Transmitting boundaries: A closed-form comparison

1981 ◽  
Vol 71 (1) ◽  
pp. 143-159
Author(s):  
Eduardo Kausel ◽  
John L. Tassoulas
Keyword(s):  
Wave Propagation ◽  
Numerical Analysis ◽  
Closed Form ◽  
Neumann Boundary ◽  
Line Load ◽  
Problem Of Time ◽  
Time Harmonic ◽  
Infinite Extent ◽  
Transmitting Boundaries ◽  
Absorption Characteristics

abstract Several transmitting boundaries which have been proposed for the numerical analysis of problems of wave propagation in continua of infinite extent are reviewed. They are grouped into three broad classes: (1) elementary boundaries (Dirichlet or Neumann boundary conditions); (2) highly absorbing local boundaries; and (3) consistent transmitting boundaries. A closed-form comparison for the problem of time-harmonic antiplane line load on a stratum shows that elementary boundaries produce strong reflections, local boundaries have good absorption characteristics, and consistent transmitting boundaries are perfect absorbers.

SPECTRAL APPROXIMATION OF A SCHRÖDINGER TYPE EQUATION

1994 ◽  
Vol 04 (01) ◽  
pp. 49-88 ◽  
Author(s):  
CHRISTINE BERNARDI ◽  
MARIE-CLAUDE PELISSIER
Keyword(s):  
Numerical Analysis ◽  
Type Equation ◽  
Neumann Boundary ◽  
Rectangular Domain ◽  
The Other ◽  
Well Posedness ◽  
Discrete Problem ◽  
Spectral Approximation ◽  
Numerical Tests ◽  
Continuous Problem

This paper deals with a linear Schrödinger type equation in a rectangular domain with mixed Dirichlet-Neumann boundary conditions. The well-posedness of the continuous problem is proved, then a discrete problem is defined by combining a Legendre type spectral method in the first direction and a leap-frog scheme in the other one. The numerical analysis of the discretization is performed and error estimates are given. Numerical tests are presented.

Boundary conditions for the numerical solution of wave propagation problems

Geophysics ◽  
1978 ◽  
Vol 43 (6) ◽  
pp. 1099-1110 ◽  
Author(s):  
Albert C. Reynolds
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Finite Difference ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Neumann Boundary ◽  
Synthetic Seismograms ◽  
Neumann Boundary Conditions ◽  
Numerical Calculations ◽  
Reflection Coefficients

Many finite difference models in use for generating synthetic seismograms produce unwanted reflections from the edges of the model due to the use of Dirichlet or Neumann boundary conditions. In this paper we develop boundary conditions which greatly reduce this edge reflection. A reflection coefficient analysis is given which indicates that, for the specified boundary conditions, smaller reflection coefficients than those obtained for Dirichlet or Neumann boundary conditions are obtained. Numerical calculations support this conclusion.

Boundary Perturbations due to the Presence of Small Cracks

2015 ◽  
Author(s):  
Habib Ammari ◽  
Elie Bretin ◽  
Josselin Garnier ◽  
Hyeonbae Kang ◽  
Hyundae Lee ◽  
...  
Keyword(s):  
Asymptotic Formula ◽  
Neumann Boundary ◽  
Representation Formula ◽  
Fundamental Solutions ◽  
Energy Functional ◽  
Finite Hilbert Transform ◽  
Time Harmonic ◽  
Elastic Potential Energy ◽  
Potential Energy Functional ◽  
Boundary Perturbations

This chapter considers the perturbations of the displacement (or traction) vector that are due to the presence of a small crack with homogeneous Neumann boundary conditions in an elastic medium. It derives an asymptotic formula for the boundary perturbations of the displacement as the length of the crack tends to zero. Using analytical results for the finite Hilbert transform, the chapter derives an asymptotic expansion of the effect of a small Neumann crack on the boundary values of the solution. It also derives the topological derivative of the elastic potential energy functional and proves a useful representation formula for the Kelvin matrix of the fundamental solutions of Lamé system. Finally, it gives an asymptotic formula for the effect of a small linear crack in the time-harmonic regime.

scholarly journals Closed-Form Expressions for the Analysis of Wave Propagation in Overhead Distribution Lines

