In particular, we want to mention our recent combination of the new version of the fast multipole method with the bem formulation for pb equation, which has been shown numerically to be faster than existing pb solvers based. Pdf a high order fast multipole boundary element method. It creates a hierarchical structure of the elements and approximates far interactions using spherical harmonics expansions. The fast multipole boundary element method for large scale. Greengard, a short course on fast multipole methods, in proceedings of.
Liu et al2017 studied the propagation of multiple fractures in an elastic solid using a dual boundary integral equation bie and fmm. Especially for exterior domains this is an enormous advantage. By properly changing a variable restart parameter for the gmresm algorithm, the iteration. In this paper, the outline of the fmbem are introduced at first, the accuracy and efficiency are verified and compared with the conventional bem, a parallel algorithm of fmbem for pc. Konarskiego 18a, 44100 gliwice, poland a threenode quadratic element version of the fast multipole boundary ele. Fast multipole boundary element method the fast multipole method is one of the most important algorithms in computing developed in the 20th century. Fast multipole acceleration of the meg eeg boundary.
The fast multipole method fmm has been regarded as one of the top 10 algorithms in scienti. The boundary element method bem the bem is a numerical method which solves the boundary integral form of a differential equation using bcs defined on the domain boundary in acoustics, this means we are solving the integral form of the helmholtz pde to calculate the pressure p andor particle velocity u on the boundary. Along with the fast multipole method, the boundary element method bem has also emerged, as a powerful method for modeling largescale problems. In this study, a modified duallevel fast multipole boundary element method based on the burtonmiller formulation is proposed for largescale 3d sound field analysis. Method the recently developed chargebased boundary element fast multipole method bemfmm is employed as an alternative to the 1st order finite element method fem most commonly used today. However, advances in the evaluation of singular integrals appearing in boundary element methods and the development of fast formulations based on hmatrices, wavelets or the fast multipole method fmm have made it possible to solve very large application problems with boundary. A wideband fast multipole boundary element method for three dimensional acoustic shape sensitivity analysis based on direct differentiation method. A tailored fast multipole boundary element method for. However, the fast multipole accelerated boundary element method fmbem is intrinsically based on an iterative solver. The volume integral is computed using a previously developed fast multipole accelerated fourthorder method. Pdf a wideband fast multipole boundary element method for. The multilevel fast multipole method mlfmm is used along with method of moments mom a numerical computational method of solving linear partial differential equations which have been formulated as integral equations of large objects almost faster without loss in accuracy. It in corporates the burton miller formulation, where two different algorithms are explained to integrate. A broadband fast multipole accelerated boundary element method for the three dimensional helmholtz equation nail a.
Fast multipole boundary element method for the analysis of. Pdf a fast multipole boundary element method for solving two. Ewald methods9,10 and the multipole expansionbased techniques such as the tree code11,12 and fast multipole methods17. Bem is good for problems with complicated geometries, stress concentration problems, infinite domain problems, wave propagation problems, and many others.
Acousto acoustics simulation tool, a free and opensource parallel bem solver for the kirchhoffhelmholtz integral. Fast multipole boundary element method of potential problems. The procedure is aimed at simplifying the integrals involved in the. In this paper, a fast multipole boundary element method fmbem for 3d multidomain acoustic problems is developed, which can have a broad range of applications, such as in the characterization of sound absorbing materials, underwater acoustics and biomedical applications. It has been shown that the number of iterations can significantly hinder the overall efficiency of the fmbem. Pdf fast multipole acceleration of the megeeg boundary. A multistage adaptive fast multipole method is used to accelerate the matrixvector products arising from the burtonmiller boundary integral equations, which are formed in a boundary element method. Fast multipole boundary element method for the solution of. An efficient poisson solver for complex embedded boundary.
A fast multipole boundary element method fmbem for 3d multidomain acoustic scattering problems based on the burtonmiller formulation is presented in this paper. Fast multipole boundary element method for the solution of 3d. Acknowledgment this work was supported in part by the u. Pdf the fast multipole boundary element methods fmbem. The fmm was implemented by 8 for solving the effective thermal conductivity etc of random microheterogeneous materials using representative elements and fmbem. The accelerated method is shown to be as accurate as the direct method, yet for large problems it is both. Pdf a fast multipole boundary element method bem for solving general uncoupled steadystate thermoelasticity problems in two dimensions is presented. Fast multipole boundary element method for poisson boltzmann electrostatics 3 the main contributions of this paper include. Boundary element acoustics and the fast multipole method. By properly changing a variable restart parameter for the gmresm algorithm, the iteration stagnation problem resulting. Applications of fast multipole method to boundary integral equation method kenichi yoshida dept. Gumerova,b and ramani duraiswamib,c perceptual interfaces and reality laboratory, institute for advanced computer studies.
