Time domain Green function technique for a point source over a dissipative stratified half‐space

We consider two types of inverse boundary problems related to the Laplace equation in planar double connected domains. The first one consists in the determining the Cauchy data on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the function (or the normal derivative) is known and, additionally, on a portion of this exterior boundary the normal derivative (or the function) is also given. For this linear inverse problem we propose a direct boundary integral approach in combination with Tikhonov regularization for stable determination of the Cauchy data on the inclusion. To determine these quantities on the inclusion, boundary integral equations are derived using Green's functions. We outline an effective way of discretizing these boundary integral equations based on the Nystrom method and trigonomtric approximations. The second set of inverse problems is the reconstruction of the interior curve from the given Cauchy data of a harmonic function on the exterior boundary. With the help of Green's function and potential theory this non-linear boundary problem is reduced to the system of non-linear boundary integral equations. We develop three iterative algorithms for its numerical solution. Full discretization of the linearized systems is realized by a trigonometric quadrature method. Due to the inherited ill-possedness in the obtained system of linear equations we apply the Tikhonov regularization. Numerical results show that the proposed approach gives good accuracy of reconstructions with economical computational cost.

In this paper, we propose a simple two-dimensional (2D) analytical threshold voltage model for deep-submicrometre fully depleted SOI MOSFETs using the three-zone Green's function technique to solve the 2D Poisson equation and adopting a new concept of the average electric field to avoid iterations in solving the position of the minimum surface potential. Firstly, we obtain the 2D potential distribution in the Si-film region by using the Green's function technique to solve the 2D Poisson equation. Then, by applying Gauss's law at the Si–SiO2 interface, the initial expression of the threshold voltage is obtained. Eventually, we introduce a modified factor to compensate for the errors resulting from the charge-sharing effect in the derivations of the final threshold voltage model. The proposed model is validated against the results obtained by 2D numerical analysis and experimental data, and excellent agreements are obtained. The proposed model has an explicit expression and can be implemented into the circuit simulator.

In the use of the time-domain integral equation (TDIE) method for the analysis of layered media, it is important to have the time-domain layered medium Green's function computed for many source-to-field distances /spl rho/ and time instants t. In this paper, a numerical method is used that computes the mixed potential Green's functions G/sub v/(/spl rho/,t) and G/sub A/(/spl rho/,t) for a multilayered medium for many /spl rho/'s and t's simultaneously. The method is applicable to multilayered media and for lossless or lossy dispersive media. Salient features of the method are: 1) the use of complex /spl omega/ so that the surface wave poles are lifted off the real k/sub /spl rho// axis such that pole extractions are not required; 2) the use of half-space extraction so that the integrand for the Sommerfeld integral decays exponentially along the k/sub /spl rho// axis to obtain fast convergence of the integral; and 3) the use of the fast Hankel transform so that the Green's function is calculated for many values of /spl rho/ simultaneously. For a four-layer medium, we illustrate the numerical results by a three-dimensional plot of /spl rho/G/sub v/(/spl rho/,t) versus /spl rho/ and t and demonstrate the space-time evolution of these Green's functions. For a maximum frequency range of 8 GHz, the method requires only a few CPU minutes to compute a table of 100 (points in /spl rho/) /spl times/ 168 (points in t) uniformly spaced values of G/sub v/(/spl rho/,t) on an 867-MHz Pentium PC.

Geophysical Inverse Theory and Regularization Problems

Inverse scattering for the homogeneous dispersive anisotropic slab using transient electromagnetic fields

Ferrite circulator operation is analyzed here by two techniques. The first employs a two-dimensional (2-D) finite-element (FE) technique, using a publicly available FE package. We show how to adapt this code to the solution of the magnetostatic equations and solve for the distribution of internal magnetic field inside a round ferrite puck of finite thickness, and use it to verify existing approximations for the demagnetizing fields. Additionally, the 2-D FE method has also been used to calculate the RF fields and scattering parameters in circulators having noncircular shapes, as well as nonuniform material properties and bias conditions. We have also investigated the field solutions for round circulators, calculated using a recursive Green's function (RGF) technique. This technique allows for radially varying properties in the material or bias fields, and thus accommodates the nonuniform demagnetizing field distribution in finite pucks. A comparison of the results of this technique with experiment is made. We show how the impedance-matching structures attached to the circulator affect the field distributions inside, and present plots of the field distributions as a function of frequency, which provide insight into circulator operation.

