Dual Boundary Research Articles

Holographic phonons by gauge-axion coupling

In this paper, we show that a simple generalization of the holographic axion model can realize spontaneous breaking of translational symmetry by considering a special gauge-axion higher derivative term. The finite real part and imaginary part of the stress tensor imply that the dual boundary system is a viscoelastic solid. By calculating quasi-normal modes and making a comparison with predictions from the elasticity theory, we verify the existence of phonons and pseudo-phonons, where the latter is realized by introducing a weak explicit breaking of translational symmetry, in the transverse channel. Finally, we discuss how the phonon dynamics affects the charge transport.

Seiberg-like dualities for orthogonal and symplectic 3d mathcal{N} = 2 gauge theories with boundaries

We propose dualities of mathcal{N} = (0, 2) supersymmetric boundary conditions for 3d mathcal{N} = 2 gauge theories with orthogonal and symplectic gauge groups. We show that the boundary ’t Hooft anomalies and half-indices perfectly match for each pair of the proposed dual boundary conditions.

Three-dimensional transient heat conduction problems in FGMs via IG-DRBEM

In this paper, the isogeometric dual reciprocity boundary element method (IG-DRBEM) is firstly applied to solve three-dimensional (3D) transient heat conduction problems in functionally graded materials (FGMs) with heat sources. Using the fundamental solution of the 3D potential problem, the integral equation of boundary-domain is established by the weighted residual method. The normalized temperature is introduced, and the domain integral is transformed into the boundary integral by the dual reciprocity method (DRM). Finally, the theoretical framework of the isogeometric BEM for FGMs problems is established. Furthermore, the effects of different approximation functions, time steps, element refinements and the distance from the inner point to the boundary on the results are discussed in detail via several examples, which verify the validity of the presented method. In order to promote the development of IGBEM, the program code of this article can be obtained by sending email to yubochina@hfut.edu.cn.

The effect of algorithm parameters on the number of iterations of the dual fat boundary method

The Dual Fat Boundary Method (DFBM) is an improvement of the Fat Boundary Method (FBM), which is proposed to solve elasticity problems defined on a perforated domain. The DFBM does not need an analytical solution in the holes, so it is suitable for any reasonable hole shapes and Dirichlet boundary conditions on the holes. However, as an iteration method, the relationship between iteration times and algorithmic parameters has not been studied. Here we give a numerical study by taking the perforated infinite plate problem as an example. It reveals that the relaxation parameters for two local domains should be equal to obtain the fastest convergence. Furthermore, the number of iterations for DFBM is smaller than FBM in the larger range of relaxation parameters despite of the decreasing range of convergence.

Holographic DC conductivity for backreacted NLED in massive gravity

In this work a holographic model with the charge current dual to a general non-linear electrodynamics (NLED) is discussed in the framework of massive gravity. Massive graviton can break the diffeomorphism invariance in the bulk and generates momentum dissipation in the dual boundary theory. The expression of DC conductivities in a finite magnetic field are obtained, with the backreaction of NLED field on the background geometry. General transport properties in various limits are presented, and then we turn to the three of specific NLED models: the conventional Maxwell electrodynamics, the Maxwell-Chern-Simons electrodynamics, and the Born-Infeld electrodynamics, to study the parameter-dependence of in-plane resistivities. Two mechanisms leading to the Mott-insulating behaviors and negative magneto-resistivities are revealed at zero temperature, and the role played by the massive gravity coupling parameters are discussed.

Quadrature method with exponential fitting for delay differential equations having Layer behavior

In this paper, we suggest a computational method for solving delay differential equations, with one end layer, dual layer and interior layer behavior using Gaussian quadrature. The problem is initially replaced with the analogous first order neutral type delay differential equation by taking the perturbation parameter within the differentiated term. For the numerical solution with boundary layer at one endpoint, dual boundary layers and internal boundary layers, the Gaussian two-point quadrature scheme was extracted with exponential fitting. Using model examples, the suggested approach is used for various perturbation and delay parameter values. The numerical scheme is validated and supported by the comparison of maximum errors with the other results in the literature. Convergence of the method is examined. For various delay parameter values, the layer structure is depicted in graphs.

