scholarly journals The Modification of Kernel Function and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Tao Zhao
Keyword(s):  
Half Space ◽  
Kernel Function ◽  
Integral Representations ◽  
Neumann Problems ◽  
Riesz Kernel

By virtue of the modified Riesz kernel introduced by Qiao (2012), we give the integral representations for solutions of the Neumann problems in a half space.

Removing Non-Uniqueness in Symmetric Galerkin Boundary Element Method for Elastostatic Neumann Problems and its Application to Half-Space Problems

2020 ◽  
Vol 36 (6) ◽  
pp. 749-761
Author(s):  
Y. -Y. Ko
Keyword(s):  
Boundary Element Method ◽  
Rigid Body ◽  
Boundary Element ◽  
Integral Equations ◽  
Half Space ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Neumann Problems ◽  
Galerkin Boundary Element Method ◽  
Element Method

ABSTRACTWhen the Symmetric Galerkin boundary element method (SGBEM) based on full-space elastostatic fundamental solutions is used to solve Neumann problems, the displacement solution cannot be uniquely determined because of the inevitable rigid-body-motion terms involved. Several methods that have been used to remove the non-uniqueness, including additional point support, eigen decomposition, regularization of a singular system and modified boundary integral equations, were introduced to amend SGBEM, and were verified to eliminate the rigid body motions in the solutions of full-space exterior Neumann problems. Because half-space problems are common in geotechnical engineering practice and they are usually Neumann problems, typical half-space problems were also analyzed using the amended SGBEM with a truncated free surface mesh. However, various levels of errors showed for all the methods of removing non-uniqueness investigated. Among them, the modified boundary integral equations based on the Fredholm’s theory is relatively preferable for its accurate results inside and near the loaded area, especially where the deformation varies significantly.

scholarly journals Integral representations of a class of harmonic functions in the half space

2016 ◽  
Vol 260 (2) ◽  
pp. 923-936 ◽  
Author(s):  
Yan Hui Zhang ◽  
Guan Tie Deng ◽  
Tao Qian
Keyword(s):  
Half Space ◽  
Harmonic Functions ◽  
Integral Representations

ELECTROMAGNETIC SCATTERING FROM CYLINDERS OF ARBITRARY CROSS‐SECTION IN A CONDUCTIVE HALF‐SPACE

Geophysics ◽  
1971 ◽  
Vol 36 (1) ◽  
pp. 67-100 ◽  
Author(s):  
J. R. Parry ◽  
S. H. Ward
Keyword(s):  
Half Space ◽  
Cross Section ◽  
Electromagnetic Scattering ◽  
Numerical Technique ◽  
Surface Current ◽  
Arbitrary Cross Section ◽  
Integral Representations ◽  
Radius Of Curvature ◽  
Current Densities ◽  
Conducting Cylinders

A general numerical technique is presented for solving the problem of electromagnetic scattering by conducting cylinders of arbitrary cross‐section located in a conductive half‐space. Solutions to the electromagnetic wave equation are required for the free space above the half‐space, for the half‐space surrounding the cylinder, and for the cylinder. The problem is formulated by choosing an integral representation for the electromagnetic fields in each of the three homogeneous regions. By enforcing the boundary conditions on tangential E and H, we obtain a set of coupled integral equations which can be solved numerically for the unknown equivalent surface current densities on the interface bounding each homogeneous region. Once these current densities have been estimated, the fields can be calculated at any point from the general integral representations. The following conclusions are among those of importance to AFMAG and VLF surveys: 1) the ratio of Re (H) to Im (H) is a function of traverse position and of ground conductivity, as well as of cylinder conductivity and of survey frequency; 2) in no case was a zero phase observed, even for perfectly conducting cylinders; and 3) reverse crossovers in Im (H) can occur in the field scattered by a single conductor whenever the radius of curvature on the upper portion of a “poor” conductor is small.

Torsion of a Rigid Cylinder Embedded in an Elastic Half Space

1976 ◽  
Vol 43 (3) ◽  
pp. 419-423 ◽  
Author(s):  
J. E. Luco
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Half Space ◽  
Elastic Constants ◽  
Elastic Half Space ◽  
Integral Representations ◽  
Axially Symmetric ◽  
Stress Singularities ◽  
Rigid Cylinder ◽  
Perfect Bonding

A study is made of the axially symmetric torsion of a rigid cylinder partially embedded into a layered elastic half space. The problem is formulated on the basis of perfect bonding between the cylinder and the surrounding material. Integral representations are used to reduce the problem to the solution of two integral equations. Stress singularities of fractional order are obtained along the perimeter of the base of the cylinder. A numerical solution of the integral equations is used to obtain the torque-twist relationship for different embedment depths and for different values of the elastic constants.

scholarly journals Solving Integral Representations Problems for the Stationary Schrödinger Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Yudong Ren
Keyword(s):  
Schrödinger Equation ◽  
Half Space ◽  
Harmonic Functions ◽  
Schrodinger Equation ◽  
Integral Representations ◽  
Representation Theorems ◽  
Stationary Schrödinger Equation

When solutions of the stationary Schrödinger equation in a half-space belong to the weighted Lebesgue classes, we give integral representations of them, which imply known representation theorems of classical harmonic functions in a half-space.

