Two-level domain decomposition methods with Lagrange multipliers for the fast iterative solution of acoustic scattering problems

2000 ◽  
Vol 184 (2-4) ◽  
pp. 213-239 ◽  
Author(s):  
Charbel Farhat ◽  
Antonini Macedo ◽  
Michel Lesoinne ◽  
Francois-Xavier Roux ◽  
Frédéric Magoulès ◽  
...  
Keyword(s):  
Domain Decomposition ◽  
Lagrange Multipliers ◽  
Acoustic Scattering ◽  
Iterative Solution ◽  
Decomposition Methods ◽  
Domain Decomposition Methods ◽  
Scattering Problems ◽  
Acoustic Scattering Problems

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.

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.

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