Rapid acoustic boundary element method for solution of 3D problems using hierarchical adaptive cross approximation GMRES approach

Brancati, A; Aliabadi, Mh

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Abstract

This paper presents a new solver for 3D acoustic problems called RABEM (Rapid Acoustic Boundary Element Method). The Adaptive Cross Approximation and a Hierarchical GMRES solver are used to generate both the system matrix and the right hand side vector by saving storage requirement, and to solve the system solution. The potential and the particle velocity values at selected internal points are evaluated using again the Adaptive Cross Approximation (ACA). A GMRES without preconditioner and with a block diagonal preconditioner are developed and tested for low and high frequency problems. Different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) are also implemented. Herein the problem of engine noise emanating from the Falcon aircraft is presented. The tests demonstrated that the new solver can achieve CPU times of almost O(N) for low frequency and O(NlogN) for high frequency problems.
Lingua originaleEnglish
Stato di pubblicazionePublished - 2009

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Boundary element method
Acoustics
Program processors
Aircraft
Boundary conditions
Engines

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title = "Rapid acoustic boundary element method for solution of 3D problems using hierarchical adaptive cross approximation GMRES approach",
abstract = "This paper presents a new solver for 3D acoustic problems called RABEM (Rapid Acoustic Boundary Element Method). The Adaptive Cross Approximation and a Hierarchical GMRES solver are used to generate both the system matrix and the right hand side vector by saving storage requirement, and to solve the system solution. The potential and the particle velocity values at selected internal points are evaluated using again the Adaptive Cross Approximation (ACA). A GMRES without preconditioner and with a block diagonal preconditioner are developed and tested for low and high frequency problems. Different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) are also implemented. Herein the problem of engine noise emanating from the Falcon aircraft is presented. The tests demonstrated that the new solver can achieve CPU times of almost O(N) for low frequency and O(NlogN) for high frequency problems.",
keywords = "Rapid Acoustic Boundary Element Method, Adaptive Cross Approximation; Hierarchical Approach; GMRES; Large scale problems; High frequency range.",
author = "{Brancati, A; Aliabadi, Mh} and Ivano Benedetti",
year = "2009",
language = "English",

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TY - CONF

T1 - Rapid acoustic boundary element method for solution of 3D problems using hierarchical adaptive cross approximation GMRES approach

AU - Brancati, A; Aliabadi, Mh

AU - Benedetti, Ivano

PY - 2009

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N2 - This paper presents a new solver for 3D acoustic problems called RABEM (Rapid Acoustic Boundary Element Method). The Adaptive Cross Approximation and a Hierarchical GMRES solver are used to generate both the system matrix and the right hand side vector by saving storage requirement, and to solve the system solution. The potential and the particle velocity values at selected internal points are evaluated using again the Adaptive Cross Approximation (ACA). A GMRES without preconditioner and with a block diagonal preconditioner are developed and tested for low and high frequency problems. Different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) are also implemented. Herein the problem of engine noise emanating from the Falcon aircraft is presented. The tests demonstrated that the new solver can achieve CPU times of almost O(N) for low frequency and O(NlogN) for high frequency problems.

AB - This paper presents a new solver for 3D acoustic problems called RABEM (Rapid Acoustic Boundary Element Method). The Adaptive Cross Approximation and a Hierarchical GMRES solver are used to generate both the system matrix and the right hand side vector by saving storage requirement, and to solve the system solution. The potential and the particle velocity values at selected internal points are evaluated using again the Adaptive Cross Approximation (ACA). A GMRES without preconditioner and with a block diagonal preconditioner are developed and tested for low and high frequency problems. Different boundary conditions (i.e. Dirichlet, Neumann and mixed Robin) are also implemented. Herein the problem of engine noise emanating from the Falcon aircraft is presented. The tests demonstrated that the new solver can achieve CPU times of almost O(N) for low frequency and O(NlogN) for high frequency problems.

KW - Rapid Acoustic Boundary Element Method, Adaptive Cross Approximation; Hierarchical Approach; GMRES; Large scale problems; High frequency range.

UR - http://hdl.handle.net/10447/56361

M3 - Paper

ER -