A finite element-based fictitious domain decomposition method for the fast solution of partially axisymmetric sound-hard acoustic scattering problems

2003 ◽  
Vol 39 (8) ◽  
pp. 707-725 ◽  
Author(s):  
Ulrich Hetmaniuk ◽  
Charbel Farhat
Keyword(s):  
Finite Element ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Domain Decomposition Method ◽  
Acoustic Scattering ◽  
Fictitious Domain ◽  
Scattering Problems ◽  
Fast Solution ◽  
Acoustic Scattering Problems

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.

FETI-DPH: A DUAL-PRIMAL DOMAIN DECOMPOSITION METHOD FOR ACOUSTIC SCATTERING

2005 ◽  
Vol 13 (03) ◽  
pp. 499-524 ◽  
Author(s):  
CHARBEL FARHAT ◽  
PHILIP AVERY ◽  
RADEK TEZAUR ◽  
JING LI
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Large Scale ◽  
Domain Decomposition Method ◽  
Acoustic Scattering ◽  
Iterative Solution ◽  
Wave Number ◽  
Problem Size ◽  
Scattering Problems ◽  
Parallel Iterative

A dual-primal variant of the FETI-H domain decomposition method is designed for the fast, parallel, iterative solution of large-scale systems of complex equations arising from the discretization of acoustic scattering problems formulated in bounded computational domains. The convergence of this iterative solution method, named here FETI-DPH, is shown to scale with the problem size, the number of subdomains, and the wave number. Its solution time is also shown to scale with the problem size. CPU performance results obtained for the acoustic signature analysis in the mid-frequency regime of mockup submarines reveal that the proposed FETI-DPH solver is significantly faster than the previous generation FETI-H solution algorithm.

Newton-Like Method for Solving Inverse Obstacle Acoustic Scattering Problems

2000 ◽  
Author(s):  
Rabia Djellouli ◽  
Charbel Farhat ◽  
Radek Tezaur
Keyword(s):  
Acoustic Scattering ◽  
Numerical Procedure ◽  
Decomposition Methods ◽  
Computationally Efficient ◽  
Scattering Problems ◽  
Absorbing Boundary ◽  
Element Discretization ◽  
Jacobian Matrices ◽  
Fast Solution ◽  
Acoustic Scattering Problems

Abstract A Newton-like method is designed for determining the shape or sought-after shape modifications of a scatterer from the knowledge of acoustic far-field patterns at a given number of observation points. This method distinguishes itself from existing numerical procedures by the following features: (a) exact Jacobian matrices for the linearized problems rather than approximate ones, (b) a fast numerical procedure for computing these Jacobian matrices, (c) a computationally efficient absorbing boundary condition for the finite element discretization, and (d) a numerically scalable domain decomposition methods for the fast solution of high-frequency direct acoustic scattering problems.

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