scholarly journals Finite element study of time-dependent Maxwell's equations in dispersive media

2007 ◽  
Vol 24 (5) ◽  
pp. 1203-1221 ◽  
Author(s):  
Jichun Li ◽  
Yitung Chen
Keyword(s):  
Finite Element ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Time Dependent ◽  
Dispersive Media ◽  
Finite Element Study ◽  
Element Study

scholarly journals Finite Element Study on Calculation of Nonlinear Soil Consolidation Using Compression and Recompression Indexes

2020 ◽  
Vol 10 (14) ◽  
pp. 4737
Author(s):  
Chao Xu ◽  
Suli Pan
Keyword(s):  
Finite Element ◽  
Case History ◽  
Time Dependent ◽  
Discrete Equation ◽  
Soil Consolidation ◽  
Coefficient Of Consolidation ◽  
Finite Element Study ◽  
Nonlinear Consolidation ◽  
Element Study

The coefficient of consolidation is traditionally considered as a constant value in soil consolidation calculations. This paper uses compression and recompression indexes to calculate the solution-dependent nonlinear compressibility, thus overconsolidation and normal consolidation are separated during the calculations. Moreover, the complex nonlinear consolidation can be described using the nonlinear compressibility and a nonlinear permeability. Then, the finite element discrete equation with consideration of the time-dependent load is derived, and a corresponding program is developed. Subsequently, a case history is conducted for verifying the proposed method and the program. The results show that the method is sufficiently accurate, indicating the necessity of considering nonlinearity for consolidation calculations. Finally, three cases are compared to reveal the importance of separating the overconsolidation and normal consolidation. Overall, this study concluded that it is inadequate to consider just one consolidation status in calculations, and that the proposed method is more reasonable for guiding construction.

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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