We address the subtle problem of formulating mesoscopic transport phenomena in the language of many-body physics. We propose a microscopic description in which the whole system (sample, leads, and detectors) is given fully-quantum-mechanical treatments. The dynamics of the system is obtained from the projection, or memory-function, formalism of nonequilibrium statistical mechanics combined with recent prescriptions for measurements that are extended in the time domain. The associated irreversible quantum dynamics contains an intrinsic doubling of the degrees of freedom identical to the real-time path-integral representation of the Keldysh formalism. We derive a simple formula relating the generating function of the charge-counting statistics to the single-particle matrix Green's function of the interacting system, thereby generalizing the Levitov-Lesovik functional determinant formula. We report an interesting sample-leads duality in our description, which has a simple interpretation in the regime of noninteracting particles, thus establishing the equivalence between the Green's-function technique and the random scattering-matrix approach. We discuss the physical conditions, within the present scheme, for the validity of the Landauer-Buttiker description of mesoscopic transport. We conclude by providing an exact solution for the problem of charge transfer into a noninteracting ballistic cavity in the presence of a periodic time-dependent voltage, using the supersymmetry method.

A rigorous analysis of surface acoustic wave tags for wireless identification (ID) systems is developed based on Green's function technique and method of moments. The SAW ID-tags can be fabricated using arbitrary finite reflector structures placed in multiple tracks and channels. From the Green's function solutions, the P matrix parameters for the reflector bits and coupling transducer are deduced. These P matrices are cascaded and interconnected using network analysis to account for the resulting quasi-2D structure. To provide more physical insights into the scattering mechanism, the cascaded network is described in terms of the more illuminating global reflection and transmission coefficients. Simulation of prototype SAW tag configuration is carried out. Response in time domain is presented to show the spurious signals due to multiple reflections.

i Displacements of Love waves generated by a two-dimensional point source in a layered medium have been studied earlier by Sezawa & Sato by the method of successive reflections at the boundaries. In this paper the same problem has been worked out by using Green's function. The paper deals with the study of attenuation of Love waves of low periods in the coastal region. Experimental observations show that Love waves of smaller periods can be obtained only in the island observing stations. A slight intervention of the continental boundary is sufficient to attenuate lower period Love waves giving a hint thereby that attenuation of lower periods takes place perhaps at the continental margin. Taking a simplified configuration for the continental boundary and using Green's function technique, the displacement of Love waves due to a point source has been obtained and it has been shown that attenuation of Love waves of smaller periods takes place in the continental margin due to the slope of the boundary.

We have proposed a numerical scheme for the non-Born–Oppenheimer density functional calculation based upon the Green function techniques within the GW approximation for evaluating quasiparticle excitations of the electronic and nuclear motion in the full quantum mechanical treatment. We calculate the excitation energy and the orbital energy of a hydrogen molecule, a muon molecule, and a positronium–hydrogen complex within the treatment of the dynamical screening. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem 84: 354–362, 2001

