An efficient discontinuous Galerkin finite element method with nested domain decomposition for simulations of microresistivity imaging

• Published in: Journal of applied geophysics Vol. 114; pp. 116 - 122
• Main Author: Chen, Jiefu
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.03.2015
• Subjects: Block Thomas method; Discontinuous Galerkin finite element method (DG-FEM); Domain decomposition; Microresistivity imaging; Well logging; Discontinuous Galerkin finite element method (DG-FEM); Microresistivity imaging; Block Thomas method; Well logging; Domain decomposition
• ISSN: 0926-9851; 1879-1859
• DOI: 10.1016/j.jappgeo.2015.01.006

A discontinuous Galerkin finite element method is employed to study the responses of microresistivity imaging tools used in the oil and gas exploration industry. The multiscale structure of an imaging problem is decomposed into several nested subdomains based on its geometric characteristics. Each subdomain is discretized independently, and numerical flux is used to couple all subdomains together. The nested domain decomposition scheme will lead to a block tridiagonal linear system, and the block Thomas algorithm is utilized here to eliminate the subdomain based iteration in the step of solving the linear system. Numerical results demonstrate the validity and efficiency of this method. •We model the responses of borehole microresistivity imaging tools in well logging.•A discontinuous Galerkin finite element method is used for simulation.•A Nested domain decomposition scheme is proposed for multiscale discretization.•The block Thomas algorithm can speed up solving the block tridiagonal system.