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

Farhat, Charbel; Macedo, Antonini; Lesoinne, Michel; Roux, François‐Xavier; Magoulès, Frédéric; Bourdonnaie, Armel de La

doi:10.1016/s0045-7825(99)00229-7

Cited by 112 publications

(93 citation statements)

References 19 publications

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“…Nevertheless, Table 1 guaranties that numerically, even when N s increases, the interface boundary conditions are correctly taken into account. An other key-parameter in the Robin-type boundary conditions is the coefficient α i (see (21)). We have thus tested the convergence of the method with respect to α i .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…After having constructed an augmented Lagrangian functional and found its saddle-point thanks to the Karush-Kuhn-Tucker conditions [21,24], we must solve the following equation, for each ith subdomain,…”

Section: Feti-dpem2 Methodsmentioning

confidence: 99%

“…Finally the solution of the interface problem serves as the right-handside of each local problem. This method has been applied in many domains like mechanics [19,20], acoustic wave propagation [21][22][23], and in electromagnetism [24][25][26][27][28][29][30][31][32]. For example, related DDM methods have been developed for simulating the interactions of photonic crystals with electromagnetic waves [33,34].…”

Section: Introductionmentioning

confidence: 99%

“…In addition, in order to further improve the convergence of the iterative process and the scalability of the method, one can notice the existence of two techniques: the first one uses the plane wave spectrum operator [21], the second one uses dual-primal techniques which can be seen as coarse grid corrections [22,26,28,36]. In this last method, the corner nodes in 2D or the corner edges in 3D (we denote by "corner" the geometrical entities which belong to more than two subdomains) are extracted from each subdomain and are globally and uniquely numbered.…”

Section: Introductionmentioning

confidence: 99%

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Scattered Field Computation With an Extended Feti-Dpem2 Method

Voznyuk¹,

Tortel²,

Litman³

2013

PIER

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Abstract-Due to the increasing number of applications in engineering design and optimization, more and more attention has been paid to full-wave simulations based on computational electromagnetics. In particular, the finite-element method (FEM) is well suited for problems involving inhomogeneous and arbitrary shaped objects. Unfortunately, solving large-scale electromagnetic problems with FEM may be time consuming. A numerical scheme, called the dual-primal finite element tearing and interconnecting method (FETI-DPEM2), distinguishes itself through the partioning on the computation domain into non-overlapping subdomains where incomplete solutions of the electrical field are evaluated independently. Next, all the subdomains are "glued" together using a modified Robin-type transmission condition along each common internal interface, apart from the corner points where a simple Neumann-type boundary condition is imposed. We propose an extension of the FETI-DPEM2 method where we impose a Robin type boundary conditions at each interface point, even at the corner points. We have implemented this Extended FETI-DPEM2 method in a bidimensional configuration while computing the field scattered by a set of heterogeneous, eventually anistropic, scatterers. The results presented here will assert the efficiency of the proposed method with respect to the classical FETI-DPEM2 method, whatever the mesh partition is arbitrary defined.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Feti-dpem2 Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scattered Field Computation With an Extended Feti-Dpem2 Method

Voznyuk¹,

Tortel²,

Litman³

2013

PIER

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“…The two-Lagrange multiplier FETI method, see Farhat et al [2000], is an iterative based domain decomposition method which consists to determine the solution of the following coupled problem:…”

Section: Introduction Of Two-lagrange Multiplier On the Interfacementioning

confidence: 99%

Approximation of Optimal Interface Boundary Conditions for Two-Lagrange Multiplier FETI Method

Roux

Magoulès

Séries

et al.

Lecture Notes in Computational Science and Engineering

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Summary. Interface boundary conditions are the key ingredient to design efficient domain decomposition methods. However, convergence cannot be obtained for any method in a number of iterations less than the number of subdomains minus one in the case of a one-way splitting. This optimal convergence can be obtained with generalized Robin type boundary conditions associated with an operator equal to the Schur complement of the outer domain. Since the Schur complement is too expensive to compute exactly, a new approach based on the computation of the exact Schur complement for a small patch around each interface node is presented for the two-Lagrange multiplier FETI method.

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Acoustics

Thompson

Pinsky

2004

Encyclopedia of Computational Mechanics

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State‐of‐the‐art computational methods for linear acoustics are reviewed. The equations of linear acoustics are summarized and then transformed to the frequency domain for time‐harmonic waves governed by the Helmholtz equation. Two major current challenges in the field are specifically addressed: numerical dispersion errors that arise in the approximation of short unresolved waves, polluting resolved scales and requiring a large computational effort, and the effective treatment of unbounded domains by domain‐based methods. A discussion of the indefinite sesquilinear forms in the corresponding weak form are summarized. A priori error estimates, including both dispersion (phase error) and global pollution effects for moderate to large wave numbers in finite element methods, are discussed. Stabilized and other wave‐based discretization methods are reviewed. Domain‐based methods for modeling exterior domains are described including Dirichlet‐to‐Neumann (DtN) methods, absorbing boundary conditions, infinite elements, and the perfectly matched layer (PML). Efficient equation‐solving methods for the resulting complex‐symmetric (non‐Hermitian) matrix systems are discussed including parallel iterative methods and domain decomposition methods including the FETI‐H method. Numerical methods for direct solution of the acoustic wave equation in the time domain are reviewed.

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

Cited by 112 publications

References 19 publications

Scattered Field Computation With an Extended Feti-Dpem2 Method

Scattered Field Computation With an Extended Feti-Dpem2 Method

Approximation of Optimal Interface Boundary Conditions for Two-Lagrange Multiplier FETI Method

Acoustics

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