In some applications, it is reasonable to assume that geodesics (rays) have a consistent orientation so that Maxwell's equations may be viewed as an evolution equation in one of the spatial directions. With such applications in mind, we propose a new Eulerian geometrical-optics method, dubbed the fast Huygens sweeping method, for computing Green's functions of Maxwell's equations in inhomogeneous media in the high-frequency regime and in the presence of caustics. The first novelty of the fast Huygens sweeping method is that a new dyadic-tensor-type geometrical-optics ansatz is proposed for Green's functions which is able to utilize some unique features of Maxwell's equations. The second novelty is that the Huygens--Kirchhoff secondary source principle is used to integrate many locally valid asymptotic solutions to yield a globally valid asymptotic solution so that caustics associated with the usual geometrical-optics ansatz can be treated automatically. The third novelty is that a butterfly algorithm is adapted to carry out the matrix-vector products induced by the Huygens--Kirchhoff integration in $O(N\log N)$ operations, where $N$ is the total number of mesh points, and the proportionality constant depends on the desired accuracy and is independent of the frequency parameter. To reduce the storage of the resulting traveltime and amplitude tables, we compress each table into a linear combination of tensor-product based multivariate Chebyshev polynomials so that the information of each table is encoded into a small number of Chebyshev coefficients. The new method enjoys the following desired features: (1) it precomputes a set of local traveltime and amplitude tables; (2) it automatically takes care of caustics; (3) it constructs Green's functions of Maxwell's equations for arbitrary frequencies and for many point sources; (4) for a specified number of points per wavelength it constructs each Green's function in nearly optimal complexity $O(N\log N)$ in terms of the total number of mesh points $N$, where the prefactor of the complexity depends only on the specified accuracy and is independent of the frequency parameter. Three-dimensional numerical experiments are presented to demonstrate the performance and accuracy of the new method.

A scalar Green's-function technique is used to derive coupled-amplitude equations for electromagnetic waves propagating in a three-dimensional structure with a radially varying refractive index. The vector nature of the problem is discussed and a method is outlined for reducing the vector wave equations to characteristic scalar equations. These scalar equations are then solved via an exact coupled-amplitude formalism, and closed-form solutions are compared with numerical results for the particular case of a spherical Bragg region. The derivation of the coupled-amplitude equations for vector spherical waves is a significant portion of the calculation, described in the companion paper [Sullivan and Hall, following paper, Phys. Rev. A 50, 2708 (1994)], of the radiative effects due to the presence of a spherical Bragg structure. Furthermore, the formulation is a powerful complement to previously developed Debye potential and transfer-matrix methods.

The resolvent Green's function technique of Marcuvitz (1951) is used to obtain a contour integral solution for the acoustic field due to a point source located in a vertically inhomogeneous ocean. The integrand of the contour integral is composed of the product of a depth-dependent Green's function and a range-dependent: Green's function. The contour must separate the singularities of the two Green's functions. Various representations are obtained by deforming the contour of the integration. The Fourier-Bessel integral representation is derived from the contour integral, and this derivation is compared with the work of Freehafer (1951), Brekhovskikh (1957), and Wait (1962). Evaluation of the various integral representations is accomplished by using Cauchy's residue theorem, stationary phase methods, and numerical integration techniques. The residue and stationary phase evaluations are then interpreted in terms of modes and rays.

A new type of Green function approach is introduced for time-domain scattering for a stratified dissipative slab. The new Green functions are defined as mappings from the transmitted field to the split fields (i.e., the right-moving and left-moving fields) at any point within the stratified slab. Unlike the usual Green functions, the present Green functions have compact support in the time variable. The new technique is illustrated for the case of normally incident electromagnetic waves on a stratified slab where the permittivity, permeability, and conductivity vary with the depth. The linear and homogeneous partial differential equations (PDEs) for these ‘‘compact Green functions’’ are derived. The PDEs together with the initial and boundary conditions are well suited for a numerical treatment. Numerical results for the compact Green functions are presented in the direct problem, while in the inverse problem the permittivity and conductivity (or the permeability and conductivity) are reconstructed simultaneously using the reflection and transmission data for the first round trip. The present method is useful and attractive for both the direct and inverse problems due to its simplicity, high speed, and high accuracy in numerical computations.

In this paper, a novel thermal analysis method for VLSI circuits based on the Green's function of heat conduction problem is proposed. With the method the temperature distribution can be very efficiently evaluated for the simulated chip via the proposed semi-analytical Green's function technique, by which the Green's function can be calculated online using the Green's function library obtained by inexpensive pre-characterization for the given chip structure. Experimental results validate the accuracy of the semi-analytical Green's function and demonstrate the efficiency of the thermal analysis method. Our thermal analysis approach can well adapt to the situation of thermal simulation for chips with multilayer heterogeneous heat conduction materials.