Numerical Green Research Articles

Matrix-Based FDTD Parallel Algorithm for Big Areas and Its Applications to High-Speed Wireless Communications

A formulation of the finite-difference time-domain (FDTD) equations as a system of linear equations in matricial form is used to develop a novel parallel algorithm that solves the variables of a 2-D FDTD simulation using less memory than required by the common FDTD algorithm, at the cost of some increase in the number of operations. For the sake of speeding-up the simulation of urban channels for personal wireless communications, the geometry of those channels and its relation with a numerical Green's function is used to increase the speed of this algorithm. Simulations are carried out in order to propose a FDTD-based model of urban microcells and their delay profiles, and some comparisons against uniform theory of diffraction based models are discussed. Finally, propagation of time division multiple access and code division multiple access signals of high bit rate in those channels are simulated, and the results allows us to evaluate the effect of multipath interference in high speed wireless communications

A numerical Green's function BEM formulation for crack growth simulation

This paper presents a crack growth prediction analysis based on the numerical Green's function (NGF) procedure and on the minimum strain energy density criterion for crack extension, also known as S-criterion. In the NGF procedure, the hypersingular boundary integral equation is used to numerically obtain the Green's function which automatically includes the crack into the fundamental infinite medium. When solving a linear elastic fracture mechanisms (LEFM) problem, once the NGF is obtained, the classical boundary element method can be used to determine the external boundary unknowns and, consequently, the stress intensity factors needed to predict the direction and increment of crack growth. With the change in crack geometry, another numerical analysis is carried out without need to rebuilding the entire element discretization, since only the crack built in the NGF needs update. Numerical examples, contemplating crack extensions for two-dimensional LEFM problems, are presented to illustrate the procedure.

Accurate modeling of TE/TM propagation and losses of integrated optical polarizer

Photonic devices based on stacked multilayer waveguides are widely used in optical integrated architectures like polarizers, filters, photodetectors, laser, transducers for sensing applications, and microelectromechanical systems. In this paper, we present an accurate modeling of a waveguide polarizer based on an antiresonant reflecting optical waveguide (ARROW) structure utilizing birefringence form. The ARROW polarizer is the case of a structure with severe "aspect-ratio" that most of numerical technique cannot handle. The electromagnetic analysis is performed by means of a transmission-line matrix integral-equation (TLMIE) method-based solver. TLMIE is a three-dimensional full-wave hybrid technique that combines the advantages of the numerical transmission-line matrix method in dense finite regions and those of the integral-equation method in homogeneous regions where analytical and/or numerical Green's functions are available. An accurate investigation of propagation/radiation properties of TE/TM modes is performed. Theoretical results of TE/TM losses are compared to measured data showing very good agreement. Starting from this validation, it seems possible to provide design criteria for the optimization of the polarizer.

Upper and lower bounds analysis of electric induction intensity factors for multiple piezoelectric cracks by the BEM

For piezoelectric cracks, the correct magnitudes of the electric induction intensity factors (EIFs) are obtained by the semi-permeable boundary condition (BC) the solution procedure of which is a non-linear iterative process that are not well established so far. We propose to use the impermeable and permeable BCs, although not correct, to obtain the upper and lower bounds of the EIFs using much simpler linear solution procedure by the boundary element method (BEM). We develop a numerical Green's function approach based on the whole crack singular element (WCSE) for the general piezoelectric solids in two-dimensions. It is used for the mixed mode boundary element analysis of multiple straight cracks for impermeable and permeable BCs. The crack opening displacement (COD) of a straight crack is represented by the continuous distribution of dislocation dipoles, with the built-in r COD behavior, which is integrated analytically to give the r COD and the 1 / r crack tip stress singularity. The proposed numerical Green's function approach does not require the post-processing for the accurate determination of the stress intensity factors (SIFs).

A numerical Green's function and dual reciprocity BEM method to solve elastodynamic crack problems

A computational model based on the numerical Green's function (NGF) and the dual reciprocity boundary element method (DR-BEM) is presented for the study of elastodynamic fracture mechanics problems. The numerical Green's function, corresponding to an embedded crack within the infinite medium, is introduced into a boundary element formulation, as the fundamental solution, to calculate the unknown external boundary displacements and tractions and in post-processing determine the crack opening displacements (COD). The domain inertial integral present in the elastodynamic equation is transformed into a boundary integral one by the use of the dual reciprocity technique. The dynamic stress intensity factors (SIF), computed through crack opening displacement values, are obtained for several numerical examples, indicating a good agreement with existing solutions.

A numerical Green's function for multiple cracks in anisotropic bodies

The numerical construction of a Green's function for multiple interacting planar cracks in an anisotropic elastic space is considered. The numerical Green's function can be used to obtain a special boundary-integral method for an important class of two-dimensional elastostatic problems involving planar cracks in an anisotropic body.

