Block Preconditioning Strategies for High Order Finite Element Discretization of the Time-Harmonic Maxwell Equations

2011 ◽  
pp. 25-33
Author(s):  
Matthias Bollhöfer ◽  
Stéphane Lanteri
Keyword(s):  
Finite Element ◽  
Maxwell Equations ◽  
High Order ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Time Harmonic ◽  
Block Preconditioning

scholarly journals New Preconditioners with Two Variable Relaxation Parameters for the Discretized Time-Harmonic Maxwell Equations in Mixed Form

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Yuping Zeng ◽  
Chenliang Li
Keyword(s):  
Finite Element ◽  
Theoretical Analysis ◽  
Maxwell Equations ◽  
Schur Complement ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Mixed Form ◽  
Numerical Tests ◽  
Relaxation Parameters ◽  
Time Harmonic

We provide new preconditioners with two variable relaxation parameters for the saddle point linear systems arising from finite element discretization of time-harmonic Maxwell equations in mixed form. The new preconditioners are of block-triangular forms and Schur complement-free. They are extensions of the results in Cheng et al., 2009, Grief and Schötzau, 2007, and Huang et al., 2009. Theoretical analysis shows that all eigenvalues of the preconditioned matrices are tightly clustered, and numerical tests confirm our analysis.

scholarly journals New Preconditioning Techniques for Saddle Point Problems Arising from the Time-Harmonic Maxwell Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Qingbing Liu
Keyword(s):  
Saddle Point ◽  
Numerical Experiments ◽  
Maxwell Equations ◽  
Saddle Point Problems ◽  
Finite Element Discretization ◽  
Preconditioning Techniques ◽  
Element Discretization ◽  
Electromagnetic Problems ◽  
Time Harmonic ◽  
Saddle Point Matrices

We study two parameterized preconditioners for iteratively solving the saddle point linear systems arising from finite element discretization of the mixed formulation of the time-harmonic Maxwell equations in electromagnetic problems. We establish some spectral properties of the preconditioned saddle point matrices, involving the choice of the parameter. Meanwhile, we provide some results of numerical experiments to show the effectiveness of the proposed parameterized preconditioners.

High-Order Low Dissipation Conforming Finite-Element Discretization of the Maxwell Equations

2012 ◽  
Vol 11 (3) ◽  
pp. 863-892 ◽  
Author(s):  
Sébastien Jund ◽  
Stéphanie Salmon ◽  
Eric Sonnendrücker
Keyword(s):  
Taylor Expansion ◽  
Maxwell Equations ◽  
High Order ◽  
Finite Element Discretization ◽  
Element Discretization ◽  
Edge Element ◽  
Discretization Methods ◽  
Low Dissipation ◽  
Conforming Finite Element ◽  
High Order Time

AbstractIn this paper, we study high order discretization methods for solving the Maxwell equations on hybrid triangle-quad meshes. We have developed high order finite edge element methods coupled with different high order time schemes and we compare results and efficiency for several schemes. We introduce in particular a class of simple high order low dissipation time schemes based on a modified Taylor expansion.

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