Use of nonsingular boundary integral formulation for reducing errors due to near-field measurements in the boundary element method based near-field acoustic holography

This research develops an Advance-Tracing Boundary Element Method in the time domain to calculate the waves that radiate from an immersed obstacle moving with random acceleration. The moving velocity of the immersed obstacle is multifrequency and is projected along the normal direction of every element on the obstacle. The projected normal velocity of every element is presented by the Fourier series and includes the advance-tracing time, which is equal to a quarter period of the moving velocity. The moving velocity is treated as a known boundary condition. The computing scheme is based on the boundary integral equation in the time domain, and the approach process is carried forward in a loop from the first time step to the last. At each time step, the radiated pressure on each element is updated until obtaining a convergent result. The Advance-Tracing Boundary Element Method is suitable for calculating the radiating problem from an arbitrary obstacle moving with random acceleration in the time domain and can be widely applied to the shape design of an immersed obstacle in order to attain security and confidentiality.

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Recent Development of the Fast Multipole Boundary Element Method for Modeling Acoustic Problems

Volume 15: Sound, Vibration and Design ◽

10.1115/imece2009-10163 ◽

2009 ◽

Author(s):

Yijun Liu ◽

Milind Bapat

Keyword(s):

Boundary Element Method ◽

Acoustic Wave ◽

Boundary Element ◽

Large Scale ◽

Boundary Integral ◽

Practical Significance ◽

Fast Multipole ◽

Tree Structures ◽

Wave Problems ◽

Element Method

Some recent development of the fast multipole boundary element method (BEM) for modeling acoustic wave problems in both 2-D and 3-D domains are presented in this paper. First, the fast multipole BEM formulation for 2-D acoustic wave problems based on a dual boundary integral equation (BIE) formulation is presented. Second, some improvements on the adaptive fast multipole BEM for 3-D acoustic wave problems based on the earlier work are introduced. The improvements include adaptive tree structures, error estimates for determining the numbers of expansion terms, refined interaction lists, and others in the fast multipole BEM. Examples involving 2-D and 3-D radiation and scattering problems solved by the developed 2-D and 3-D fast multipole BEM codes, respectively, will be presented. The accuracy and efficiency of the fast multipole BEM results clearly demonstrate the potentials of the fast multipole BEM for solving large-scale acoustic wave problems that are of practical significance.

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A Boundary Element Method for Multi-Body Contact Problems and its Application to the Analysis of a Huge Excavator

ASME 1995 15th International Computers in Engineering Conference and the ASME 1995 9th Annual Engineering Database Symposium ◽

10.1115/cie1995-0760 ◽

1995 ◽

Author(s):

Chong-De Liu ◽

Jiyuan Yu ◽

Xiaoming Wang

Keyword(s):

Boundary Element Method ◽

Boundary Element ◽

Contact Problems ◽

Fortran Program ◽

Boundary Integral ◽

Element Formulation ◽

Body Contact ◽

Boundary Integral Formulation ◽

Discretization Technique ◽

Multi Body

Abstract The derivation of a boundary integral formulation and discretization technique in terms of boundary elements for the solution of multi-body contact problems has been carried out. A FORTRAN program has been developed based on this boundary element formulation and has been applied to the stress analysis of a huge caterpillar excavator woth 16 m3 bucket capacity.

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An Improved Assembling Algorithm in Boundary Elements With Galerkin Weighting Applied to Three-Dimensional Stokes Flows

Journal of Fluids Engineering ◽

10.1115/1.4037690 ◽

2017 ◽

Vol 140 (1) ◽

Author(s):

Sofia Sarraf ◽

Ezequiel López ◽

Laura Battaglia ◽

Gustavo Ríos Rodríguez ◽

Jorge D'Elía

Keyword(s):

Boundary Element Method ◽

Linear System ◽

Boundary Element ◽

Numerical Solutions ◽

Three Dimensional ◽

Boundary Integral ◽

Computational Time ◽

Creeping Flows ◽

Order Of Magnitude ◽

Element Method

In the boundary element method (BEM), the Galerkin weighting technique allows to obtain numerical solutions of a boundary integral equation (BIE), giving the Galerkin boundary element method (GBEM). In three-dimensional (3D) spatial domains, the nested double surface integration of GBEM leads to a significantly larger computational time for assembling the linear system than with the standard collocation method. In practice, the computational time is roughly an order of magnitude larger, thus limiting the use of GBEM in 3D engineering problems. The standard approach for reducing the computational time of the linear system assembling is to skip integrations whenever possible. In this work, a modified assembling algorithm for the element matrices in GBEM is proposed for solving integral kernels that depend on the exterior unit normal. This algorithm is based on kernels symmetries at the element level and not on the flow nor in the mesh. It is applied to a BIE that models external creeping flows around 3D closed bodies using second-order kernels, and it is implemented using OpenMP. For these BIEs, the modified algorithm is on average 32% faster than the original one.

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