Numerical Green's Function of a Point Current Source in Horizontal Multilayer Soils by Utilizing the Vector Matrix Pencil Technique

Numerical Green's function approach is proposed to calculate Green's function of a point current source in an arbitrary horizontal multilayer soil. The coefficients of Green's function are straightforwardly sampled in an iterative way in terms of the simultaneous equation system satisfying the pertinent boundary value problem, then the closed-form expression of Green's function for multilayer soil can be given by the vector matrix pencil technology. The approach proposed could be practically applied in grounding problems in an arbitrarily layered soil without needing to derive the analytical expression of Green's function.

Capacitance extraction for multiconductor transmission lines in multilayered dielectric media using the numerical Green's function

AbstractAn effective and universal method for calculating capacitance matrix is presented in this paper. Calculations for extracting the capacitance of a multilayer medium are rather time consuming when traditional approaches are used. To accelerate the procedure, the concept of the numerical Green's function is proposed. A database is constructed using the technique of interpolation to acquire the elements of the matrix, and then the Method of Moments (MoM) is used to solve the integral equations. The effectiveness of the present method is justified by the results given in the literature. The present approach is particularly effective in synthetic problems. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 529–531, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20024

非定常温度履歴を利用した熱的境界条件同定の試み(一般セッション 伝熱解析及び理論 I)

A non-iterative approach based on adjoint formulation of conduction heat transfer is proposed to identify the thermal boundary conditions from a transient temperature history measured in a solid body. Using a numerical solution of the adjoint problem, which can be regarded as a numerical Green's function, the temperature at the measuring point can be evaluated under arbitrary thermal boundary conditions. As a result, we can inversely predict the thermal boundary conditions from the measured temperature history by assuming the step-wise profiles of thermal boundary conditions both in time and space.

Analysis of a Two-Scale, Locally Conservative Subgrid Upscaling for Elliptic Problems

We present a two-scale theoretical framework for approximating the solution of a second order elliptic problem. The elliptic coefficient is assumed to vary on a scale that can be resolved on a fine numerical grid, but limits on computational power require that computations be performed on a coarse grid. We consider the elliptic problem in mixed variational form over $W \times {\bf V} \subset L^2 \times H({\rm div})$. We base our scale expansion on local mass conservation over the coarse grid. It is used to define a direct sum decomposition of $W \times {\bf V}$ into coarse and subspaces $W_c \times {\bf V}_c$ and $\delta W \times \delta{\bf V}$ such that (1) $\nabla \cdot {\bf V}_c=W_c$ and $\nabla \cdot \delta{\bf V} = \delta W$, and (2) the space $\delta{\bf V}$ is locally supported over the coarse mesh. We then explicitly decompose the variational problem into coarse and subgrid scale problems. The subgrid problem gives a well-defined operator taking $W_c \times {\bf V}_c$ to $\delta W \times \delta{\bf V}$, which is localized in space, and it is used to upscale, that is, to remove the subgrid from the coarse-scale problem. Using standard mixed finite element spaces, two-scale mixed spaces are defined. A mixed approximation is defined, which can be viewed as a type of variational multiscale method or a residual-free bubble technique. A numerical Green's function approach is used to make the approximation to the subgrid operator efficient to compute. A mixed method $\pi$-operator is defined for the two-scale approximation spaces and used to show optimal order error estimates.

A general method for numerical Green's function in arbitrarily layered soils *

Abstract A straightforward approach is developed to calculate Green's function of a point current source in horizontal multi-layer soils. The sampling value of the coefficient of Green's function is obtained in an iterative way in terms of the equation group satisfying the pertinent boundary value problem. Further, the closed-form expression of multilayered soil Green's function can be given by the vector matrix pencil technology. The numerical results are in agreement with those by using other softwares. The approach proposed here is applicable to grounding problems with the structure of arbitrarily layered soil without needing the analytical expression of Green's function.

A general method for numerical Green's function in arbitrarily layered soils

A straightforward approach is developed to calculate Green's function of a point current source in horizontal multi-layer soils. The sampling value of the coefficient of Green's function is obtained in an iterative way in terms of the equation group satisfying the pertinent boundary value problem. Further, the closed-form expression of multilayered soil Green's function can be given by the vector matrix pencil technology. The numerical results are in agreement with those by using other softwares. The approach proposed here is applicable to grounding problems with the structure of arbitrarily layered soil without needing the analytical expression of Green's function.

An efficient multi‐layer planar 3D fracture growth algorithm using a fixed mesh approach

AbstractWe present a planar three‐dimensional (3D) fracture growth simulator, based on a displacement discontinuity (DD) method for multi‐layer elasticity problems. The method uses a fixed mesh approach, with rectangular panel elements to represent the planar fracture surface. Special fracture tip logic is included that allows a tip element to be partially fractured in the tip region. The fracture perimeter is modelled in a piece‐wise linear manner. The algorithm can model any number of interacting fractures that are restricted to lie on a single planar surface, located orthogonal to any number of parallel layers. The multiple layers are treated using a Fourier transform (FT) approach that provides a numerical Green's function for the DD scheme. The layers are assumed to be fully bonded together. Any fracture growth rule can be postulated for the algorithm. We demonstrate this approach on a number of test problems to verify its accuracy and efficiency, before showing some more general results. Copyright © 2001 John Wiley & Sons, Ltd.

