scholarly journals Preconditioners With Low Memory Requirements for Higher-Order Finite-Element Method Applied to Solving Maxwell’s Equations on Multicore CPUs and GPUs

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 53072-53079 ◽  
Author(s):  
Adam Dziekonski ◽  
Grzegorz Fotyga ◽  
Michal Mrozowski
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Higher Order ◽  
Element Method ◽  
Multicore Cpus

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.

Nonconforming Mixed Finite Element Method for Time-dependent Maxwell's Equations with ABC

2016 ◽  
Vol 9 (2) ◽  
pp. 193-214
Author(s):  
Changhui Yao ◽  
Dongyang Shi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Absorbing Boundary Conditions ◽  
Time Dependent ◽  
Backward Euler ◽  
Element Method

AbstractIn this paper, a nonconforming mixed finite element method (FEM) is presented to approximate time-dependent Maxwell's equations in a three-dimensional bounded domain with absorbing boundary conditions (ABC). By employing traditional variational formula, instead of adding penalty terms, we show that the discrete scheme is robust. Meanwhile, with the help of the element's typical properties and derivative transfer skills, the convergence analysis and error estimates for semidiscrete and backward Euler fully-discrete schemes are given, respectively. Numerical tests show the validity of the proposed method.

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