Unconditionally stable Crank-Nicolson algorithm with enhanced absorption for rotationally symmetric multi-scale problems in anisotropic magnetized plasma

Large calculation error can be formed by directly employing the conventional Yee’s grid to curve surfaces.In order to alleviate such condition,unconditionally stable CrankNicolson Douglas-Gunn(CNDG)algorithm with is proposed for rotationally symmetric multi-scale problems in anisotropic magnetized plasma.Within the CNDG algorithm,an alternative scheme for the simulation of anisotropic plasma is proposed in body-of-revolution domains.Convolutional perfectly matched layer(CPML)formulation is proposed to efficiently solve the open region problems.Numerical example is carried out for the illustration of effectiveness including the efficiency,resources,and absorption.Through the results,it can be concluded that the proposed scheme shows considerable performance during the simulation.

A Stable FE-FD Method for Anisotropic Parabolic PDEs with Moving Interfaces

In this paper,a new finite element and finite difference(FE-FD)method has been developed for anisotropic parabolic interface problems with a known moving interface using Cartesian meshes.In the spatial discretization,the standard P,FE discretization is applied so that the part of the coefficient matrix is symmetric positive definite,while near the interface,the maximum principle preserving immersed interface discretization is applied.In the time discretization,a modified Crank-Nicolson discretization is employed so that the hybrid FE-FD is stable and second order accurate.Correction terms are needed when the interface crosses grid lines.The moving interface is represented by the zero level set of a Lipschitz continuous function.Numerical experiments presented in this paper confirm second orderconvergence.

On the Coupled of NBEM and CFEM for an Anisotropic Quasilinear Problem in an Unbounded Domain with a Concave Angle

In this paper, based on the Kirchhoff transformation and the natural boundary element method, a coupled natural boundary element and curved edge finite element is applied to solve the anisotropic quasi-linear problem in an unbounded domain with a concave angle. By using the principle of the natural boundary reduction, we obtain the natural integral equation on the artificial boundary of circular arc boundary, and get the coupled variational problem and its numerical method. Then the error and convergence of coupling solution are analyzed. Finally, some numerical examples are verified to show the feasibility of our method.

Anisotropic nonconforming Crouzeix-Raviart type FEM forsecond-order elliptic problems

The nonconforming Crouzeix-Raviart type linear triangular finite element approximate to second-order elliptic problems is studied on anisotropic general triangular meshes in 2D satisfying the maximal angle condition and the coordinate system condition. The optimal-order error estimates of the broken energy norm and L2-norm are obtained.

Comparisons between Isotropic and Anisotropic TV Regularizations in Inverse Acoustic Scattering

This article compares the isotropic and anisotropic TV regularizations used in inverse acoustic scattering. It is observed that compared with the traditional Tikhonov regularization, isotropic and anisotropic TV regularizations perform better in the sense of edge preserving. While anisotropic TV regularization will cause distortions along axes. To minimize the energy function with isotropic and anisotropic regularization terms, we use split Bregman scheme. We do several 2D numerical experiments to validate the above arguments.

PROBLEM OF THE PERIODIC WELDING OF ANISOTROPIC ELASTIC PLANE WITH DIFFERENT MATERIALS

In this paper, the problem of the periodic welding of an anisotropic elastic half_plane and a strip with different materials is studied. By means of the complex variable method for plane elasticity and the theory of boundary value problems for analytic function, the stress distribution is given in closed forms.

Composite penalty method of a low order anisotropic nonconforming finite element for the Stokes problem

Composite penalty method of a low order anisotropic nonconforming quadrilateral finite element for the Stokes problem is presented. This method with a large penalty parameter can achieve the same accuracy as the stand method with a small penalty parameter and the convergence rate of this method is two times as that of the standard method under the condition of the same order penalty parameter. The superconvergence for velocity is established as well. The results of this paper are also valid to the most of the known nonconforming finite element methods.

Symmetry Reductions of Cauchy Problems for Fourth-Order Quasi-Linear Parabolic Equations

This paper is devoted to studying symmetry reduction of Cauchy problems for the fourth-order quasi-linear parabolic equations that admit certain generalized conditional symmetries （GCSs）. Complete group classification results are presented, and some examples are given to show the main reduction procedure.

A Robin Problem for Quasi-linear System

In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.

SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING

Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors, so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some ill-conditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.