Electromagnetic analysis of an antenna embedded in a composite environment

This paper addresses the problem of an antenna embedded in a hole dug in the ground. The composite medium configuration consists of a half-space dielectric (representing the Earth-air interface) containing a cylindrical hole filled with a different dielectric medium. The wire antenna resides within this hole, on the axis. The solution strategy is based on decomposing the problem into simpler subproblems, which are treated sequentially. First we calculate a numerical dyadic Green's function for the composite medium by solving an integral equation formulated over a background consisting of the unperturbed dielectric half space (for which the Green's functions are known in a spectral integral form). This integral equation is solved via the fictitious currents method, which is a special case of the method of moments. We then solve the integral equation for the antenna currents using this numerical Green's function and determine the input impedance and radiation pattern.

Experimental and Numerical Analysis of Soil Motions Caused by Free Vibrations of a Building Model

Effects of vibrating structure on the free-field motion are presented through a field experiment at the Euro-Seistest and a corresponding numerical simu- lation. Ground motion has been recorded by a dense temporary three-component (3C), two-dimensional (2D) seismic network installed at increasing distances from a model building forced into vibration by pull-out tests. The building is a five-story RC structure at a one-third scale, resting on the soil through surface square footing. A traction force, F0, applied at the building top and suddenly released forced it into vibrations. Two sequences of a pull-out test (POT) have been performed, each one made of two vibration tests in the two horizontal directions of the building (longi- tudinal and transverse). The experimental data are then compared to the results of the numerical simulation. The soil-structure system is modeled by a three degree of freedom (3DOF) system. The soil-structure interaction (SSI) is accounted for through the help of impedance functions, and the motion induced by POT are estimated together with the base force and moment developed at the soil-structure interface. By representing the base forces by surface point seismic sources, the induced wavefield radiated in the surrounding free field is then computed by numerical Green's functions. The results presented here do validate the numerical computation method, which gave distant motions in close relation with the experimental data, from a qualitative and quantitative point of view. The spectral analysis does also exhibit surface waves trapped in the topmost layer. Results confirm the significant contamination of ground motion due to building vibration.

General Application of Numerical Green's Functions for SIF Computations With Boundary Elements

General Application of Numerical Green's Functions for SIF Computations With Boundary Elements

Green's function: a numerical generation for fracture mechanics problems via boundary elements

The paper discusses the application of the hyper-singular boundary integral equation to obtain Green's function solution to general geometry fracture mechanics problems, such as curved multifracture crack simulation, static and harmonic (extended to transient dynamic through inverse numerical transforms), in 2D and 3D. The numerical Green's function (NGF) can be implemented into a boundary element computer program, as the fundamental solution, to produce an accurate and efficient boundary element procedure. The complete formulation is presented in a unified manner, generalizing previous problem oriented procedures proposed by the authors. The results to some typical linear fracture mechanics problems are presented.

The 3-D BEM implementation of a numerical Green's function for fracture mechanics applications

The use of Green's functions has been considered a powerful technique in the solution of fracture mechanics problems by the boundary element method (BEM). Closed-form expressions for Green's function components, however, have only been available for few simple 2-D crack geometry applications and require complex variable theory. The present authors have recently introduced an alternative numerical procedure to compute the Green's function components that produced BEM results for 2-D general geometry multiple crack problems, including static and dynamic applications. This technique is not restricted to 2-D problems and the computational aspects of the 3-D implementation of the numerical Green's function approach are now discussed, including examples. Copyright © 2000 John Wiley & Sons, Ltd.

Positrons from particle dark-matter annihilation in the Galactic halo: Propagation Green’s functions

We calculate the propagation of positrons from dark-matter particle annihilation in the Galactic halo in different models of the dark matter halo distribution using our three-dimensional code, and present fits to our numerical propagation Green's functions. We show that the Green's functions are not very sensitive to the dark matter distribution for the same local dark matter energy density. We compare our predictions with the computed cosmic ray positron spectra (``background'') for the ``conventional'' cosmic ray nucleon spectrum which matches the local measurements, and a modified spectrum which respects the limits imposed by measurements of diffuse Galactic $\ensuremath{\gamma}$ rays, antiprotons, and positrons. We conclude that significant detection of a dark matter signal requires favorable conditions and precise measurements unless the dark matter is clumpy which would produce a stronger signal. Although our conclusion qualitatively agrees with those of previous authors, it is based on a more realistic model of particle propagation and thus reduces the scope for future speculations. A reliable background evaluation requires new accurate positron measurements and further developments in modeling production and propagation of cosmic ray species in the Galaxy.

A hyper-singular numerical Green's function generation for BEM applied to dynamic SIF problems

This paper introduces the extension of the numerical Green's function approach for elastodynamic fracture mechanics problems. The formulation uses the hyper-singular boundary integral equation to obtain the fundamental solution for the cracked unbounded medium. The procedure is general and can be applied to multiple crack problems of general geometry. Applications to time harmonic and transient (through inverse numerical Fourier and Laplace transforms) stress intensity factor (SIF) computations are presented and compared with other numerical and analytical results, showing the good accuracy of the present strategy for these kinds of problems.