Symmetric positive-definite representation of frequency-domain finite-element system matrix for efficient electromagnetic analysis

2016 ◽  
Author(s):  
Woochan Lee ◽  
Dan Jiao
Keyword(s):  
Finite Element ◽  
Frequency Domain ◽  
Positive Definite ◽  
Electromagnetic Analysis ◽  
System Matrix ◽  
Symmetric Positive Definite ◽  
Element System

Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver

2014 ◽  
Vol 15 (4) ◽  
pp. 1045-1067 ◽  
Author(s):  
Wenqiang Feng ◽  
Xiaoming He ◽  
Yanping Lin ◽  
Xu Zhang
Keyword(s):  
Finite Element ◽  
Stiffness Matrix ◽  
Positive Definite ◽  
Algebraic Multigrid ◽  
Interface Problems ◽  
Multigrid Solver ◽  
Immersed Finite Element ◽  
Symmetric Positive Definite ◽  
Moving Interface ◽  
Moving Interface Problems

AbstractThis article is to discuss the bilinear and linear immersed finite element (IFE) solutions generated from the algebraic multigrid solver for both stationary and moving interface problems. For the numerical methods based on finite difference formulation and a structured mesh independent of the interface, the stiffness matrix of the linear system is usually not symmetric positive-definite, which demands extra efforts to design efficient multigrid methods. On the other hand, the stiffness matrix arising from the IFE methods are naturally symmetric positive-definite. Hence the IFE-AMG algorithm is proposed to solve the linear systems of the bilinear and linear IFE methods for both stationary and moving interface problems. The numerical examples demonstrate the features of the proposed algorithms, including the optimal convergence in both L2and semi-H1norms of the IFE-AMG solutions, the high efficiency with proper choice of the components and parameters of AMG, the influence of the tolerance and the smoother type of AMG on the convergence of the IFE solutions for the interface problems, and the relationship between the cost and the moving interface location.

Efficient Electromagnetic Analysis for Cryptographic Module on the Frequency Domain

2015 ◽  
Vol 135 (9) ◽  
pp. 515-521
Author(s):  
Yu-ichi Hayashi ◽  
Naofumi Homma ◽  
Takaaki Mizuki ◽  
Takafumi Aoki ◽  
Hideaki Sone
Keyword(s):  
Frequency Domain ◽  
Electromagnetic Analysis

The BERSAFE finite element system

1974 ◽  
Vol 6 (1) ◽  
pp. 15-24 ◽  
Author(s):  
T.K. Hellen ◽  
S.J. Protheroe
Keyword(s):  
Finite Element ◽  
Element System
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