scholarly journals A shape optimisation with the isogeometric boundary element method and adjoint variable method for the three-dimensional Helmholtz equation

2021 ◽  
pp. 103126
Author(s):  
Toru Takahashi ◽  
Daisuke Sato ◽  
Hiroshi Isakari ◽  
Toshiro Matsumoto
Keyword(s):  
Boundary Element Method ◽  
Helmholtz Equation ◽  
Boundary Element ◽  
Three Dimensional ◽  
Variable Method ◽  
Shape Optimisation ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Element Method

Acoustic Shape Optimization Based on Isogeometric Wideband Fast Multipole Boundary Element Method with Adjoint Variable Method

2020 ◽  
Vol 28 (02) ◽  
pp. 2050015
Author(s):  
Jie Wang ◽  
Changjun Zheng ◽  
Leilei Chen ◽  
Haibo Chen
Keyword(s):  
Boundary Element Method ◽  
Shape Optimization ◽  
Boundary Element ◽  
Acoustic Scattering ◽  
Variable Method ◽  
Optimization Approach ◽  
Adjoint Variable Method ◽  
Adjoint Variable ◽  
Fast Multipole ◽  
Element Method

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.

scholarly journals The implementation of the boundary element method to the Helmholtz equation of acoustics

2021 ◽  
pp. 13-19
Author(s):  
Sergey Sivak ◽  
Mihail Royak ◽  
Ilya Stupakov ◽  
Aleksandr Aleksashin ◽  
Ekaterina Voznjuk
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Numerical Methods ◽  
Helmholtz Equation ◽  
Boundary Value Problems ◽  
Boundary Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Element Method

Introduction: To solve the Helmholtz equation is important for the branches of engineering that require the simulation of wave phenomenon. Numerical methods allow effectiveness’ enhancing of the related computations. Methods: To find a numerical solution of the Helmholtz equation one may apply the boundary element method. Only the surface mesh constructed for the boundary of the three-dimensional domain of interest must be supplied to make the computations possible. This method’s trait makes it possible toconduct numerical experiments in the regions which are external in relation to some Euclidian three-dimensional subdomain bounded in the three-dimensional space. The later also provides the opportunity of not using additional geometric techniques to consider the infinitely distant boundary. However, it’s only possible to use the boundary element methods either for the homogeneous domains or for the domains composed out of adjacent homogeneous subdomains. Results: The implementation of the boundary elementmethod was committed in the program complex named Quasar. The discrepancy between the analytic solution approximation and the numerical results computed through the boundary element method for internal and external boundary value problems was analyzed. The results computed via the finite element method for the model boundary value problems are also provided for the purpose of the comparative analysis done between these two approaches. Practical relevance: The method gives an opportunityto solve the Helmholtz equation in an unbounded region which is a significant advantage over the numerical methods requiring the volume discretization of computational domains in general and over the finite element method in particular. Discussion: It is planned to make a coupling of the two methods for the purpose of providing the opportunity to conduct the computations in the complex regions with unbounded homogeneous subdomain and subdomains with substantial inhomogeneity inside.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

3D simulation of emulsion flow using the boundary element method on the heterogeneous computational systems

2012 ◽  
Vol 9 (1) ◽  
pp. 142-146
Author(s):  
O.A. Solnyshkina
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Problem Size ◽  
Low Reynolds Numbers ◽  
Infinite Domains ◽  
The Matrix ◽  
Computational Systems ◽  
Element Method

In this work the 3D dynamics of two immiscible liquids in unbounded domain at low Reynolds numbers is considered. The numerical method is based on the boundary element method, which is very efficient for simulation of the three-dimensional problems in infinite domains. To accelerate calculations and increase the problem size, a heterogeneous approach to parallelization of the computations on the central (CPU) and graphics (GPU) processors is applied. To accelerate the iterative solver (GMRES) and overcome the limitations associated with the size of the memory of the computation system, the software component of the matrix-vector product

Reduced-Order Modeling of Unsteady Flows About Complex Configurations Using the Boundary Element Method

2002 ◽  
Vol 124 (4) ◽  
pp. 988-993 ◽  
Author(s):  
V. Esfahanian ◽  
M. Behbahani-nejad
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Three Dimensional ◽  
Unsteady Flows ◽  
Reduced Order Modeling ◽  
Element Formulation ◽  
Reduced Order Models ◽  
Reduced Order ◽  
Naca 0012 ◽  
Element Method

An approach to developing a general technique for constructing reduced-order models of unsteady flows about three-dimensional complex geometries is presented. The boundary element method along with the potential flow is used to analyze unsteady flows over two-dimensional airfoils, three-dimensional wings, and wing-body configurations. Eigenanalysis of unsteady flows over a NACA 0012 airfoil, a three-dimensional wing with the NACA 0012 section and a wing-body configuration is performed in time domain based on the unsteady boundary element formulation. Reduced-order models are constructed with and without the static correction. The numerical results demonstrate the accuracy and efficiency of the present method in reduced-order modeling of unsteady flows over complex configurations.

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