Finite-difference Frequency-domain Scheme Research Articles

Finite-difference frequency-domain method with QR-decomposition-based complex-valued adaptive coefficients for 3D diffusive viscous wave modelling

Abstract The diffusive viscous (DV) model is a useful tool for interpreting low-frequency seismic attenuation and the influence of fluid saturation on frequency-dependent reflections. Among present methods for the numerical solution of the corresponding DV wave equation, the finite-difference frequency-domain (FDFD) method with complex-valued adaptive coefficients (CVAC) has the advantage of efficiently suppressing both numerical dispersion and numerical attenuation. In this research, the FDFD method with CVAC is first generalized to a 3D DV equation. In addition, the current calculation of CVAC involves the numerical integration of propagation angles, conjugate gradient (CG) iterative optimization, and the sequential selection of initial values, which is difficult and inefficient for implementation. An improved method is developed for calculating CVAC, in which a complex-valued least-squares problem is constructed by substituting the 3D complex-valued plane-wave solutions into the FDFD scheme. The QR-decomposition method is used to efficiently solve the least-squares problem. Numerical dispersion and attenuation analyses reveal that the FDFD method with CVAC requires ∼2.5 spatial points in a wavelength within a dispersion deviation of 1% and an attenuation deviation of 10% for the 3D DV equation. An analytic solution for 3D DV wave equation in homogeneous media is proposed to verify the effectiveness of the proposed method. Numerical examples also demonstrate that the FDFD method with CVAC can obtain accurate wavefield modelling results for 3D DV models with a limited number of spatial points in a wavelength, and the FDFD method with QR-based CVAC requires less computational time than the FDFD method with CG-based CVAC.

Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers

Finite-Difference Frequency-Domain Scheme for Sound Scattering by a Vortex with Perfectly Matched Layers

Trapezoid-grid finite difference frequency domain method for seismic wave simulation

Abstract The large computational cost and memory requirement for the finite difference frequency domain (FDFD) method limit its applications in seismic wave simulation, especially for large models. For conventional FDFD methods, the discretisation based on minimum model velocity leads to oversampling in high-velocity regions. To reduce the oversampling of the conventional FDFD method, we propose a trapezoid-grid FDFD scheme to improve the efficiency of wave modeling. To alleviate the difficulty of processing irregular grids, we transform trapezoid grids in the Cartesian coordinate system to square grids in the trapezoid coordinate system. The regular grid sizes in the trapezoid coordinate system correspond to physical grid sizes increasing with depth, which is consistent with the increasing trend of seismic velocity. We derive the trapezoid coordinate system Helmholtz equation and the corresponding absorbing boundary condition, then get the FDFD stencil by combining the central difference method and the average-derivative method (ADM). Dispersion analysis indicates that our method can satisfy the requirement of maximum phase velocity error less than $1\%$ with appropriate parameters. Numerical tests on the Marmousi model show that, compared with the regular-grid ADM 9-point FDFD scheme, our method can achieve about $80\%$ computation efficiency improvement and $80\%$ memory reduction for comparable accuracy.

Linearized 3-D Electromagnetic Contrast Source Inversion and Its Applications to Half-Space Configurations

One of the main computational drawbacks in the application of 3-D iterative inversion techniques is the requirement of solving the field quantities for the updated contrast in every iteration. In this paper, the 3-D electromagnetic inverse scattering problem is put into a discretized finite-difference frequency-domain scheme and linearized into a cascade of two linear functionals. To deal with the nonuniqueness effectively, the joint structure of the contrast sources is exploited using a sum-of-l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> -norm optimization scheme. A cross-validation technique is used to check whether the optimization process is accurate enough. The total fields are, then, calculated and used to reconstruct the contrast by minimizing a cost functional defined as the sum of the data error and the state error. In this procedure, the total fields in the inversion domain are computed only once, while the quality and the accuracy of the obtained reconstructions are maintained. The novel method is applied to ground-penetrating radar imaging and through-the-wall imaging, in which the validity and the efficiency of the method are demonstrated.