IG-DRBEM of three-dimensional transient heat conduction problems

In this paper, the isogeometric dual reciprocity boundary element method (IG-DRBEM) is proposed to solve three-dimensional transient heat conduction problems. It is well known that the error of traditional BEM mainly comes from element dispersion, and the introduction of isogeometric ideas makes BEM become a veritable high-precision numerical method. At present, most of the problems solved by isogeometric BEM (IGBEM) are time-independent. The reason is similar to the traditional BEM, which cannot avoid solving domain integrals when solving time-dependent problems. In this paper, based on the potential fundamental solution the boundary-domain integral equation is obtained by the weighted residual method, where the classic dual reciprocity method is adopted to transform domain integrals into boundary integrals. Meanwhile, a two-level time integration scheme is used to solve the discretized differential equations. In addition, the adaptive integration scheme, the radial integral transform method and the power series expansion method are adopted to solve the boundary regular, nearly singular and singular integrals. Several classical numerical examples show that the presented method has good numerical stability and high precision by considering different factors such as the approximation function, the time step, the number of interior points and so on.

A Hybrid Shapeless Radial Basis Function Applied With the Dual Reciprocity Boundary Element Method

The so-called Dual Reciprocity Boundary Element Method (DRBEM) has been a popular alternative scheme designed to alleviate problems encountered when using the traditional BEM for numerically solving engineering problems that are described by PDEs. The method starts with writing the right-hand-side of Poisson equation as a summation of a pre-chosen multivariate function known as ‘Radial Basis Function (RBF)’. Nevertheless, a common undesirable feature of using RBFs is the appearance of the so-called ‘shape parameter’ whose value greatly affects the solution accuracy. In this work, a new form of RBF containing no shape (so that it can be called ‘shapefree/shapeless’) is invented, proposed and applied in conjunction with DRBEM is validated numerically. The solutions obtained are compared against both exact ones and those presented in literature where appropriate, for validation. It is found that reasonably and comparatively good approximated solutions of PDEs can still be obtained without the difficulty of choosing a good shape for RBF used.

Hydrodynamic analysis of a seaside quarter-circular breakwater with an array of porous cages using DBEM

ABSTRACT The gravity wave interaction with an array of porous cages in the presence of a seaside submerged quarter-circular porous breakwater (QCPBW) is analyzed within the framework of linearized water wave theory. A quadratic pressure drop is adopted for the wave past the porous structures to capture the effect of wave height on the energy dissipation. The boundary value problem is solved using the iterative Dual Boundary Element Method (DBEM). The numerical code is validated with known results in the literature. One or upto four units of submerged and bottom fixed porous cages are considered. The effect of porosity on QCPBW and porous cages are investigated pragmatically to study the scattering and wave forces. It is found that introducing a single porous cage with 10% porosity at the rear side of a QCPBW with a porosity of 25% can reduce the wave transmission coefficient by about 50% for relative water depth . Increasing the porosity of the single cage from 10% to 40% has a significant reduction on the horizontal and vertical force coefficients on the cage, whereas the change is insignificant on QCPBW. The horizontal wave force is three to four times higher when compared to the vertical wave force for both QCPBW as well as on the porous cage. For a system comprising four units of cages, both the horizontal and vertical wave forces on cage 1, 2, 3, and 4 reduce progressively (cage 2 is at the lee side of cage 1 and so on). The results of the present study can be used for the optimal design of open sea porous systems.

Performance of an U-Shaped Oscillating Water Column Wave Energy Converter Device under Oblique Incident Waves

The present study deals with the performance of an U-shaped oscillating water column device under the action of oblique incident waves. To solve the associated boundary value problem, the dual boundary element method (DBEM) is used. Various physical parameters associated with the U-shaped OWC device, such as the radiation susceptance and conductance coefficients, and the hydrodynamic efficiency, are analyzed for a wide range of wave and structural parameters. The study reveals that the resonance in the efficiency curve occurs for smaller values of wavenumber with an increase in chamber length, submergence depth of the front wall and opening duct, and width of the opening duct. It is observed that with appropriate combinations of the angle of incidence and incident wavenumber, more than 90% efficiency in the U-shaped OWC device can be achieved.

