Papers by Keyword: Helmholtz Equation

Abstract: In this paper, a set of computer simulation techniques are put forward according to Helmholtz equation and the boundary conditions of the metallic circular waveguide, the different expressions on propagation modes of electromagnetic wave are given, and then the distribution rules of the tube-wall currents and charges are analyzed and discussed in different modes. The algorithm and techniques presented are helpful for the industrial application of measurements and design of the relevant devices.

Abstract: In this paper control problems for 2-D Helmholtz equation are formulated and investigated. These problems are associated with developing technology of acoustic cloaking. Helmholtz equation is considered in an unbounded domain with the impedance boundary condition. The role of control in control problems under study is played by surface impedance.

Abstract: The paper deals with the application of the so-called T-type finite elements [1] to the calculation of the exterior acoustic problems in two dimensions. The method is based on the use of asuitably truncated T-complete set of Trefftz functions over individual subdomains linked by means ofa least square procedure. The vertex singularities and the Sommerfeld radiation condition are readilyincorporated in the trial functions. In order to show the performance of the approach two examples ofcomputations for infinite cylinders (of circular and square cross section) are presented and comparedwith those obtained by means of h-adaptive FE method [2].

Abstract: We consider control problems for 2-D Helmholtz equation in a bounded domain with partially coated boundary. These problems are associated with acoustic cloaking. Dirichlet boundary condition is given on one part of the boundary and the impedance boundary condition is given on another part of the boundary. The role of control in control problem under study is played by surface impedance. Solvability of control problem is proved and optimality system is derived.

Abstract: Control problems are considered for a two-dimensional model describing wave scattering in an unbounded homogenous medium containing an impenetrable covered (cloaked) boundary. The control is a surface impedance which enters the boundary condition as a coefficient. The solvability of the original scattering problem for 2-D Helmholtz equation and of the control problem is proved. Optimality system dгescribing the necessary extremum conditions are derived. The algorithm for numerical solving of the control problem based on the optimality system and boundary element method is designed.

Abstract: In this paper, the Taylor polynomial method is used to solve the Helmholtz equation. Using the Taylor polynomial for the method, the Helmholtz equation is transformed into solving matrix equation. The error analysis of this equation is given. A numerical experiment is given to prove the efficiency and dependability of the method.

Abstract: In this paper, the acoustic Helmholtz boundary integral equation is solved using Coiflet scaling functions with interpolation approximation property. The scaling functions are utilized as base and test functions in Galerkin method and the expanded coefficients are the values of the function in sampling points, so the number of numerical integral is reduced. Two numerical examples are given and the calculation results agree well with the theoretical results, which show the high accuracy of the estimation and demonstrate validity and applicability of the method.

Abstract: To overcome the non-uniqueness of solution at eigenfrequencies in the boundary integral equation method for structural acoustic radiation, wave superposition method is introduced to study the acoustics characteristics including acoustic field reconstruction and sound power calculation. The numerical method is implemented by using the acoustic field from a series of virtual sources which are collocated near the boundary surface to replace the acoustic field of the radiator, namely the principle of equivalent. How to collocate these equivalent sources is not indicated definitely. Once wave superposition method is applied to sound power calculation, it is necessary to evaluate its accuracy and impact factors. In the paper, the basic principle of wave superposition method is described, and then the integral equation is discretized. Also, the impact factors including element numbers, frequency limitation, and distance between virtual source and integral surface are analyzed in the process of calculate the acoustic radiation from the simply supported thin plate under concentrated force. The extensive measures of acoustic field at the thin plate are compared with results obtain using different numerical methods. The results show that: (a) The agreement between the results from the above numerical methods is excellent. The wave superposition method requires fewer elements and hence is faster. But the extensive numerical modeling suggests that as long as the volume velocity matching yields more than adequate accuracy. (b) The equivalent sources should be collocated inside the radiator. And the accuracy of a given Gauss integration formula will decrease as the source approaches the boundary surface. (c) The numerical method is applicable to the acoustic radiation of structure with complicated shape. (d) The method described in this paper can be used to perform effectively sound power calculation, and its application range can be extended on the basis of these conclusions.

Abstract: A functional nodal method for numerical solution of a two-dimensional Helmholtz equation is considered. The method uses a compact 7-point difference scheme and provides continuity of averaged fluxes and the numerical solution. Truncation analysis of the difference scheme is done and it is shown that the considered difference scheme is of the 2nd order of precision inside the domain.

Abstract: To solve truncation questions of calculation area(unbounded) of Helmhotlz equation, Berenger first proposed concept of Perfectly Matched Layer(PML) in 1994, the method optimizes boundary conditions and reduces computation quantities greatly. By choosing constants p,d,e of PML parameters , we obtain an optimal PML parameter in this paper . The final numerical experiments show that the result obtained by the PML parameter is almost same as accurate result of references [4].