_Schur algorithm followed,Schwarz alternating the slowest.To sum up,the algorithm proposed in this paper can greatly reduce the required memory,and has a great advantage in solving large-scale problems.It provides a new idea for the forward and inverse calculation of electromagnetic multi-dimensional large-scale problems.