| Acoustic analysis has much important affection on improving productperformance, and further enhancing the competitiveness of the product. Theboundary face method (BFM), which is a development of boundary element methodand boundary node method, is a new implementation of the conventional boundaryelement method (BEM) based on the boundary representation data structure (B-rep)as used in most CAD packages for geometry modeling. Compared with the BEM,the BFM performs the boundary integration and variable approximation in the2-Dparametric space of the surface which is available in most CAD packages. Thegeometric data at the Gaussian integration points, such as the coordinates, theJacobians and the out normals, are calculated directly from the faces rather thanfrom elements, thus it avoids to introduce the geometric error in the numericalintegral of the boundary element. At the same time, the BFM inherits thecharacteristics of the BEM, where only the boundary discretization is required, oneorder dimension is automatically reduced for the analyzed problems.Especially, in the exterior acoustic problems, the Sommerfeld boundarycondition can be automatically satisfied at infinity by the boundary integralequation, thus it is more suitable to solve the exterior acoustic problems comparingwith the finite element method(FEM). In addition, the BFM which is directly basedon the boundary representation (B-rep) data, can be seamlessly interact with CADsoftware. Acoustic analysis using the BFM, has a great significance on improvingthe efficiency of product design, saving investment and reducing time on researchand development of product. However, the same as the BEM, the system matrix isdense and unsymmetrical, requiring O(N2) memory and O(N~3) operations with Nbeing the number of nodes, when the direct solvers are used. As a result, the BFM isprohibitively expensive when it is used to solve large scale acoustic problems. Tocircumvent this problem, this paper presents an adaptive fast multipole boundaryface method (FMBFM) for three dimensional large scale radiation and scattering ofacoustic problems based on the BFM and fast multipole method (FMM).The following studies are carried out in this dissertation:(1) Application of the BFM to solve the exterior acoustic problems. Applicationof the BFM to solve the small scale exterior acoustic problems is the basis of dealing with the large scale exterior acoustic problems. In this paper, we use theBurton-Miller equation, which is a complex line combine of conventional boundaryintegral equation and its hyper-singular boundary integral equation, to solve thewhole frequency domain acoustic problems. The BFM firstly meshes on the twodimensional parametric surfaces, then map to the three dimensional solid surfaces toobtain the discretization of the solid boundary. The geometric data in the BFM isobtained based on the boundary representation data, which can ensure the geometricdata in computational model is the same as the original model. Thus, the BFM hasthe features of seamlessly interacting with CAD software. In this paper, the BFMcoupling with the commerce CAD Software, UG-NX, is used to solve the acousticproblems. It unifies the CAD and CAE models into a unique framework, thus thepresent method provides a new way toward automatic simulation.(2) An adaptive fast multipole boundary face method using higher orderelements based on the well-known Burton-Miller equation is presented in this paperfor solving the large-scale three-dimensional exterior acoustic wave problems. Thesystem matrix of the BFM is dense, full rank and unsymmetrical, thus the BFM isprohibitively expensive when it is used to solve large-scale acoustic problems. Thepresent method in this paper inherits the characteristics of the BFM, such as thecomputational model is the original model, having the feature of seamlessconnectivity with CAD software etc. In addition, the FMBFM reduces the storageand computation of BFM both to O(N), the large-scale acoustic problems can behandled effectively. An adaptive tree structure is employed. Especially for slenderand plate-like objects, the adaptive tree structure can huge improve thecomputational efficiency of presented method. More importantly, we determine thenumber of expansion terms in multipole to local translations according to thedistancebetween the two interaction boxes. The numerical example withcomputational DOFs (Degree of freedom) up to100,000demonstrates that thepresent method can effectively deal with the large-scale acoustic problems.(3) Analysis of acoustic problems for the model with end-open tubular holes. Inpractical engineering applications, the mesh of the model with end-open tubularholes usually needs a lot of grids. Simultaneously, the excessive and concentratedgrids increase the computational difficulty. However, when the model has a lot ofholes, the mesh may be failed. In this paper, the adaptive FMBFM is introduced toreadily analyse acoustic problems of solids containing tubular shaped holes. A newtube surface element is presented, which is obtained based on the2D parametric space, then mapped to the solid boundary surfaces. In this way, the holes can berepresented by several elements. The numerical examples demonstrate the presentmethod can handle the acoustic problems analysis for the model with end-opentubular holes effectively.(4) An half space adaptive FMBFM is presented based on the full spaceadaptive FMBFM. The present method is based on the half space Green’s function,only the solid boundary discretization is required. The computational DOFs can bereduced and the computational difficulty will be cut down. The tree structure in theFMM can be used only for the real domain, thus the depth and the number of M2Lwill be reduced. According to the feature of the half space Green’s function, theintegrand of hyper-singular equation and its weakly integral forms will be modified,thus the Burton-Miller equation will be employed to solve the acoustic problems.The numerical examples demonstrate the present method can be used for thepractical engineering application. |
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