Feti-Dph: A Dual-Primal Domain Decomposition Method for Acoustic Scattering

Abstract

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.

Scattered Field Computation With an Extended Feti-Dpem2 Method

“…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].…”

“…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.…”

Why it is Difficult to Solve Helmholtz Problems with Classical Iterative Methods

“…The second algorithm in the FETI class specialized for Helmholtz problems is FETI-DPH, see [24]. This is a FETI-DP formulation, which means that some interface unknowns are kept as primal variables, where continuity is enforced, and which serve at the same time as coarse space components.…”

“…Furthermore, a Dirichlet preconditioner is used on top, like in the classical FETI formulation. A convergence analysis exists for this algorithm, see [25], but it needs the assumption that subdomains are small enough. A systematic comparison of all currently existing domain decomposition algorithms for Helmholtz problems is in preparation, see [38].…”

A damping preconditioner for time-harmonic wave equations in fluid and elastic material

“…Domain decomposition methods have been proposed for Helmholtz problems in [7,8,9,10,11,12], and for elastic problems in [13,14,15,16]. Controllability methods have been proposed for both Helmholtz and Navier problems in [17,18].…”