PENENTUAN JENIS FUNGSI BASIS RADIAL DALAM DUAL RECIPROCITY BOUNDARY ELEMENT METHOD

Problems involving modified Helmholtz equation are considered in this paper. To solve the problem numerically, dual reciprocity boundary element method (DRBEM) is employed. Some stage have been passed, using reciprocal relation to approximate boundary integral and domain integral in modified Helmholtz equation . Until, linear equation system are obtained in matrix form. MATLAB is used to calculate the solutions of Solutions of are compared between the exact solution and the numerical solution of modified Helmholtz equation. The numerical results are based on the using of three types of radial basis function to approximate domain integral, such as polinomial, poliharmonik spline and linear types. The solutions show that the polinomial and poliharmonik spline types are more stable and approach to exact solution than linear types.

A method for dynamic response of a multilayered pavement loaded by FWD

AbstractThe dynamic response of a viscoelastic multilayered pavement under falling weight deflectometer (FWD) loading is an attractive topic for the pavement engineers. Starting from the governing equations, the Laplace transform is first applied to suppress the time variable. The ordinary differential equations (ODE) of the governing equations in Laplace domain are derived by the cylindrical vector functions systems. On the basis of the facts that the top and bottom boundary conditions dual appear, a novel analytical method called dual variable and dual boundary (DVDB) for the ODE is proposed combined with dual variable and position method (DVP). The final solution in time domain is obtained by the inverse Laplace transform that is accelerated by Epsilon algorithm. The solutions of the thin layer issues and imperfect interface conditions are also investigated. Some numerical results from DVDB for the dynamic response of multilayered pavement loaded by FWD discrete pulse series are compared and discussed. It can be concluded that the DVDB combined with Laplace transform can efficiently solve the dynamic response of multilayered pavement in time domain. Furthermore, it can also be suited for some cases, such as material anisotropy properties, thin layers in the structure and interface conditions.

Time series dual boundary element model for P and SV waves propagation in half-space

This paper details the implementation of a new time-domain boundary element analysis for solving wave propagation problems inside the half-space. Initially, by developing a new set of half-plane fundamental solutions and implementing them into the dual reciprocity boundary element analysis (DRBEM), the discretization of the ground surface boundaries were eliminated. To convert DRBEM inertia domain integrals into the boundary integrals, a set of Fourier series was selected as the displacement field and required fundamental solutions were obtained. The series displacement field, then was implemented into the 2-dimensional elastodynamic equilibrium Equations and the time-dependent series coefficients were calculated using an algorithm called TSBEM (Time Series Boundary Element Method). The accuracy and efficiency of the presented method were tested compared to the available analytical solutions by modelling several examples. The Results showed that, the method can be sufficiently used for analyzing wave propagation and also any other dynamic problems.

On the evaluation of Poisson equation with dual interpolation boundary face method

This paper presents a new implementation of the dual reciprocity method (DRM) in connection with the dual interpolation boundary face method (DiBFM) for the Poisson equation. In DiBFM, the nodes of an element are categorized into two groups: (i) source nodes (ii) virtual nodes. First layer interpolation is used to interpolate the physical variables, while boundary integrals are evaluated on the source nodes only. Moreover, moving least squares (MLS) interpolation is used and provides additional constraints equations to establish the relationship between source and virtual nodes. Additionally, augmented thin plate spline (ATPS) is used to better interpolate the non-homogeneous term. Finally, it is claimed that the proposed method is much superior to the DRM for Poisson type equation with different geometries, especially for complex geometry. Numerical examples are evaluated and compared with the DRM to ensure the superiority of the proposed method.

Deterministic fatigue crack-growth simulations for a railway axle by Dual Boundary Element Method

The maintenance of railway axles requires an optimization of their inspection intervals in order to reduce costs. Such components can endure more than 30 years of service life and are subjected to scheduled Non Destructive Testing (NDT) inspections. It is therefore important to assess the influence of the severe in-service loads on the propagation of cracks in the axles. This manuscript reports deterministic fracture calculations, for the simulation of cracks propagating through a railway axle, by the Dual Boundary Element Method. Once Stress Intensity Factors along the crack front are obtained, the residual fatigue life estimates were calculated through a user made spreadsheet, taking into account the complex loading conditions of the axles. The presented results support the application of the crack propagation simulation for the determination of axle NDT intervals under different loading conditions.

