Fast Induction Logging Modeling With Hierarchical Sudoku Meshes Based on DGFD

This letter extends the discontinuous Galerkin frequency domain (DGFD)-based domain decomposition method (DDM) to model the open borehole environment accurately with a newly developed hierarchical sudoku mesh. Both the borehole and mud invasion effects can be modeled by this framework efficiently. Furthermore, deep reading measurements can be modeled conveniently by inserting arbitrarily shaped objects into the hierarchical sudoku mesh; the capability to distinguish a cavity saturated with either oil or water with different borehole-object distances are then studied for a deep reading tool in an open borehole carbonate environment. The DGFD with the hierarchical sudoku mesh shows six times faster speed than the traditional finite-element method (FEM) for the deep reading case.