A Study On Average Source Boundary Node Method For Helmholtz Problems

Acoustics has emerged in many scientific and engineering areas,such as high-speed train noise,medical ultrasound,underwater sonar,acoustic cloak,phonon crystal and seismic wave.Currently the most important solution to the acoustic problem is numerical simulation while such traditional way is being challenged by many new circumstances.As finite element and finite difference method of Regional mainstream algorithm,the boundary truncation technique,like non reflective artificial boundary and perfectly matched layer,can be harmful to the arithmetic precision and stability,which is inevitable given the dependency on that technique when dealing with infinite field sound field.Compared to Regional discrete algorithm,boundary element method can easily escape from artificial boundary truncation by using Acoustic field control equation and the elementary solution of infinite distance Sommerfeld Radiation boundary conditions,boundary discretization method needed.That solution reduces the dimension of the problem and shrinks the discrete matrix,which reduces the workload of calculation;So it's safe to say that boundary element method has an advantage in handling Scattering sound field problems over Regional discrete method such as finite element.However,unfortunately,boundary element method has its own limitation:division of Complex surface grid is a ton of work;besides,calculating amount of numerical integration is quite large;what's more,bigger wave number may lower the computation efficiency.The mentor of the present author has brought up a new boundary-type meshless method------The average source boundary node method to the stable temperature field problem.Based on the coupling regulation boundary integral equation and average source technology,the new method is of pure boundary node without calculating integral,which makes it simple,efficient and accurate.Moreover,average source boundary nodes method retains the good qualities of boundary element method including maintaining the stability of system and naturally satisfying sound infinity Sommerfeld Radiation boundary conditions,which makes it resolve the scattering field problem with ease.In this paper,the author will make the first try on average boundary node method over the acoustic problem.It is common knowledge that when it comes outer sound field problem,we should pay attention to the uniqueness of boundary integral equation which means that corresponding to characteristic wave number of inner Dirichlet(Neumann)there is no only answer to the boundary integral equation of outside Neumann(Neumann).Such solutions to direct boundary element method are CHIEF and Burton-Miller;to indirect boundary element method is CHIEF and Leis.This paper is on the basis of entire regularization indirect variable boundary integral equation exported Helmholtz problem from Leis formula.On such basis,by the average source technology,the theory and method of average source boundary node of Helmholtz problem has been founded.THE discrete grid of the method is simply used to calculate the area and jacobian,without referring to unite and numerical integration;therefore,you may call it a true meshless method.A quantity of results from 2D and 3D acoustic radiation,scattering have shown that the method stressed in this paper is easily to design,efficient and accurate.