Axisymmetric polyharmonic spline approximation in the dual reciprocity method

AbstractThe paper is devoted to developing the dual reciprocity boundary element method for axisymmetric problems based on usage of axisymmetric polyharmonic splines. The axisymmetric polyharmonic spline is introduced as a linear combination of polyharmonic radial basic functions and polynomial terms. The analytical expressions for proposed axisymmetric polyharmonic radial basic functions are obtained for splines with arbitrary degrees. These expressions include special elliptic integrals that are analyzed and calculated for the first time. The relationships between radial basic functions with positive and negative degree numbers are obtained that allows us to receive the recurrence formulae for specific elliptic integrals with nearest indexes. It reveals the possibility of calculating radial basic functions with arbitrary orders by using the combination of only the first two members in recursive sequence. Implementation of the Gauss well‐known arithmetic‐geometric mean technique provides calculation of the specific elliptic integrals and axisymmetric polyharmonic splines with any given accuracy. Numerical examples for solving two axisymmetric problems in potential theory using the proposed dual reciprocity boundary element method demonstrate high calculation accuracy with low computational costs.

Investigation on behaviors of acoustoelastic cavities using a novel reduced finite element–dual reciprocity boundary element formulation

This paper presents the acoustic and structure characteristics of chambers with elastic/rigid baffles and elastic walls using a novel formulation. The acoustic fluid is assumed to be compressible and inviscid, and the effect of mean flow is neglected. The acoustic field is formulated based on the dual reciprocity boundary element method (DRBEM), and the finite element method (FEM) is used to model the structural dynamics of elastic walls. The reduced-order model (ROM) of the coupled system is derived based on modal analysis of the acoustic field with rigid boundaries and the structure in a vacuum. Numerical examples are presented, and the acoustic modes and frequencies of the chambers are determined by analysis of eigenvalues of the coupled governing equations. The accuracy of the introduced model, which is based on the reduced-order DRBEM-FEM formulation, is examined by comparing the results with analytical and numerical predictions reported in the literature, and good agreements are achieved. Besides, the effects of baffles are studied for different configurations and the elasticity of a wall in a combustion chamber is investigated.

宽边界法参数分析以及基于双宽边界法的插值方法

宽边界法参数分析以及基于双宽边界法的插值方法

Application of DRBEM for 2D sine-Gordon equation

This research paper introduces an application of dual reciprocity boundary element method (DRBEM) for the solution of sine-Gordon equation (SGE) in two-space dimension. Initially, the time derivatives are expanded using central difference schemes. After inserting the finite difference approximations into the governing equation, the pattern of the modified Helmholtz equation is obtained. The fundamental solution of modified Helmholtz equation is employed in the integral equation formulation. The inhomogeneous terms of the equation cause a domain integral in the integral equation formulation which leads to loss of advantage of the method. The DRBEM provides to transform the domain integral into the boundary integral by approximating the inhomogeneous term of the equation with thin plate spline (). First, code validation of the procedure is done using a test problem and then proposed method is applied for several cases involving line and ring solitons to display its capacity to treat the problem. Presented numerical results are observed to be in good agreement with other numerical results available in the literature.

Monte Carlo Simulation of Fractures Using Isogeometric Boundary Element Methods Based on POD-RBF

This paper presents a novel framework for stochastic analysis of linear elastic fracture problems. Monte Carlo simulation (MCs) is adopted to address the multi-dimensional uncertainties, whose computation cost is reduced by combination of Proper Orthogonal Decomposition (POD) and the Radial Basis Function (RBF). In order to avoid re-meshing and retain the geometric exactness, isogeometric boundary element method (IGABEM) is employed for simulation, in which the Non-Uniform Rational B-splines (NURBS) are employed for representing the crack surfaces and discretizing dual boundary integral equations. The stress intensity factors (SIFs) are extracted by M integral method. The numerical examples simulate several cracked structures with various uncertain parameters such as load effects, materials, geometric dimensions, and the results are verified by comparison with the analytical solutions.