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Coupling of mixed finite elements and boundary elements

IMA JOURNAL OF numerical ANALYSIS 2000年第3期20卷 461-480页

作者： Carstensen, C Funken, SA Univ Kiel Math Seminar D-24098 Kiel Germany

The symmetric coupling of mixed finite element and boundary element methods is analysed for a model interface problem with the Laplacian. The coupling involves a further continuous ansatz function on the interface to link the discontinuous displacement field to the necessarily continuous boundary ansatz function. Quasi-optimal a priori error estimates and sharp a posteriori error estimates are established which justify adaptive mesh-refining algorithms. numerical experiments prove the adaptive coupling as an efficient tool for the numerical treatment of transmission problems.

关键词： boundary value problems -- numerical solutions FINITE element method boundary element methods ERROR analysis (Mathematics)

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Analytic solutions for Gaussian gain profile resonators

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OPTICS COMMUNICATIONS 2005年第4-6期255卷 241-247页

作者： Iparraguirre, I Gaztelurrutia, TD ETS Ingn Dpto Fis Aplicada 1 Bilbao 48013 Spain

The problem of transversally gain-limited resonators is studied applying the Fresnel-Huygens integral operator including gain. For simplicity, only symmetric resonators with a Gaussian gain profile confined in a centered thin plate are considered, but the results are valid for more general cases. The solutions obtained are Hermite-Gaussian and Laguerre-Gaussian functions with complex argument and the method yields also the eigenvalues. The analysis of the eigenfunctions leads to the result that the beam-waist is not located in general at the center of the resonator, and could be outside the resonator in some cases. (c) 2005 Elsevier B.V. All rights reserved.

关键词： RESONATORS GAUSSIAN processes INTEGRAL operators EIGENvalueS boundary value problems -- numerical solutions

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B-spline solution of a singularly perturbed boundary value problem arising in biology

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CHAOS SOLITONS & FRACTALS 2009年第5期42卷 2934-2948页

作者： Lin, Bin Li, Kaitai Cheng, Zhengxing Xi An Jiao Tong Univ Coll Sci Xian 710049 Peoples R China

We use B-spline functions to develop a numerical method for solving a singularly perturbed boundary value problem associated with biology science. We use B-spline collocation method, which leads to a tridiagonal linear system. The accuracy of the proposed method is demonstrated by test problems. The numerical result is found in good agreement with exact solution. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： boundary value problems -- numerical solutions SPLINE theory PERTURBATION (Mathematics) BIOLOGICAL mathematical modeling SINGULARITIES (Mathematics) LINEAR systems COLLOCATION methods FUNCTIONS (Mathematics)

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A new Legendre wavelet operational matrix of derivative and its applications in solving the singular ordinary differential equations

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JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS 2011年第8期348卷 1787-1796页

作者： Mohammadi, F. Hosseini, M. M. Yazd Univ Fac Math Yazd Iran

In the present paper, a new Legendre wavelet operational matrix of derivative is presented. Shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The application of the proposed operational matrix for solving initial and boundary value problems is explained. Then the scheme is tested for linear and nonlinear singular examples. The obtained results demonstrate efficiency and capability of the proposed method. (C) 2011 Published by Elsevier Ltd. on behalf of The Franklin Institute.

关键词： DIFFERENTIAL equations -- numerical solutions MATRICES WAVELETS (Mathematics) LEGENDRE'S polynomials boundary value problems -- numerical solutions NONLINEAR theories MATHEMATICAL analysis

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Global solutions and smoothing effects for semi-linear evolution equations in circular domains

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2008年第5-6期69卷 1540-1558页

作者： Varlamov, Vladimir Univ Texas Pan Amer Dept Math Edinburg TX 78539 USA

The paper deals with global-in-time solutions of semi-linear evolution equations in circular domains. These solutions are constructed by means of the series of eigenfunctions of the Laplace operator in the corresponding region. A forced Cahn-Hilliard-type equation in a unit disc Omega is considered as an example. The current work focuses on revealing the mechanism of nonlinear smoothing, i.e., on tracing the influence of smoothness of the source term on the regularity of solutions of the nonlinear mixed problem. To this end convolutions of Rayleigh functions with respect to the Bessel index are employed. The study of this new family of special functions was initiated in [V. Varlamov, Convolution of Rayleigh functions with respect to the Bessel index, J. Math. Anal. Appl. 306 (2005) 413-424;V. Varlamov, Convolutions of Rayleigh functions and their application to semi-linear equations in circular domains, J. Math. Anal. Appl. 327 (2007) 1461-1478]. In order to reveal the effect of nonlinear smoothing, anisotropic Sobolev spaces H-s,H-alpha (Omega) are introduced. They are based on the Sobolev spaces H-s(Omega) "weighted" by tangential derivatives, so that the index alpha is responsible for the smoothness in theta and s is the usual Sobolev index. Global-in-time solutions of the mixed problem in question are constructed, and additional smoothness with respect to the angular coordinate is established in the anisotropic Sobolev spaces. The above mentioned special functions are essentially used for this purpose. (C) 2008 Published by Elsevier Ltd.