A fourth-order accurate compact 2-D FDFD method for waveguide problems

In this work, a fourth-order accurate 2-D finite difference frequency domain method is proposed for the analysis of general waveguide structures. Finite difference techniques have been extensively used to solve electromagnetic problems over the decades. These methods discretize the computational domain using the Yee cell, but the standard Yee scheme used in these methods is only second-order accurate. In order to demonstrate the advantages of the proposed scheme compared to the multiresolution frequency domain method and the traditional 2-D finite difference frequency domain scheme, the dispersion characteristics of various waveguide structures are analyzed.

Efficient 2-D Finite-Difference Frequency-Domain Method for Switching Noise Analysis in Multilayer Boards

A new numerical algorithm is presented to solve the problem of switching noise in multilayer circuit boards and packages. The algorithm is based on domain decomposition using the finite-difference frequency-domain (FDFD) method. Each layer of the multilayer board or package is modeled using a standard 2-D FDFD scheme and linked to other layers through a multiport network that effectively incorporates the via circuit models between the layers. It is shown that the algorithm is simple to implement and is highly efficient for multilayer boards or packages as the overall FDFD system matrix is highly sparse, thus can be solved very efficiently using advanced sparse matrix solvers. Furthermore, successive solution of the system matrix for different source and victim locations does not call for new fill of the system matrix, thus allowing efficient analysis of different source and victim locations. To validate the new algorithm, we manufacture a three-layer board, measure the scattering parameters between two specific locations, and obtain strong agreement with the solution obtained using the FDFD scheme introduced here.

Design of generalized invisible scatterers

A nonlinear signal processing method is applied to the design of strongly scattering objects to realize a defined angular response. Investigated as the complement of inverse scattering problems, k-space design methods are combined with cepstral filtering to obtain a permittivity distribution that scatters with the desired response. Starting with the rigorously computed angular spectrum of the scattering amplitude of an object of simple geometric shape, the corresponding k-space is modified to provide the desired scattering behavior. In order to account for strong scattering, cepstral filtering is applied to map the associated distribution of secondary sources to a unique permittivity distribution. The inversion process results in a structure that exhibits the desired properties and which can be interpreted as a perturbation of the initial structure. Simulation results are presented which illustrate the usefulness of this method. In particular, objects are modified to enhance forward scattering and suppress scattering in all other direction. Results are verified using a rigorous finite-difference frequency-domain scheme to simulate scattering. The method is demonstrated as a novel means for designing invisible objects that act as electromagnetic cloaks.

THE MULTIRESOLUTION FREQUENCY DOMAIN METHOD FOR GENERAL GUIDED WAVE STRUCTURES

Abstract—A multiresolution frequency domain (MRFD) analysis similar to the finite difference frequency domain (FDFD) method is presented. This new method is derived by the application of MoM to frequency domain Maxwell’s equations while expanding the fields in terms of biorthogonal scaling functions. The dispersion characteristics of waveguiding structures are analyzed in order to demonstrate the advantages of this proposed MRFD method over the traditional FDFD scheme.

An FDFD eigenvalue formulation for computing port solutions in FDTD simulators

At the pre- and post-processing stages of a finite-difference time-domain (FDTD) simulation, important tasks are carried out that require knowledge of the port data (propagation constants, fields, impedances, and so on) of the problem structure. This paper introduces a 2D finite-difference frequency-domain (FDFD) eigenvalue formulation specifically tailored for the computation of port data to be used in conjunction with the 3D-FDTD method. A key feature of the proposed FDFD scheme is that it leads to the same numerical dispersion equation as that of the 3D-FDTD method. This means that, for a given frequency, the numerical propagation constants and mode patterns calculated by the two methods are identical. This is desirable for preserving the accuracy of the FDTD simulation. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 45: 1–3, 2005; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.20704