A new explicit higher-order time-domain finite element method for solving maxwell’s equations

2007 ◽  
Author(s):  
Zheng Lou ◽  
Jian-Ming Jin
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Time Domain ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Higher Order ◽  
Element Method

Numerical Simulation of a Multi-Frequency Resistivity Logging-While-Drilling Tool Using a Highly Accurate and Adaptive Higher-Order Finite Element Method

2012 ◽  
Vol 4 (04) ◽  
pp. 439-453 ◽  
Author(s):  
Zhonghua Ma ◽  
Dejun Liu ◽  
Hui Li ◽  
Xinsheng Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
High Efficiency ◽  
Higher Order ◽  
Physical Models ◽  
Logging While Drilling ◽  
Resistivity Logging ◽  
Element Method

AbstractA 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 automatichp-adaptivity strategy. The newhp-FEM can select optimal refinement and calculation strategies based on the practical formation model and error estimation. Numerical experiments show that the newhp-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 adaptiveh-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.

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