@Article{AAMM-4-439, author = {Ma , ZhonghuaLiu , DejunLi , Hui and Gao , Xinsheng}, title = {Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2012}, volume = {4}, number = {4}, pages = {439--453}, abstract = {

A novel, highly efficient and accurate adaptive higher-order finite element method ($hp$-FEM) is used to simulate a multi-frequency resistivity logging-while-drilling (LWD) tool response in a borehole environment. Presented in this study are the vector expression of Maxwell's equations, three kinds of boundary conditions, stability weak formulation of Maxwell's equations, and automatic $hp$-adaptivity strategy. The new $hp$-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation. Numerical experiments show that the new $hp$-FEM has an exponential convergence rate in terms of relative error in a user-prescribed quantity of interest against the degrees of freedom, which provides more accurate results than those obtained using the adaptive $h$-FEM. The numerical results illustrate the high efficiency and accuracy of the method at a given LWD tool structure and parameters in different physical models, which further confirm the accuracy of the results using the Hermes library (http://hpfem.org/hermes) with a multi-frequency resistivity LWD tool response in a borehole environment.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.10-m11158}, url = {http://global-sci.org/intro/article_detail/aamm/129.html} }