scholarly journals A Pollution Effect in the Boundary Element Method for Acoustic Problems

2018 ◽  
Vol 26 (02) ◽  
pp. 1850018 ◽  
Author(s):  
Steffen Marburg
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Phase Error ◽  
Numerical Dispersion ◽  
The Finite Element Method ◽  
Pollution Effect ◽  
Numerical Damping ◽  
Element Method

The pollution effect is a well-known and well-investigated phenomenon of the finite element method for wave problems in general and for acoustic problems in particular. It is understood as the problem that a local mesh refinement cannot compensate the numerical error which is generated and accumulated in other regions of the model. This is the case for the phase error of the finite element method which leads to dispersion resulting in very large numerical errors for domains with many waves in them and is of particular importance for low order elements. Former investigations have shown that a pollution effect resulting from dispersion is unlikely for the boundary element method. However, numerical damping in the boundary element method can account for a pollution effect. A further investigation of numerical damping reveals that it has similar consequences as the phase error of the finite element method. One of these consequences is that the number of waves within the domain may be controlling the discretization error in addition to the size and the order of the boundary elements. This will be demonstrated in computational examples discussing traveling waves in rectangular ducts. Different lengths, element types and mesh sizes are tested for the boundary element collocation method. In addition to the amplitude error which is due to numerical damping, a rather small phase error is observed. This may indicate numerical dispersion.

scholarly journals Acoustic Noise Computation of Electrical Motors Using the Boundary Element Method

Energies ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 245
Author(s):  
Sabin Sathyan ◽  
Ugur Aydin ◽  
Anouar Belahcen
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Finite Element Simulation ◽  
Acoustic Noise ◽  
The Finite Element Method ◽  
Magnetic Forces ◽  
Element Simulation ◽  
Element Method

This paper presents a numerical method and computational results for acoustic noise of electromagnetic origin generated by an induction motor. The computation of noise incorporates three levels of numerical calculation steps, combining both the finite element method and boundary element method. The role of magnetic forces in the production of acoustic noise is established in the paper by showing the magneto-mechanical and vibro-acoustic pathway of energy. The conversion of electrical energy into acoustic energy in an electrical motor through electromagnetic, mechanical, or acoustic platforms is illustrated through numerical computations of magnetic forces, mechanical deformation, and acoustic noise. The magnetic forces were computed through 2D electromagnetic finite element simulation, and the deformation of the stator due to these forces was calculated using 3D structural finite element simulation. Finally, boundary element-based computation was employed to calculate the sound pressure and sound power level in decibels. The use of the boundary element method instead of the finite element method in acoustic computation reduces the computational cost because, unlike finite element analysis, the boundary element approach does not require heavy meshing to model the air surrounding the motor.

scholarly journals Elongation determination using finite element and boundary element method

2015 ◽  
Vol 61 (4) ◽  
pp. 389-394
Author(s):  
Piotr Kisała ◽  
Waldemar Wójcik ◽  
Nurzhigit Smailov ◽  
Aliya Kalizhanova ◽  
Damian Harasim
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Boundary Element Method ◽  
Boundary Element ◽  
Experimental Studies ◽  
Numerical Algorithms ◽  
Mathematical Structure ◽  
The Finite Element Method ◽  
Fbg Sensor ◽  
Element Method

AbstractThis paper presents an application of the finite element method and boundary element method to determine the distribution of the elongation. Computer simulations were performed using the computation of numerical algorithms according to a mathematical structure of the model and taking into account the values of all other elements of the fiber Bragg grating (FBG) sensor. Experimental studies were confirmed by elongation measurement system using one uniform FBG.

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.

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