PERIODICAL INTERFACIAL CRACKS IN ANISOTROPIC ELASTOPLASTIC MEDIA

By using Fourier transformation the boundary problem of periodical interfacial cracks in anisotropic elastoplastic bimaterial was transformed into a set of dual integral equations and then it was further reduced by means of definite integral transformation into a group of singular equations. Closed form of its solution was obtained and three corresponding problems of isotropic bimaterial, of a single anisotropic material and of a bimaterial of isotropy- anisotropy were treated as the specific cases. The plastic zone length of the crack tip and crack openning displacement ( COD) decline as the smaller yield limit of the two bonded materials rises, and they were also determined by crack length and the space between two neighboring cracks . In addition , COD also relates it with moduli of the materials .

Reconstruction of Temperature Field in 3-D, Absorbing, Emitting, and Anisotropically Scattering Medium

The soft measurement technology of flame temperature field is an efficient method to learn the combustion status in furnace. Generally, it reconstructs the temperature field in furnace through the image of flame, which is a process to solve radiative inverse problem. In this paper, the flame of pulverized coal is considered as 3-D, absorbing, emitting, and anisotropically scattering non-gray medium. Through the study on inverse problem of radiative heat transfer, the temperature field in this kind of medium has been reconstructed. The mechanism of 3-D radiative heat transfer in a rectangular media, which is 2 m×3 m× 5 m and full of CO2, N2 and carbon particles, is studied with Monte Carlo method. The 3-D temperature field in this rectangular space is reconstructed and the influence of particles density profile is discussed.

各向异性问题的多子域区域分解算法

在自然边界归化原理的基础上,构造了一种无界凹角区域上各向异性问题的多子域非重叠区域分解算法,这是两子域的非重叠区域分解法的推广.本文给出了多子域区域分解算法的离散和变分形式,利用等价性理论,通过详细的理论证明说明此算法是收敛的,且与网格参数h无关.

MULTIPLE POSITIVE SOLUTIONS FOR A CLASS OF QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENT

In this paper, we study the multiplicity results of positive solutions for a class of quasi-linear elliptic equations involving critical Sobolev exponent. With the help of Nehari manifold and a mini-max principle, we prove that problem admits at least two or three positive solutions under different conditions.

Global Smooth Solution for the Quasi-linear Wave Equation

In this paper, we study the Cauchy problem for the following quasi-linear wave equation utt-2kuxxt=β（ux^n）x, where k〉0 and β are real numbers, and n ≥ 2 is an integer. We prove that for any T〉0, the Cauchy problem admits a unique global smooth solution u∈C^∞（（0, T]; H^∞（R）） ∩ C（[0, T]; H^2（R）） ∩ C^1（[0, T]; L^2（R）） under suitable assumptions on the initial data.

Solution of two-dimensional scattering problem in piezoelectric/piezomagnetic media using a polarization method

Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezomagnetic ＂comparison body＂ is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green＇s function, which is obtained using the Radon transform. The expression is further simplified under conditions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelectric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section.

Numerical Solution of 2-D Diffusion Problems Using Discrete Duality Finite Volume Method on General Boundary Conditions

In this paper, we present a discrete duality finite volume (DDFV) method for 2-D flow problems in nonhomogeneous anisotropic porous media under diverse boundary conditions. We use the discrete gradient defined in diamond cells to compute the fluxes. We focus on the case of Dirichlet, full Neumann and periodic boundary conditions. Taking into account the periodicity is the main new ingredient with respect to our recent works. We explain the procedures step by step, for numerical solutions. We develop a matlab code for algebraic equations. Numerical tests were provided to confirm our theoretical results.

Regularity for solutions to anisotropic obstacle problems

For Ω a bounded subset of R n,n 2,ψ any function in Ω with values in R∪{±∞}andθ∈W1,(q i)(Ω),let K(q i)ψ,θ(Ω)={v∈W1,(q i)(Ω):vψ,a.e.and v-θ∈W1,(q i)0(Ω}.This paper deals with solutions to K(q i)ψ,θ-obstacle problems for the A-harmonic equation-divA(x,u(x),u(x))=-divf(x)as well as the integral functional I(u;Ω)=Ωf(x,u(x),u(x))dx.Local regularity and local boundedness results are obtained under some coercive and controllable growth conditions on the operator A and some growth conditions on the integrand f.

A LOW ORDER NONCONFORMING ANISOTROPIC FINITE ELEMENT APPROXIMATION TO PARABOLIC PROBLEM

A low order nonconforming finite element is applied to the parabolic problem with anisotropicmeshes.Both the semidiscrete and fully discrete forms are studied.Some superclose properties andsuperconvergence are obtained through some novel approaches and techniques.

CONVERGENCE OF A MIXED FINITE ELEMENT FOR THE STOKES PROBLEM ON ANISOTROPIC MESHES

The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works .