To solve large scale linear equations involved in the fast multipole boundary element method fmbem efficiently, an iterative method named the generalized minimal residual method gmresm algorithm with variable restart parameter vrpgmresm algorithm is proposed. The standard boundary element method which is used to solve this surface integral formula quickly exceeds the memory capacity of modern computers for problems involving hundreds of thousands of unknowns. The recently developed chargebased boundary element fast multipole method bemfmm is employed as an alternative to the 1st order finite element method fem most commonly used today. A high order fast multipole boundary element method. Inexact fast multipole boundary element tearing and. Parallel fast multipole boundary element method for.
Fast multipole boundary element method by yijun liu. Efficient calculation for evaluating vast amounts of. The development of a fast multipole method fmm accelerated iterative solution of the boundary element method bem for the helmholtz. D elastostatic problems based on the direct boundary integral equation bie formulation.
The fast multipole boundary element method for potential problems. This cited by count includes citations to the following articles in scholar. A new simple multidomain fast multipole boundary element method. We consider a canonic multisphere problem and an external magneticdipole excitation where the analytical solution is available. No part of the packages, either the executable or the source codes, can be used for any commercial applications and distributions without prior written permissions of the original authors. An adaptive fast multipole boundary element method for. A broadband fast multipole accelerated boundary element method.
Uniform grid boundary integral periodic array microstrip antenna fast multipole method these keywords were added by machine and not by the authors. Fast multipole bem can also solve a model with 1 million dofs on a pc with 1 gb ram. Boundary element solutions for broadband 3d geoelectromagnetic problems accelerated by an adaptive multilevel fast multipole method. A broadband fast multipole accelerated boundary element method for the 3d helmholtz equation naila. Fast multipole method fmm is applied to accelerate the solution of an isogeometric bem igabem. Request pdf a new simple multidomain fast multipole boundary element method a simple multidomain fast multipole boundary element method bem for solving potential problems is presented in. A tailored fast multipole boundary element method for viscous. Fast multipole acceleration of the megeeg boundary element method. Nishimura b,1 a department of mechanical, industrial and nuclear engineering, university of cincinnati, p. A fast multipole galerkin boundary element method for the. Pdf sensitivity analysis by the fast multipole boundary. Pdf parallel fast multipole boundary element method for.
See also for a recent description of the link algorithm. A new fast multipole boundary element method for solving. Fast multipole boundary element method to calculate head. According to the concept of iga, this work develops a boundary element method bem using nonuniform rational bsplines nurbs as basis functions for the 2d halfspace acoustic problems with absorbing boundary condition.
Box 210072, cincinnati, oh 452210072, usa received 27 january 2007. A broadband fast multipole accelerated boundary element. The ones marked may be different from the article in the profile. The particular choice is largely influenced by computational efficiency and scope with regard to geometry, mesh, boundary conditions and type of pde. A fast multipole boundary element method for 3d multidomain. The fast multipole boundary element method fast bem tackles the di culty of handling the intricate volume meshes and high resolution of crustal data that has put classical finite 3d approaches in a performance crisis. Crustal faults and sharp material transitions in the crust are usually represented as triangulated surfaces in structural geological models. If straight line elements and piecewise constant basis functions are used for q. Abstract combined with the fast multipole method, the boundary element method become quite efficient to deal with largescale engineering and scientific problems. This method is an alternative formulation of the technology behind the mom and is applicable to. The above fast multipole boundary element method fastbem software packages are ed materials of the authors.
Application of the fast multipole method to hybrid finite. Engineering analysis with boundary elements 32 2008 9151 a new fast multipole boundary element method for solving 2d stokes. Implementation of isogeometric fast multipole boundary. The fast multipole boundary element method fast bem tackles the difficulty of handling the intricate volume meshes and high resolution of crustal data that has put classical finite 3d approaches. A new fast multipole boundary element method for solving 2d. The fast multipole method for electromagnetic field. Finite element method can solve a model with 1 million dofs on a pc with 1 gb ram. The fast multipole boundary element method for potential.
Based on the single layer potential theory, poroelastic free. Fast multipole accelerated boundary element method for elastic wave propagation in multiregion domains. A new simple multidomain fast multipole boundary element. A differential algebraic framework for the fast indirect. An adaptive fast multipole boundary element method for poissonboltzmann electrostatics. This process is experimental and the keywords may be updated as the learning algorithm improves.
Application of fast multipole boundary element method for. In section 4, we describe the ingredients from which the preconditioner and the solver for the twofold saddle point problem that we. Fastbem free fast multipole boundary element programs for solving 2d3d potential, elasticity, stokes flow and acoustic problems. Fast iterative boundary element methods for highfrequency. Boundary element method, among which is the fast multipole method fmm. A new fast multipole boundary element method for solving large. The bemfmm approach provides high accuracy and unconstrained field resolution close to and across cortical interfaces. The complex range of volumes separating such surfaces is typically threedimensionally meshed in order to. However, these dofs are on the boundary of the model only, which would require 1 billion dofs for the corresponding domain model. Kifmm3d the kernelindependent fast multipole 3d method kifmm3d is a new fmm implementation which does not require the explicit multipole expansions of the underlying kernel, and it is based on kernel evaluations. Theory and applications in engineering, authoryijun liu, year2009. A fast multipole accelerated indirect boundary element method is developed to efficiently solve the scattering of broadband waves by inhomogeneity in a fluid. A variety of solution methodologies exist such as fft, multigrid methods, boundary integral methods such as fast multipole method fmm, krylov subspace methods such as gmres, bicgstab, etc. Along with the fast multi pole method, the boundary element method bem has also emerged as a powerful method for modeling largescale problems.
