A prescription for the multilevel Helmholtz FMM

Gyure, Mark F.; Stalzer, Mark A.

doi:10.1109/99.714592

Cited by 64 publications

(35 citation statements)

References 10 publications

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“…and by an additional transmission condition which is introduced later by eqn (6). The Laplacian is denoted by D and T represents the traction operator.…”

Section: Governing Equations Of the Coupled Problemmentioning

confidence: 99%

“…For exterior acoustic fluid domains, the application of the boundary element method (BEM) is advantageous, since the Sommerfeld radiation condition is automatically fulfiled [4]. There are fast methods to overcome the drawback of the fully populated matrices like the fast multipole method (FMM) [5,6] and H-matrices [7]. With these fast methods it is possible to solve large-scale problems in acoustics with some thousand degrees of freedom [8,9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Gaul¹,

Brunner²,

Junge³

2017

Int. J. CMEM

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The vibration behaviour of ships is noticeably influenced by the surrounding water, which represents a fluid of high density. In this case, the feedback of the fluid pressure onto the structure cannot be neglected and a strong coupling scheme between the fluid domain and the structural domain is necessary. In this work, fast boundary element methods (BEMs) are used to model the semi-infinite fluid domain with the free water surface. Two approaches are compared: A symmetric mixed formulation is applied where a part of the water surface is discretized. The second approach is a formulation with a special half-space fundamental solution, which allows the exact representation of the Dirichlet boundary condition on the free water surface without its discretization. Furthermore, the influence of the compressibility of the water is investigated by comparing the solutions of the Helmholtz and the Laplace equation. The ship itself is modeled with the finite element method (FEM). A binary interface to the commercial finite element package ANSYS is used to import the mass matrix and the stiffness matrix. The coupled problems are formulated using Schur complements. To solve the resulting system of equations, a combination of a direct solver for the finite element matrix and a preconditioned GMRES for the overall Schur complement is chosen. The applicability of the approach is demonstrated using a realistic model problem.

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“…and by an additional transmission condition which is introduced later by eqn (6). The Laplacian is denoted by D and T represents the traction operator.…”

Section: Governing Equations Of the Coupled Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Gaul¹,

Brunner²,

Junge³

2017

Int. J. CMEM

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“…This choice guarantees to maintain the chosen accuracy. Gyure and Stalzer [16] show that it is exact for the set of spherical harmonics that form the base of the multipole expansion. The total number of directions then adds up to .…”

Section: A Fmmmentioning

confidence: 99%

Accurate numerical modeling of the TARA reflector system

Rius

Heldring

Ligthart

et al. 2003

Twelfth International Conference on Antennas and Propagation (ICAP 2003)

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Abstract-The radiation pattern of the large parabolic reflectors of the Transportable Atmospheric RAdar system (TARA), developed at Delft University of Technology, has been accurately simulated. The electric field integral equation (EFIE) formulation has been applied to a model of the reflectors including the feed housing and supporting struts, discretised using the method of moments. Because the problem is electrically large (the reflector has a diameter of 33 ) and nonsymmetrical, this lead to a badly conditioned linear system of approximately half a million unknowns. In order to solve this system, an iterative solver (generalized minimum residual method) was used, in combination with the multilevel fast multipole method. Because of the bad conditioning, the system could only be solved by using a huge preconditioner. A new block-incomplete LU preconditioner (ILU) algorithm has been employed to allow for efficient out-of-computer core memory preconditioning.Index Terms-01reflector antennas, integral equations, method of moments (MoM), multilevel fast multipole method (MLFMA), numerical modeling, preconditioning.

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“…There are two major ways of implementing interpolations (and anterpolations), namely, through global and local interpolation methods. Global interpolations are usually based on the fast Fourier transform (FFT) along the direction and the Legendre transform along the direction, performed via one-dimensional FMM [4], [7]. Using uniform sampling, FFT can also be used along the direction [8].…”

mentioning

confidence: 99%

“…By reducing the computational complexity from to , FMM enabled the solution of large-scale problems on relatively inexpensive computing platforms. A few years later, the idea behind FMM was extended and applied in a recursive manner, leading to the multilevel fast multipole algorithm (MLFMA) [3], which provides the solution of larger problems by reducing the complexity of MVMs to [4] or [5]. Elements of matrices obtained by discretizating integral-equation formulations can be interpreted as electromagnetic interactions between pairs of discretization elements, i.e., basis and testing functions.…”

mentioning

confidence: 99%

Two-Step Lagrange Interpolation Method for the Multilevel Fast Multipole Algorithm

Ergül

Bosch

Gürel

2009

Antennas Wirel. Propag. Lett.

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Abstract-We present a two-step Lagrange interpolation method for the efficient solution of large-scale electromagnetics problems with the multilevel fast multipole algorithm (MLFMA). Local interpolations are required during aggregation and disaggregation stages of MLFMA in order to match the different sampling rates for the radiated and incoming fields in consecutive levels. The conventional one-step method is decomposed into two one-dimensional interpolations, applied successively. As it provides a significant acceleration in processing time, the proposed two-step method is especially useful for problems involving large-scale objects discretized with millions of unknowns.Index Terms-Lagrange interpolation, large-scale problems, multilevel fast multipole algorithm (MLFMA).

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A prescription for the multilevel Helmholtz FMM

Cited by 64 publications

References 10 publications

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Accurate numerical modeling of the TARA reflector system

Two-Step Lagrange Interpolation Method for the Multilevel Fast Multipole Algorithm

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