A coupling algorithm based on the finite element method and the wideband fast multipole boundary element method (FEM/wideband FMBEM) is proposed for the simulation of fluid-structure interaction and structural-acoustic sensitivity... more
A coupling algorithm based on the finite element method and the wideband fast multipole boundary element method (FEM/wideband FMBEM) is proposed for the simulation of fluid-structure interaction and structural-acoustic sensitivity analysis using the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. The FEM/Wideband FMBEM algorithm makes it possible to predict the effects of arbitrarily shaped vibrating structures on the sound field numerically. Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm.
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The vibration behavior of thin elastic structures is noticeably influenced by the surrounding water, which represents a heavy fluid. In this case, the feedback of the fluid pressure onto the structures cannot be neglected and a strong... more
The vibration behavior of thin elastic structures is noticeably influenced by the surrounding water, which represents a heavy fluid. In this case, the feedback of the fluid pressure onto the structures cannot be neglected and a strong coupling scheme between the structural domain and the fluid domain is required. In this paper, a coupled finite element and boundary element (FE-BE) solver is developed for the modal analysis of three-dimensional submerged elastic structures. The structures are modeled by means of the finite element method (FEM). The compressibility of the surrounding fluid is taken into consideration, and thus the Helmholtz equation is used as the governing equation and solved by using the boundary element method (BEM). The resulting nonlinear eigenvalue problem (NEVP) is converted into a small linear one by using a contour integral method. A numerical example is finally given to demonstrate the effectiveness and applicability of the developed method.
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Abstract The paper presents a level set based topology optimization method for unidirectional phononic structures with finite layers of lattice cells . Boundary element method(BEM) is employed as the numerical approach to solve the... more
Abstract The paper presents a level set based topology optimization method for unidirectional phononic structures with finite layers of lattice cells . Boundary element method(BEM) is employed as the numerical approach to solve the acoustic problems governed by Helmholtz equation . A sized reduced coefficient matrix is derived due to the iteration forms for input and output quantities on the periodic boundary of unit cells. Topological derivatives are formulated by boundary integral equation combined with adjoint variable method and computed for each layer. An average topological sensitivity of a single design domain is proposed for the updating of the level set function(LSF) governed by an evolution equation. Numerical models with different number of layers are considered and several optimized structures of unit cells are obtained in concerned frequencies. A further investigation into the transmission of acoustic waves is carried out by employing more layers of the periodic structures between the input and output domains. The results demonstrate the effectiveness of the proposed optimization method for the finite unidirectional phononic structures.
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This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by... more
This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton–Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.
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Abstract This study presents a combined shape and topology optimization method for designing sound barriers by using the isogeometric boundary element method. The objective function of combined optimization is defined as the sound... more
Abstract This study presents a combined shape and topology optimization method for designing sound barriers by using the isogeometric boundary element method. The objective function of combined optimization is defined as the sound pressure in reference plane. The sensitivity analysis for the combined optimization is conducted by using either the direct differentiation method or the adjoint variable method. For a shape design, the design variables are the positions of control points in isogeometric analysis, which can control the barrier shape flexibly. In the topology update, the artificial density of an integral element is selected as the design variable to find the optimal distribution of sound absorbing material (SAM) on the barrier surface. In the combined optimization process, the shape and SAM distribution of the sound barrier can be changed in each iteration process to improve the noise reduction. Four different iteration schemes for combined optimization are compared to find an effective one. Numerical tests are provided to demonstrate the validity and efficiency of the proposed methods.
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A fast multipole boundary element approach to the shape sensitivity analysis of three dimensional acoustic wave problems is developed in this study based on the adjoint variable method. The concept of material derivative is employed in... more
A fast multipole boundary element approach to the shape sensitivity analysis of three dimensional acoustic wave problems is developed in this study based on the adjoint variable method. The concept of material derivative is employed in the derivation. The Burton-Miller formula which is a linear combination of the conventional and normal derivative boundary integral equations is adopted to cope with the non-uniqueness problem when solving exterior acoustic wave problems. Constant elements are used to discretize the boundary surface so that the stronglyand hyper-singular boundary integrals contained in the formulations can be evaluated explicitly and the numerical process can be performed efficiently. Numerical examples are given to demonstrate the accuracy and efficiency of the present algorithm.
