From the Boundary Element Domain Decomposition Methods to Local Trefftz Finite Element Methods on Polyhedral Meshes

2009 ◽  
pp. 315-322 ◽  
Author(s):  
Dylan Copeland ◽  
Ulrich Langer ◽  
David Pusch
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Boundary Element ◽  
Finite Element Methods ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Polyhedral Meshes ◽  
Trefftz Finite Element

scholarly journals Non-conformal domain decomposition methods for time-harmonic Maxwell equations

2012 ◽  
Vol 468 (2145) ◽  
pp. 2433-2460 ◽  
Author(s):  
Yang Shao ◽  
Zhen Peng ◽  
Kheng Hwee Lim ◽  
Jin-Fa Lee
Keyword(s):  
Integral Equation ◽  
Finite Element ◽  
Domain Decomposition ◽  
Wave Scattering ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Surface Integral ◽  
Scattering Problems

We review non-conformal domain decomposition methods (DDMs) and their applications in solving electrically large and multi-scale electromagnetic (EM) radiation and scattering problems. In particular, a finite-element DDM, together with a finite-element tearing and interconnecting (FETI)-like algorithm, incorporating Robin transmission conditions and an edge corner penalty term , are discussed in detail. We address in full the formulations, and subsequently, their applications to problems with significant amounts of repetitions. The non-conformal DDM approach has also been extended into surface integral equation methods. We elucidate a non-conformal integral equation domain decomposition method and a generalized combined field integral equation method for modelling EM wave scattering from non-penetrable and penetrable targets, respectively. Moreover, a plane wave scattering from a composite mockup fighter jet has been simulated using the newly developed multi-solver domain decomposition method.

scholarly journals Finite Element Tearing and Interconnecting Method and its Algorithms for Parallel Solution of Magnetic Field Problems

2013 ◽  
Vol 3 (1) ◽  
pp. 25-30
Author(s):  
Dániel Marcsa ◽  
Miklós Kuczmann
Keyword(s):  
Magnetic Field ◽  
Finite Element ◽  
Domain Decomposition ◽  
Data Exchange ◽  
Domain Decomposition Method ◽  
Decomposition Methods ◽  
Engineering Practice ◽  
Domain Decomposition Methods ◽  
Parallel Solution ◽  
Solution Algorithms

Abstract Because of the exponential increase of computational resource requirement for numerical field simulations of more and more complex physical phenomena and more and more complex large problems in science and engineering practice, parallel processing appears to be an essential tool to handle the resulting large-scale numerical problems. One way of parallelization of sequential (singleprocessor) finite element simulations is the use of domain decomposition methods. Domain decomposition methods (DDMs) for parallel solution of linear systems of equations are based on the partitioning of the analyzed domain into sub-domains which are calculated in parallel while doing appropriate data exchange between those sub-domains. In this case, the non-overlapping domain decomposition method is the Lagrange multiplier based Finite Element Tearing and Interconnecting (FETI) method. This paper describes one direct solver and two parallel solution algorithms of FETI method. Finally, comparative numerical tests demonstrate the differences in the parallel running performance of the solvers of FETI method. We use a single-phase transformer and a three-phase induction motor as twodimensional static magnetic field test problems to compare the solvers

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