@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 = {<p style="text-align: justify;">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&#39;s equations, three kinds of boundary conditions, stability weak formulation of
Maxwell&#39;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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.10-m11158},
url = {http://global-sci.org/intro/article_detail/aamm/129.html}
}