关键词： numerical analysis Eigenfunctions boundary value problems -- numerical solutions Laplace transformation

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Analysis of Transient Conduction and Radiation problems Using the Lattice Boltzmann and Discrete Ordinates Methods

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numerical HEAT TRANSFER PART A-APPLICATIONS 2015年第6期68卷 619-637页

作者： Sun, Yujia Zhang, Xiaobing Nanjing Univ Sci & Technol Sch Energy & Power Engn Nanjing 210014 Jiangsu Peoples R China

In this paper, the lattice Boltzmann method (LBM) and the discrete ordinates method (DOM) are coupled to solve transient conduction and radiation heat transfer problems. These are used to solve the energy equation and obtain the radiative heat source, respectively. To avoid additional interpolations between these two solvers when adding the radiative heat source to the energy equation, we propose using the same grid systems for both LBM and DOM. This is achieved by adopting a halfway bounce-back boundary scheme for LBM. This scheme is shown to be invalid in regard to solving 1D conduction problems with the D1Q2 lattice structure, while D1Q3 is shown to be correct and is adopted in this work. Good agreement with the available literature is obtained for both 1D and 2D conditions. The effects of conduction-radiation parameter and scattering albedo on the transient temperature distribution are presented and discussed. The method proposed in this study can readily solve combined conduction and radiation problems.

关键词： HEAT conduction HEAT -- Radiation & absorption LATTICE Boltzmann methods boundary value problems -- numerical solutions HEAT equation

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Stress recovery procedure for solving boundary value problems in the mechanics of a deformable solid by the finite element method

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PMM JOURNAL OF APPLIED MATHEMATICS AND MECHANICS 2010年第3期74卷 341-348页

作者： Rogovoi, A. A. Stolbova, O. S. [a] Perm Russia

A stress recovery procedure, based on the determination of the forces at the mesh points using a stiffness matrix obtained by the finite element method for the variational Lagrange equation, is described. The vectors of the forces reduced to the mesh points are constructed for the known stiffness matrices of the elements using the displacements at the mesh points found from the solution of the problem. On the other hand, these mesh point forces are determined in terms of the unknown forces distributed over the surface of an element and given shape functions. As a result, a system of Fredholm integral equations of the first kind is obtained, the solution of which gives these distributed forces. The stresses at the mesh points are determined for the values of these forces found on the surfaces of the finite element mesh (including at the mesh points) using the Cauchy relations, which relate the forces, stresses and the normal to the surface. The special features of the use of the stress recovery procedure are demonstrated for a plane problem in the linear theory of elasticity. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： STRAINS & stresses (Mechanics) boundary value problems -- numerical solutions DEFORMATIONS (Mechanics) FINITE element method FORCE & energy VARIATIONAL principles LAGRANGE equations INTEGRAL equations

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Acoustic radiation from a phased line source at a fluid-solid boundary

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IMA JOURNAL OF APPLIED MATHEMATICS 1997年第2期58卷 93-110页

作者： Rogoff, ZM Tew, RH UNIV NOTTINGHAM DEPT THEORET MECHNOTTINGHAM NG7 2RDENGLAND

The coupled wave dynamics of a compressible fluid and an elastic solid are studied when the motion is forced by a nonuniform line source lying in their common interface. The nonuniformity arises as a result of a distribution in phase along the forcing site, and this is taken as being representative of the effects of the scattering of an acoustic plane wave which is obliquely incident upon a shallow, surface-breaking inhomogeneity in the solid. An appropriate boundary-value problem is posed and solved exactly using an integral transform. This solution is then decomposed into its constituent asymptotic wave contributions, and the structure of each of these contributions is examined in the far field for all values of the phasing parameter.

关键词： ACOUSTIC radiation FLUID-structure interaction ELASTICITY INTEGRAL transforms boundary value problems -- numerical solutions PARAMETER estimation

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A parallel boundary fitted dynamic mesh solver for applications to flapping flight

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COMPUTERS & FLUIDS 2009年第8期38卷 1592-1607页

作者： Gopalakrishnan, Pradeep Tafti, Danesh K. Virginia Polytech Inst & State Univ Blacksburg VA 24061 USA

A parallel numerical solution procedure for unsteady incompressible flow is developed for simulating the dynamics of flapping flight. A collocated finite volume multiblock approach in a general curvilinear coordinate is used with Cartesian velocities and pressure as dependent variables. The Navier-Stokes equations are solved using a fractional-step algorithm. The dynamic grid algorithm is implemented by satisfying the space conservation law by computing the grid velocities in terms of the volume swept by the faces. The dynamic movement of grid in a multiblock approach is achieved by using a combination of spring analogy and Trans-Finite Interpolation. The spring analogy is used to compute the displacement of block corners, after which Trans-Finite Interpolation is applied independently on each computational block. The performance of the code is validated in forced transverse oscillations of a cylinder in cross-flow, a heaving airfoil, and hovering of a fruitfly. Finally, the unsteady aerodynamics of flapping flight at Re = 10,000 relevant to the development of Micro Air Vehicles is analyzed for forward flight. The results show the capability of the solver in predicting unsteady aerodynamics characterized by complex boundary movements. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： numerical analysis numerical grid generation (numerical analysis) PARTIAL differential equations -- numerical solutions boundary value problems -- numerical solutions

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Etalon boundary-value problem technique for three-dimensional diffraction problems

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ELECTROMAGNETICS 2000年第1期20卷 55-63页

作者： Bass, FG Slepyan, AY Slepyan, GY Bar Ilan Univ Dept Phys IL-52900 Ramat Gan Israel

The etalon boundary-value problem technique for approximately solving three-dimensional diffraction problems has been suggested. On etalon boundary-value problems, we use two-dimensional problems which are capable of exact solutions (for example, by the Wiener-Hopf technique). The field sought along one of the coordinate axes is taken to be locally coincident with that in the corresponding etalon problem. The amplitude coefficient (constant for the etalon problem) is assumed to be varying and is determined by substituting the above-mentioned solution representation into wave equations. Applications of the approach developed for the problem of electromagnetic-wave coastal refraction for a coast with a curved (random) coastal line and for the problem of wave diffraction by a perfectly conducting half-plane with a curvilinear edge have been considered.

关键词： boundary value problems -- numerical solutions OPTICAL diffraction ELECTROMAGNETIC wave scattering

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