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Asymptotics for Helmholtz and Maxwell Solutions in 3-D OpenWaveguides

Communications in Computational Physics 2012年第2期11卷 629-646页

作者： Carlos Jerez-Hanckes Jean-Claude Nedelec Seminar fur AngewandteMathematik ETH ZurichRamistrasse 1018092 ZurichSwitzerland Escuela de Ingenierıa Pontificia Universidad Catolica de ChileAv.Vicu˜naMackenna 4860SantiagoChile Centre de Mathematiques Appliquees Ecole Polytechnique91128 PalaiseauFrance

We extend classic Sommerfeld and Silver-Muller radiation conditions for bounded scatterers to acoustic and electromagnetic fields propagating over three isotropic homogeneous layers in three *** x=(x1,x2,x3)∈R^(3),with x_(3)denoting the direction orthogonal to the layers,standard conditions only hold for the outer layers in the region|x_(3)|>||x||^(γ),forγ∈(1/4,1/2)and x ***|x_(3)|<||x||^(γ)and inside the slab,asymptotic behavior depends on the presence of surface or guided modes given by the discrete spectrum of the associated operator.

关键词： Open waveguide radiation condition Helmholtz equation

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AN ADAPTIVE OPEN BOUNDARY condition

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Acta Mechanica Sinica 1990年第4期6卷 305-310页

作者： Chen Yaosong Zou Guangyuan (Dept.of Mechanics,Peking University)Gong Jie (Inst.of Software,Academia Sinica) Dept. of Mechanics Peking University Beijing China

A significant improvement of the open boundary condition which was originally studied by Engquist and Majda is *** method given here is applicable without limitation of the angle between the direction of the incident wave and the normal to the *** also improves the precision of the method from order one to *** test examples show that this method is much better than the method mentioned above.

关键词： boundary condition open boundary condition radiation condition

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AN ANALYTICAL SOLUTION OF SECOND－ORDER WAVE FORCE ON A VERTICAL CIRCULAR CYLINDER

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Applied Mathematics and Mechanics(English Edition) 1994年第9期15卷 849-863页

作者：邹志利戴遗山 Dalian University of Technology Dalian Harbin Shipbuilding Engineering Institute Harbin

So far many investigations have been made on nonlinear wave diffraction problemfor a large-diameter vertical circular cylinder. However,there are still some problemsworthy to be further discussed. It includes that the second order radiation condition isnot very clear and the inhomogeneous term of second order free surface boundarycondition makes the calculation of second order wave force either not easier to beperformed accurately due to its slowly decaying with radial distance or toocomplicated for practical application. In this paper, the second order radiationcondition is posed of the circumferential Fourier components of second orderpotential, instead of the second order potential. It is found that the circumferenatialFourier cormponents of second order potential have to satisfy Sommerfeld radiationcondition. By means of the mathematical formulae derived in this paper, theinhomogeneous term of second order free surface boundary condition were simplifiedand then an exact expression of second order wave force was obtained, which issimpler in form and easier to be used in practical calculation. The calculation resultsagree well with some experimental data.

关键词： water wave second-order force radiation condition diffraction

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Analytical Solution of Boundary Integral Equations for 2-D Steady Linear Wave Problems

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Journal of Ocean University of China 2005年第4期4卷 357-365页

作者： J.M. Chuang Naval Architecture and Marine Engineering Program Dalhouse University P.O. Box 1000 Halifax Nava Scotia B3J2X4 Canada

Based on the Fourier transform, the analytical solution of boundary integral equations formulated for the complex velocity of a 2-D steady linear surface flow is derived. It has been found that before the radiation condition is imposed,free waves appear both far upstream and downstream. In order to cancel the free waves in far upstream regions, the eigensolution of a specific eigenvalue, which satisfies the homogeneous boundary integral equation, is found and superposed to the analytical solution. An example, a submerged vortex, is used to demonstrate the derived analytical solution. Furthermore,an analytical approach to imposing the radiation condition in the numerical solution of boundary integral equations for 2-D steady linear wave problems is proposed.

关键词： boundary integral equation Cauchy's formula Rankine source method Fourier transform radiation condition

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