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Shape design and topology sensitivity formulations for acoustic problems based on adjoint method and the boundary element method are presented and are applied to shape sensitivity analysis and topology optimization of acoustic field. The... more
Shape design and topology sensitivity formulations for acoustic problems based on adjoint method and the boundary element method are presented and are applied to shape sensitivity analysis and topology optimization of acoustic field. The objective function is assumed to consist only of boundary integrals and quantities defined at certain number of discrete points. The adjoint field is defined so that the sensitivity of the objective function does not include the unknown sensitivity coefficients of the sound pressures and particle velocities on the boundary and in the domain. Since the final sensitivity expression does not have the sensitivity coefficients of the sound pressure and particle velocity on the boundary, BEM analyses only for the primary acoustic field and the adjoint field are needed to calculate the sensitivities of the objective function. The derived formulations are applied to shape sensitivity analyses and a topology optimization of a sound scatterer placed in an inf...
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In this paper, a half-space fast multipole BEM is developed for the simulation of three-dimensional acoustic problems above an infinite impedance plane. The half-space impedance Green’s function involving a complex line source is used, so... more
In this paper, a half-space fast multipole BEM is developed for the simulation of three-dimensional acoustic problems above an infinite impedance plane. The half-space impedance Green’s function involving a complex line source is used, so that both mass-like and spring-like impedance boundary conditions on the infinite plane can be explicitly satisfied and the infinite plane is not required to be discretized. The Burton–Miller method is employed to tackle the fictitious eigenfrequency problem involved in the conventional boundary integral equation method. Image relations of the multipole expansion coefficients are used and the half-space impedance Green’s function is modified to apply such relations to avoid calculating, translating and saving the multipole/local expansion coefficients in the image domain. An automatic integrator with adaptive interval subdivision is further adopted to calculate the line integral contained in the M2L translation formula accurately and efficiently. N...
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A shape optimization approach based on isogeometric wideband fast multipole boundary element method (IGA WFMBEM) in 2D acoustics is developed in this study. The key treatment is shape sensitivity analysis by using the adjoint variable... more
A shape optimization approach based on isogeometric wideband fast multipole boundary element method (IGA WFMBEM) in 2D acoustics is developed in this study. The key treatment is shape sensitivity analysis by using the adjoint variable method under isogeometric analysis (IGA) conditions. A set of efficient parameters of the wideband fast multipole method has been identified for IGA boundary element method. Shape optimization is performed by applying the method of moving asymptotes. IGA WFMBEM is validated through an acoustic scattering example. The proposed optimization approach is tested on a sound barrier and two multiple structures to demonstrate its potential for engineering problems.
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SummaryFor thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the... more
SummaryFor thin elastic structures submerged in heavy fluid, e.g., water, a strong interaction between the structural domain and the fluid domain occurs and significantly alters the eigenfrequencies. Therefore, the eigenanalysis of the fluid–structure interaction system is necessary. In this paper, a coupled finite element and boundary element (FE–BE) method is developed for the numerical eigenanalysis of the fluid–structure interaction problems. The structure is modeled by the finite element method. The compressibility of the fluid is taken into consideration, and hence the Helmholtz equation is employed as the governing equation and solved by the boundary element method (BEM). The resulting nonlinear eigenvalue problem is converted into a small linear one by applying a contour integral method. Adequate modifications are suggested to improve the efficiency of the contour integral method and avoid missing the eigenvalues of interest. The Burton–Miller formulation is applied to tackl...
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An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into... more
An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR ( s ) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as α = i / k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method.
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This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by... more
This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton–Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm.