A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. Part I: Dirichlet boundary conditions

2002 ◽  
Vol 54 (9) ◽  
pp. 1309-1332 ◽  
Author(s):  
Charbel Farhat ◽  
Ulrich Hetmaniuk
Keyword(s):  
Boundary Conditions ◽  
Domain Decomposition ◽  
Decomposition Method ◽  
Dirichlet Boundary ◽  
Domain Decomposition Method ◽  
Acoustic Scattering ◽  
Dirichlet Boundary Conditions ◽  
Fictitious Domain ◽  
Scattering Problems ◽  
Acoustic Scattering Problems

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.

scholarly journals A Finite Difference Fictitious Domain Wavelet Method for Solving Dirichlet Boundary Value Problem

2021 ◽  
Vol 14 (3) ◽  
pp. 706-722
Author(s):  
Francis Ohene Boateng ◽  
Joseph Ackora-Prah ◽  
Benedict Barnes ◽  
John Amoah-Mensah
Keyword(s):  
Finite Difference ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Finite Difference Methods ◽  
Dirichlet Boundary Conditions ◽  
Fictitious Domain ◽  
Dirichlet Boundary Value Problem ◽  
Wavelet Method ◽  
Difference Methods

In this paper, we introduce a Finite Difference Fictitious Domain Wavelet Method (FDFDWM) for solving two dimensional (2D) linear elliptic  partial differential equations (PDEs) with Dirichlet boundary conditions on regular geometric domain. The method reduces the 2D PDE into a 1D system of ordinary differential equations and applies a compactly supported wavelet to approximate the solution. The problem is embedded in a fictitious domain to aid the enforcement of the Dirichlet boundary conditions. We present numerical analysis and show that our method yields better approximation to the solution of the Dirichlet problem than traditional methods like the finite element and finite difference methods.

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