Thematische Bibliographien / Fast Boundary Element Methods

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Auswahl der wissenschaftlichen Literatur zum Thema „Fast Boundary Element Methods“

Autor: Grafiati

Veröffentlicht am 23. November 2024

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Zeitschriftenartikel zum Thema "Fast Boundary Element Methods"

Kravčenko, Michal, Michal Merta, and Jan Zapletal. "Distributed fast boundary element methods for Helmholtz problems." Applied Mathematics and Computation 362 (December 2019): 124503. http://dx.doi.org/10.1016/j.amc.2019.06.017.

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Gumerov, Nail A., and Ramani Duraiswami. "Fast multipole accelerated boundary element methods for room acoustics." Journal of the Acoustical Society of America 150, no. 3 (2021): 1707–20. http://dx.doi.org/10.1121/10.0006102.

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Of, G., O. Steinbach, and P. Urthaler. "Fast Evaluation of Volume Potentials in Boundary Element Methods." SIAM Journal on Scientific Computing 32, no. 2 (2010): 585–602. http://dx.doi.org/10.1137/080744359.

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Harbrecht, H., and M. Peters. "Comparison of fast boundary element methods on parametric surfaces." Computer Methods in Applied Mechanics and Engineering 261-262 (July 2013): 39–55. http://dx.doi.org/10.1016/j.cma.2013.03.022.

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Gumerov, Nail, and Ramani Duraiswami. "Simulations of room acoustics using fast multipole boundary element methods." Journal of the Acoustical Society of America 148, no. 4 (2020): 2693–94. http://dx.doi.org/10.1121/1.5147458.

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MUKHERJEE, SUBRATA, and YIJUN LIU. "THE BOUNDARY ELEMENT METHOD." International Journal of Computational Methods 10, no. 06 (2013): 1350037. http://dx.doi.org/10.1142/s0219876213500370.

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The boundary element method (BEM), along with the finite element and finite difference methods, is commonly used to carry out numerical simulations in a wide variety of subjects in science and engineering. The BEM, rooted in classical mathematics of integral equations, started becoming a useful computational tool around 50 years ago. Many researchers have worked on computational aspects of this method during this time.This paper presents an overview of the BEM and related methods. It has three sections. The first, relatively short section, presents the governing equations for classical applications of the BEM in potential theory, linear elasticity and acoustics. The second describes specialized applications in bodies with thin features including micro-electro-mechanical systems (MEMS). The final section addresses current research. It has three subsections that present the boundary contour, boundary node and fast multipole methods (BCM, BNM and FMM), respectively. Several numerical examples are included in the second and third sections of this paper.

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Dargush, G. F., and M. M. Grigoriev. "Fast and Accurate Solutions of Steady Stokes Flows Using Multilevel Boundary Element Methods." Journal of Fluids Engineering 127, no. 4 (2005): 640–46. http://dx.doi.org/10.1115/1.1949648.

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Most recently, we have developed a novel multilevel boundary element method (MLBEM) for steady Stokes flows in irregular two-dimensional domains (Grigoriev, M.M., and Dargush, G.F., Comput. Methods. Appl. Mech. Eng., 2005). The multilevel algorithm permitted boundary element solutions with slightly over 16,000 degrees of freedom, for which approximately 40-fold speedups were demonstrated for the fast MLBEM algorithm compared to a conventional Gauss elimination approach. Meanwhile, the sevenfold memory savings were attained for the fast algorithm. This paper extends the MLBEM methodology to dramatically improve the performance of the original multilevel formulation for the steady Stokes flows. For a model problem in an irregular pentagon, we demonstrate that the new MLBEM formulation reduces the CPU times by a factor of nearly 700,000. Meanwhile, the memory requirements are reduced more than 16,000 times. These superior run-time and memory reductions compared to regular boundary element methods are achieved while preserving the accuracy of the boundary element solution.

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van 't Wout, Elwin, Reza Haqshenas, Pierre Gélat, and Nader Saffari. "Fast and accurate boundary element methods for large-scale computational acoustics." Journal of the Acoustical Society of America 154, no. 4_supplement (2023): A179. http://dx.doi.org/10.1121/10.0023190.

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The boundary element method (BEM) is a powerful algorithm to solve the Helmholtz equation for harmonic acoustic waves. The explicit use of Green’s functions avoids domain truncation of unbounded regions and accurately models wave propagation through homogeneous materials. Furthermore, fast multipole and hierarchical compression techniques provide efficient computations for dense matrix multiplications. However, the convergence of the iterative linear solvers deteriorates significantly when frequencies are high or materials have large contrasts in density or speed of sound. This talk presents several algorithmic improvements of the BEM. First, a preconditioner based on on-surface radiation conditions drastically reduces the iteration count of linear solvers at high frequencies. Second, anovel boundary integral formulation remains well-conditioned for high-contrast transmission problems. We used our fast and accurate BEM implementation to simulate focused ultrasound propagation in the human body, which can be translated to important biomedical applications such as the non-invasive treatment of liver cancer and neuromodulation of the brain. We validated the methodology within the benchmarking exercise of the International Transcranial Ultrasonic Stimulation Safety and Standards (ITRUSST) consortium. As a second application, we simulated the collective resonances of water-entrained arrays of air bubbles. Finally, we implemented all functionality in our open-source Python library, OptimUS.

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Newman, J. N., and C. H. Lee. "Boundary-Element Methods In Offshore Structure Analysis." Journal of Offshore Mechanics and Arctic Engineering 124, no. 2 (2002): 81–89. http://dx.doi.org/10.1115/1.1464561.

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Boundary-element methods, also known as panel methods, have been widely used for computations of wave loads and other hydrodynamic characteristics associated with the interactions of offshore structures with waves. In the conventional approach, based on the low-order panel method, the submerged surface of the structure is represented by a large number of small quadrilateral plane elements, and the solution for the velocity potential or source strength is approximated by a constant value on each element. In this paper, we describe two recent developments of the panel method. One is a higher-order method where the submerged surface can be represented exactly, or approximated to a high degree of accuracy by B-splines, and the velocity potential is also approximated by B-splines. This technique, which was first used in the research code HIPAN, has now been extended and implemented in WAMIT. In many cases of practical importance, it is now possible to represent the geometry exactly to avoid the extra work required previously to develop panel input files for each structure. It is also possible to combine the same or different structures which are represented in this manner, to analyze multiple-body hydrodynamic interactions. Also described is the pre-corrected Fast Fourier Transform method (pFFT) which can reduce the computational time and required memory of the low-order method by an order of magnitude. In addition to descriptions of the two methods, several different applications are presented.

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Chen, Leilei, Steffen Marburg, Wenchang Zhao, Cheng Liu, and Haibo Chen. "Implementation of Isogeometric Fast Multipole Boundary Element Methods for 2D Half-Space Acoustic Scattering Problems with Absorbing Boundary Condition." Journal of Theoretical and Computational Acoustics 27, no. 02 (2019): 1850024. http://dx.doi.org/10.1142/s259172851850024x.

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Isogeometric Analysis (IGA), which tries to bridge the gap between Computer Aided Engineering (CAE) and Computer Aided Design (CAD), has been widely proposed in recent research. According to the concept of IGA, this work develops a boundary element method (BEM) using non-Uniform Rational B-Splines (NURBS) as basis functions for the 2D half-space acoustic problems with absorbing boundary condition. Fast multipole method (FMM) is applied to accelerate the solution of an isogeometric BEM (IGA-BEM). Several examples are tested and it is shown that this advancement on isogeometric fast multipole boundary element method improves the accuracy of simulations.

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