Appraisal of near-field solutions for a Hertzian dipole over a conducting half-space

1970 ◽  
Vol 48 (6) ◽  
pp. 737-743 ◽  
Author(s):  
David C. Chang ◽  
James R. Wait
Keyword(s):  
Half Space ◽  
Significant Influence ◽  
Input Impedance ◽  
Integral Formula ◽  
Near Field ◽  
Integral Representations ◽  
Numerical Comparisons ◽  
Formal Integral ◽  
Approximate Form

Various approximations to the exact formal integral representations of the near-field and the impedance are considered. A new approximate form is obtained which appears to be valid even when the dipole is near a poorly conducting earth. Numerical comparisons with the exact integral formula verify some of the conjectures. The result shows that the ground has a significant influence on the input impedance of the dipole, particularly for low heights.

An algorithm for computation of resistivity soundings over inhomogeneous layers

Geophysics ◽  
1985 ◽  
Vol 50 (7) ◽  
pp. 1166-1172 ◽  
Author(s):  
S. P. Dasgupta
Keyword(s):  
Half Space ◽  
Kernel Function ◽  
Transition Layer ◽  
Recurrence Relations ◽  
The Other ◽  
Dc Resistivity ◽  
Resistivity Sounding ◽  
Transition Layers ◽  
Homogeneous Form ◽  
Layered Half Space

Calculation of dc resistivity sounding curves for a multilayer earth with transition layers has been treated by several authors since Mallick and Roy (1968). However, derivation of the kernel function for such problems has remained difficult for more than three‐layer models for want of a proper algorithm. The problem was first solved by Pekeris (1942) in the case of uniformly resistive layers. Other forms of recurrence relations for the kernel function of a half‐space containing such homogeneous layers were forwarded by Flathe (1955), Kunetz (1966), and Koefoed (1968). Patella (1977) considered the kernel function for a half‐space which contained a series of alternate layers, one having a linearly varying conductivity with depth while the other was homogeneously conductive. Koefoed (1979a) considered the case of a half‐space containing a transition layer situated anywhere among a series of homogeneous layers and possessing a resistivity that changed linearly with depth. In this article a very general form of algorithm is developed for generating the kernel function for a layered half‐space containing any number of transition layers having an arbitrary resistivity distribution [Formula: see text] in such ith layer. This new general form is very similar to the homogeneous form derived by Pekeris (1942).

Vibration Cosine Solutions of Free Orthotropic Rectangular Plates on the Elastic Half-Space

2011 ◽  
Vol 291-294 ◽  
pp. 2094-2097
Author(s):  
Chun Ling Wang ◽  
Huan Ding ◽  
Hai Xia Zhang
Keyword(s):  
General Solution ◽  
Rectangular Plate ◽  
Half Space ◽  
Analytic Solutions ◽  
Elastic Half Space ◽  
Integral Representations ◽  
Rectangular Plates ◽  
Practical Applications ◽  
Cosine Series ◽  
Orthotropic Rectangular Plate

In this paper, the analytic solutions of steady vibration of free orthotropic rectangular plate loaded with vertical steady loading on the elastic half-space was given by combining the general solution of double trigonometrically cosine series with supplementary terms with dynamic integral representations for displacements of the elastic half-space loaded with arbitrary vertical steady loading. This solution not only is four-order derivative, but also has less undetermined coefficients. It can be used to solve the problems of bending and steady vibration of orthotropic rectangular plates on the elastic half-space without be classified and be superimposed. This causes this kind of things, bending and steady vibration of orthotropic rectangular plates with four free edges on the elastic half-space, unionization, simplification and systematization. When the material is isotropic, the solutions are turned into analytic solutions of steady vibration of free rectangular plate on the elastic half-space. At last some computational examples are presented and the results are coincided with those in literatures. Then the method in this paper will be of important practical applications.

scholarly journals Composition Formulas of Bessel-Struve Kernel Function

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
K. S. Nisar ◽  
S. R. Mondal ◽  
P. Agarwal
Keyword(s):  
Fractional Calculus ◽  
Kernel Function ◽  
Exponential Function ◽  
Integral Representations ◽  
Generalized Fractional Calculus ◽  
Fractional Calculus Operators ◽  
Generalized Fractional Calculus Operators

The object of this paper is to study and develop the generalized fractional calculus operators involving Appell’s functionF3(·)due to Marichev-Saigo-Maeda. Here, we establish the generalized fractional calculus formulas involving Bessel-Struve kernel functionSαλz,  λ,z∈Cto obtain the results in terms of generalized Wright functions. The representations of Bessel-Struve kernel function in terms of exponential function and its relation with Bessel and Struve function are also discussed. The pathway integral representations of Bessel-Struve kernel function are also given in this study.

Numerical Analysis of the Age-Sex-Structured Population Dynamics Taking into Account Spatial Diffusion

2005 ◽  
Vol 10 (4) ◽  
pp. 365-381 ◽  
Author(s):  
Š. Repšys ◽  
V. Skakauskas
Keyword(s):  
Population Dynamics ◽  
Numerical Analysis ◽  
Population Model ◽  
Local Stability ◽  
Deterministic Model ◽  
Random Mating ◽  
Spatial Diffusion ◽  
Neumann Problems ◽  
Structured Population ◽  
Structured Population Dynamics

We present results of the numerical investigation of the homogenous Dirichlet and Neumann problems to an age-sex-structured population dynamics deterministic model taking into account random mating, female’s pregnancy, and spatial diffusion. We prove the existence of separable solutions to the non-dispersing population model and, by using the numerical experiment, corroborate their local stability.

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