Grouping of transmitter-receiver positions when using the direct solvers of finite element equation systems in induction logging problems

摘要

The paper is devoted to investigating the possibilities to increase the computational efficiency of the finite element (FE) 3D-modeling of electromagnetic fields in solving the induction logging problems. In order to perform the FE approximation, the non-structured optimized meshes with local refinements are used. It is suggested to apply the direct solvers for FE linear algebraic equation systems (SLAE) and the same mesh for approximation for several neighboring positions of a logging tool at the trajectory, i.e. to perform the grouping of positions. This allows us to perform the most time-consuming operation - SLAE matrix decomposition - only once for a group. The paper considers the problem of optimizing the grouping of transmitter-receiver positions in computing on multi-core PCs. The mathematical model for computing the electromagnetic field induced by arbitrary oriented induction coil is presented. For the geoelectrical model, which is typical of the induction logging problems, computational costs required for different grouping variants are compared. The comparison is presented for the different number of parallel threads. The performed investigations show that the grouping of transmitter-receiver positions for the typical induction logging trajectory makes it possible to significantly (by an order or more) decrease the computational costs required to calculating the 3D electromagnetic fields.