The BEM for solving the nonhomogeneous Helmholtz equation with variable coefficients

Considering the fundamental solution of the Laplace equation as the weight function, we give the iterative format for solving the nonhomogeneous Helmholtz equation with variable coefficients. Furthermore, the iteration method of BEM for solving the equation mentioned above is obtained. The numerical example is given in this paper. Finally, the iteration method of BEM mentioned above is compared with the coupled method of BEM that was presented before then by authors.     

关于-RTlnK_c~■=Δ_rG_m~■(c~■)的讨论

在等温等压条件下,通过pB=cBRT关系转换,所得关系式证明了-RTlnK—cΟ=ΔrG—mΟ(c—Ο)。还分析推证出ΔrG—mΟ(c—Ο)和ΔrG—mΟ(p—Ο)、ΔrH—Οm(c—Ο)和ΔrHΟ—m(p—Ο)、ΔrSΟ—m(c—Ο)和ΔrSΟ—m(p—Ο)、ΔrUΟ—m(c—Ο)和ΔrHΟ—m(cΟ—)以及ΔrG—Οm(c—Ο)和ΔrA—mΟ(c—Ο)之间的几个关系式,进一步证实了-RTlnK—cΟ=ΔrGΟ—m(c—Ο)。     

ERROR ESTIMATION FOR NUMERICAL METHODS USING THE ULTRA WEAK VARIATIONAL FORMULATION IN MODEL OF NEAR FIELD SCATTERING PROBLEM

In this paper, we investigate the use of ultra weak variational formulation to solve a wave scattering problem in near field optics. In order to capture the sub-scale features of waves, we utilize evanescent wave functions together with plane wave functions to approximate the local properties of the field. We analyze the global convergence and give an error estimation of the method. Numerical examples are also presented to demonstrate the effectiveness of the strategy.     

Analysis of the convected Helmholtz equation with a uniform mean flow in a waveguide with complete radiation boundary conditions

In this paper, we propose complete radiation boundary conditions (CRBCs) for solutions of the convected Helmholtz equation with a uniform mean flow in a waveguide. We first study CRBCs for the Helmholtz equation in a waveguide. Noting that the convected Helmholtz equation is associated with the Helmholtz equation via the Prandtl–Glauert transformation, CRBCs for the convected Helmholtz equation is derived from CRBCs for the Helmholtz equation. We analyse well-posedness and convergence of approximate solutions satisfying CRBCs for the convected Helmholtz equation. In addition, simple numerical experiments will be presented to confirm the theoretical results.     

A Class of Operator Equations in Nonlinear Mechanics

A nonlinear evolution equation in Hilbert space is introduced and is shown to govern a broad class of problems of nonlinear solid mechanics. The simplest oscillations of this equation are described by a “generalized Liénard equation.”

AMS(MOS) Classification Nos: 73D35, 73F15, 58D25, 35L35, 34G20, 34C15.     

The Neumann problem and Helmholtz decomposition in convex domains

We show that the Neumann problem for Laplace's equation in a convex domain Ω with boundary data in Lp(∂Ω) is uniquely solvable for 1<p<∞. As a consequence, we obtain the Helmholtz decomposition of vector fields in Lp(Ω,Rd).     

Asymptotics of optimal control in the problem of harmonic wave scattering by an obstacle

Optimal impedance control for the Helmholtz equation in an unbounded domain is studied. Asymptotics of the optimal control with respect to a regularization parameter are constructed.     

Modified boundary integral formulations for the Helmholtz equation

In this paper we describe some modified regularized boundary integral equations to solve the exterior boundary value problem for the Helmholtz equation with either Dirichlet or Neumann boundary conditions. We formulate combined boundary integral equations which are uniquely solvable for all wave numbers even for Lipschitz boundaries Γ=∂Ω. This approach extends and unifies existing regularized combined boundary integral formulations.     

一个扩散问题的自然边界元法与有限元法组合

本文讨论由Helmholtz方程描述的扩散问题的自然边界元法与有限元法的组合．取一个圆作为公共边界，用Fourier展开建立边界积分方程，将无界区域上的问题化为有界区域上的非局部边值问题．在变分方程中公共边界上的未知量只包含函数本身而不包含其法向导数，从而减少了未知数的数目，并且边界元剐度矩阵只有极少量不同的元素，有利于数值计算．这种组台方法优越于建立在直接边界元法基础上的组合方法．文中证明了变分解的唯一性，数值解的收敛性和误差估计．最后讨论了数值技术并给出一个算倒．     

2-D/3-D finite-element solution of the steady Euler equations for transonic lifting flow by stream vector correction

In this paper we study the validation of the new formulation (potential-stream vector) of the steady Euler equations in 2-D/3-D transonic lifting regime flow. This approach, which is based on the Helmholtz decomposition of a velocity vector field, is designed to extend the potential approximation of Euler equations for severe situations such as high transonic or rotational subsonic flows. Different results computed by a fixed point algorithm on the stream vector correction are shown and discussed by comparing them with those obtained by the full potential approach.