To include boundary conditions for complicated structures, the boundary element method bem has shown excellent results in various elds. Implementing the fast multipole boundary element method. Pdf vrpgmresm iteration algorithm for fast multipole. To demonstrate the versatility of integral equation methods, the homogeneous problem is solved in bounded and unbounded, as well as simply and multiplyconnected domains. Boundary element and meshless methods on acoustics and vibrations. Development of the fast multipole boundary element method for.
Because of the application of the burtonmiller formulation, it is observed that the nonuniqueness problem for exterior acoustic problems is solved. Fast multipole boundary element method to calculate headrelated transfer functions for a wide frequency range wolfgang kreuzer, piotr majdak, and zhengsheng chen acoustics research institute, austrian academy of sciences, wohllebengasse 1214, a1040 vienna, austria. Fast multipole accelerated boundary element techniques for. The fmbems improve the efficiency of conventional bems, accelerate the computing, enlarge the solving scale, and it is applied in various engineering fields. Combined with the fmm, the boundary element method bem can now solve largescale problems with several million degrees of. Finite elementfast integral methods for antenna analysis. Nishimura b,1 a department of mechanical, industrial and nuclear. In this contribution a high order fast multipole boundary element method is presented. It has been shown that the number of iterations can significantly hinder the overall efficiency of the fm. Fast multipole boundary element method for the solution of 3d electrostatic field problems a. The fast multipole method is an efficient technique to accelerate the solution of large scale 3d scattering problems with boundary integral equations. A multitree structure is designed for the multidomain fmbem. Implementing the fast multipole boundary element method with. Paper ica2016309 efficient calculation for evaluating vast amounts of quadrupole sources in bem using fast multipole method takayuki masumotoa, arief gunawanb, masaaki moric, yosuke yasudad, takuya oshimae, tetsuya sakumaf.
Because of this reduction of the dimensionality biem was. Request pdf on feb 10, 2019, zhoufang xiao and others published a tailored fast multipole boundary element method for viscous layer mesh generation find, read and cite all the research you. Interface debonding is implemented by decoupling the node pair. A simple multidomain fast multipole boundary element method bem for solving potential problems is presented in this paper, which can be applied to solve a true multidomain problem or a largescale single domain problem using the domain decomposition technique. Just the surface has to be discretized, but a solution for the complete domain is obtained. A fast multipole accelerated indirect boundary element. Comparative performance of the finite element method and the. Pumaem an opensource and highperformance method of moments multilevel fast multipole method parallel program. A fast multipole boundary element method bem is used herein to simulate the twodimensional interfacial debonding of particulate composites. Rucker university of stuttgart, institute for theory of electrical engineering, germany abstract direct and indirect boundary element methods are applied to the numerical solution of electrostatic field problems. A new method named mixed fast multipole boundary element mfmbem is introduced in this paper to solve the contact problem of mill roller bearing. The present paper intends to couple the fast multipole method with the boundary element method in 2d inverse acoustic problems. Pdf fast multipole accelerated boundary element method for.
The boundary element method can be used to solve the helmholtz equation in three dimensions. Department of energy, o ce of high energy physics, under contract no. Pdf fast multipole burtonmiller boundary element method. It is well known e ects due to the beam pipe become important for highintensity beams. In this multidomain bem, the coefficient matrix is formed simply by assembling the coefficient matrices of each subdomain and the. A modified duallevel fast multipole boundary element method. A software toolkit for tms electricfield modeling with. The two main performance enhancements of this method. Boundary element acoustics and the fast multipole method fmm traditional boundary element methods bem for acoustic analysis have difficulty with large models and are thus limited. Advanced acoustic simulation software based on the boundary element method bem accelerated by the fast multipole fmm, adaptive cross approximation aca, highly optimized direct equation solver, and highfrequency bem hfbem, using parallel computing.
Fast multipole accelerated boundary element method for. The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Fast multipole boundary element method fastbem software. A fast multipole boundary element method for 3d multi. The blackbox fast multipole method bbfmm was applied to the elastic formulation of the displacement discontinuity method. Jul 26, 2006 2011 a fast multipole boundary element method based on the improved burtonmiller formulation for threedimensional acoustic problems. A new fast multipole boundary element method bem is presented in this paper for large. In particular, we want to mention our recent combination of the new version of the fast multipole method.
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