Energies ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 4519
Author(s):  
Theofilos A. Papadopoulos ◽  
Andreas I. Chrysochos ◽  
Christos K. Traianos ◽  
Grigoris Papagiannis
Keyword(s):  
Wave Propagation ◽  
Closed Form ◽  
System Analysis ◽  
Complex Form ◽  
Displacement Current ◽  
Decomposition Algorithms ◽  
Overhead Lines ◽  
Power System Analysis ◽  
Electromagnetic Transient ◽  
Time Domain Electromagnetic

The calculation of the influence of the imperfect earth on overhead conductors is an important issue in power system analysis. Rigorous solutions contain infinite integrals; thus, due to their complex form, different simplified closed-form expressions have been proposed in the literature. This paper presents a detailed analysis of the effect of different closed-form expressions on the investigation of the wave propagation of distribution overhead lines (OHLs). A sensitivity analysis is applied to determine the most important properties influencing the calculation of the OHL parameters. The accuracy of several closed-form earth impedance models is evaluated as well as the influence of the displacement current and imperfect earth on the shunt admittance, which are further employed in the calculation of the propagation characteristics of OHLs. The frequency-dependence of the soil electrical properties, as well as the application of different modal decomposition algorithms, are also investigated. Finally, results on the basis of frequency-domain signal scans and time-domain electromagnetic transient responses are also discussed.

Asymmetric Wave Propagation in an Elastic Half-Space by a Method of Potentials

1987 ◽  
Vol 54 (1) ◽  
pp. 121-126 ◽  
Author(s):  
R. Y. S. Pak
Keyword(s):  
Wave Propagation ◽  
Dynamic Response ◽  
Half Space ◽  
Elastic Half Space ◽  
Displacement Potential ◽  
Uniform Distributions ◽  
Time Harmonic ◽  
Method Of Potentials ◽  
Transformed Stress ◽  
Asymmetric Wave

A method of potentials is presented for the derivation of the dynamic response of an elastic half-space to an arbitrary, time-harmonic, finite, buried source. The development includes a set of transformed stress-potential and displacement-potential relations which are apt to be useful in a variety of wave propagation problems. Specific results for an embedded source of uniform distributions are also included.

The numerical analysis of fluid-solid interactions for blood flow in arterial structures Part 2: Development of coupled fluid-solid algorithms

1998 ◽  
Vol 212 (4) ◽  
pp. 241-252 ◽  
Author(s):  
S Z Zhao ◽  
X Y Xu ◽  
M W Collins
Keyword(s):  
Blood Flow ◽  
Wave Propagation ◽  
Numerical Analysis ◽  
Blood Vessels ◽  
Applied Mechanics ◽  
Specific Topic ◽  
Numerical Techniques ◽  
Wall Effects ◽  
Clinical Context ◽  
Local Flow

In this paper, the authors extend their study of wall mechanics given in Part 1 to the overall problem of fluid-solid interactions in arterial flows. Fluid-solid coupling has become a specific topic in computational methods and applied mechanics. In this review, firstly, the effects of elasticity of blood vessels on wave propagation and local flow patterns in large arteries are discussed. Then, numerical techniques are reviewed together with the alternative coupled methods available in fluid—wall models. Finally, a novel numerical algorithm combining two commercial codes for coupled solid/fluid problems is presented. As a consequence of the present studies, wall effects are now able to be included in predictions of haemodynamics in a clinical context.

Closed-Form Representation of Beam Response to Moving Line Loads

2000 ◽  
Vol 68 (2) ◽  
pp. 348-350 ◽  
Author(s):  
Lu Sun
Keyword(s):  
Closed Form ◽  
Moving Load ◽  
Closed Form Solution ◽  
Form Solution ◽  
Winkler Foundation ◽  
Line Load ◽  
State Response ◽  
Form Representation ◽  
Mach Numbers ◽  
Moving Line

Fourier transform is used to solve the problem of steady-state response of a beam on an elastic Winkler foundation subject to a moving constant line load. Theorem of residue is employed to evaluate the convolution in terms of Green’s function. A closed-form solution is presented with respect to distinct Mach numbers. It is found that the response of the beam goes to unbounded as the load travels with the critical velocity. The maximal displacement response appears exactly under the moving load and travels at the same speed with the moving load in the case of Mach numbers being less than unity.

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