scholarly journals AN EFFICIENT APPROACH FOR MULTIFRONTAL ALGORITHM TO SOLVE NON-POSITIVE-DEFINITE FINITE ELEMENT EQUATIONS IN ELECTROMAGNETIC PROBLEMS

2009 ◽  
Vol 95 ◽  
pp. 121-133 ◽  
Author(s):  
Jin Tian ◽  
Zhi-Qing Lv ◽  
Xiao-Wei Shi ◽  
Le Xu ◽  
Feng Wei
Keyword(s):  
Finite Element ◽  
Positive Definite ◽  
Electromagnetic Problems ◽  
Efficient Approach

scholarly journals A New Positive Definite Expanded Mixed Finite Element Method for Parabolic Integrodifferential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Yang Liu ◽  
Hong Li ◽  
Jinfeng Wang ◽  
Wei Gao
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Mixed Finite Element ◽  
Mixed Finite Element Method ◽  
Positive Definite ◽  
Integrodifferential Equations ◽  
Fully Discrete ◽  
Mixed Scheme ◽  
Expanded Mixed Finite Element ◽  
Element Method

A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.

An Enhanced Multigrid Method for Fast Numerical Computation of the Magnetic Vector Potential

2010 ◽  
Vol 670 ◽  
pp. 311-317
Author(s):  
T. Arudchelvam ◽  
D. Rodger ◽  
S.R.H. Hoole
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vector Potential ◽  
Computation Time ◽  
Grid Method ◽  
Magnetic Vector Potential ◽  
The Finite Element Method ◽  
Magnetostatic Field ◽  
Electromagnetic Problems ◽  
Element Method

An enhanced multi-grid method eliminating the error correction process of the conventional multi-grid method is presented for solving Poissonian problems and tested on two simple two-dimensional magnetostatic field problems. The finite element method (FEM) was used to solve for the vector potential in a sequence of grids. The gains in computation time are shown to be immense compared to the standard multi-grid methods, especially as the matrix system grows in size. These gains are very useful in solving electromagnetic problems using the finite element method.

scholarly journals Well Posedness and Finite Element Approximability of Three-Dimensional Time-Harmonic Electromagnetic Problems Involving Rotating Axisymmetric Objects

Symmetry ◽  
2020 ◽  
Vol 12 (2) ◽  
pp. 218 ◽  
Author(s):  
Praveen Kalarickel Ramakrishnan ◽  
Mirco Raffetto
Keyword(s):  
Finite Element ◽  
Boundary Value Problems ◽  
Three Dimensional ◽  
Sufficient Conditions ◽  
Finite Element Approximation ◽  
Element Approximation ◽  
Well Posedness ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
First Time

A set of sufficient conditions for the well posedness and the convergence of the finite element approximation of three-dimensional time-harmonic electromagnetic boundary value problems involving non-conducting rotating objects with stationary boundaries or bianisotropic media is provided for the first time to the best of authors’ knowledge. It is shown that it is not difficult to check the validity of these conditions and that they hold true for broad classes of practically important problems which involve rotating or bianisotropic materials. All details of the applications of the theory are provided for electromagnetic problems involving rotating axisymmetric objects.

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