Plane Wave Time Domain Algorithm Research Articles

A Wavelet-Enhanced PWTD-Accelerated Time-Domain Integral Equation Solver for Analysis of Transient Scattering From Electrically Large Conducting Objects

A wavelet-enhanced plane-wave time-domain (PWTD) algorithm for efficiently and accurately solving time-domain surface integral equations (TD-SIEs) on electrically large conducting objects is presented. The proposed scheme reduces the memory requirement and computational cost of the PWTD algorithm by representing the PWTD ray data using local cosine wavelet bases (LCBs) and performing PWTD operations in the wavelet domain. The memory requirement and computational cost of the LCB-enhanced PWTD-accelerated TD-SIE solver, when applied to the analysis of transient scattering from smooth quasi-planar objects with near-normal incident pulses, scale nearly as $O(N_{s} \log N_{s})$ and $O(N_{s}^{1.5})$ , respectively. Here, $N_{s} $ denotes the number of spatial unknowns. The efficiency and accuracy of the proposed scheme are demonstrated through its applications to the analysis of transient scattering from a 185-wavelength long NASA almond and a 123-wavelength long Airbus A-320 model.

An efficient high order plane wave time domain algorithm for transient electromagnetic scattering analysis

An efficient high order plane wave time domain algorithm is presented for analyzing the transient scattering from three dimensional electrically large conducting objects. This method uses a set of hierarchical divergence-conforming vector basis functions to accurately represent the current distribution on the perfect electrically conducting (PEC) surface. The higher order functions can significantly reduce the number of unknowns without compromise on the accuracy. The time domain combined field integral equation (TD-CFIE) is then discretized using the hierarchical divergence-conforming vector basis functions and shifted Lagrange polynomial functions in spatial and time domain, respectively. The final matrix equation can be accelerated using the plane wave time domain (PWTD) algorithm. Finally, a parallel algorithm that can execute on a distributed-memory parallel cluster is developed, which provides an appealing avenue for analyzing the transient scattering from three-dimensional electrically large complex PEC objects. Numerical examples are given to demonstrate the accuracy and efficiency of the method.

A fast biem algorithm to evaluate seismic ground response in 2d elastic time domain

Since the topography and surface irregularities of the terrain have a significant effect on the seismic response of the earth's surface, the numerical analysis using boundary element method in elastodynamics, which leads to a significant increase in the number of DOF and stiffness matrix dimension, as well as the sparse and unsymmetrical structure of stiffness matrix, indicates the inefficiency of the conventional method. This paper presents a fast boundary element algorithm in seismic analysis of two-dimensional elastic media for the first time. In the proposed method, instead of the usual node-to-node, a method of cell-to-cell relation method is implemented by hierarchy tree structure. In addition, the Plane Wave Time Domain algorithm and the Iterative method has been used to solve a system of equations which increases the speed of network convergence, especially in high degrees of freedom that has not been used in the study of the seismic waves’ response yet. Nowadays, this new algorithm adopts for investigating the response wave fields of electrical, magnet [1], acoustic and thermal conductivity which are discussed in details in various articles and books.

Graphics Processing Unit Implementation of Multilevel Plane-Wave Time-Domain Algorithm

A graphics processing unit implementation of the multilevel plane-wave time-domain algorithm for rapidly evaluating transient electromagnetic fields generated by large-scale dipole constellations is proposed. The implementation achieves 50 × speedup and 60%-75% memory reduction compared to its serial CPU implementation.

An interpolation-based fast-multipole accelerated boundary integral equation method for the three-dimensional wave equation

A new fast multipole method (FMM) is proposed to accelerate the time-domain boundary integral equation method (TDBIEM) for the three-dimensional wave equation. The proposed algorithm is an enhancement of the interpolation-based FMM for the time-domain case, adopting the notion of the plane-wave time-domain algorithm. With the application being targeted at a low-frequency regime, the proposed time-domain interpolation-based FMM can reduce the computational complexity of the TDBIEM from O(Ns2Nt) to O(Ns1+δNt) (where δ=1/3 or 1/2) with the help of multilevel space–time hierarchy, where Ns and Nt are the spatial and temporal degrees of freedom, respectively. The computational accuracy and speed of the proposed accelerated TDBIEM are verified in comparison with those of the conventional (direct) TDBIEM via numerical experiments.

Fast evaluation of time domain fields in sub-wavelength source/observer distributions using accelerated Cartesian expansions (ACE)

Time domain integral equation solvers for transient scattering from electrically large objects have benefitted significantly from acceleration techniques like the plane wave time domain (PWTD) algorithm; these techniques reduce the asymptotic CPU and memory cost. However, PWTD breaks down when used in the analysis of structures that have subwavelength features or features whose length scales are orders of magnitude smaller than the smallest wavelength in the incident pulse. Instances of these occurring in electromagnetics range from antenna topologies, to feed structures, etc. In this regime, it is the geometric constraints that dictate the computational complexity, as opposed to the wavelength of interest. In this work, we present an approach for efficient analysis of such sub-wavelength source/observer distributions in time domain. The methodology that we seek to exploit is the recently developed algorithm based on Cartesian expansions for accelerating the computation of potentials of the form R^@n. In this paper, we present an efficient methodology for computing these polynomials for two different scenarios; where the size of the domain spans the distance travelled by light in (i) one time step and (ii) multiple time steps. These algorithms are cast within the framework of both uniform and non-uniform distributions. Results that demonstrate the efficiency and convergence of the proposed algorithm are presented.

Plane-wave time-domain accelerated radiation boundary kernels for FDTD analysis of 3-D electromagnetic phenomena

Truncating finite difference time domain meshes using exact radiation boundary conditions is computationally expensive. The computational bottleneck stems from the global nature of the resulting boundary update scheme, which calls for the evaluation of retarded-time boundary integrals at each time step. The classical evaluation of such integrals requires O(N/sub s//sup 2/) operations per time step where N/sub s/ is the number of spatial field sampling points on the boundary. Here, the plane wave time domain algorithm is used to evaluate retarded-time boundary integrals in O(N/sub s/log/sup 2/N/sub s/) operations per time step and thereby accelerate finite difference time domain solvers that impose exact radiation boundary conditions. The effectiveness of the resulting approach and its computational complexity are demonstrated through several numerical examples.

A fast time domain integral equation based scheme for analyzing scattering from dispersive objects

A fast integral equation-based scheme for analyzing transient scattering from inhomogeneous dispersive bodies is presented. A time domain integral equation in terms of the electric flux inside the body is constructed by invoking the volume equivalence principle, i.e., by equating the sum of the incident electric field and that radiated by equivalent volume polarization currents to the total electric field. The proposed algorithm for solving this time domain integral equation incorporates a recursive convolution scheme that updates the polarization current from knowledge of the electric flux. To reduce the computational cost and memory requirement of the resulting marching-on-in-time scheme, it is augmented with the plane wave time domain algorithm. Numerical results that validate the proposed approach and demonstrate its accuracy are presented.

Fast Time Domain Integral Equation Solvers for Analyzing Two-Dimensional Scattering Phenomena; Part II: Full PWTD Acceleration

The primary impediment to using marching-on-in-time (MOT) schemes for solving time domain integral equations pertinent to the analysis of large-scale two-dimensional (2D) transient electromagnetic scattering phenomena is their high computational complexity. If Ns and Nt are the number of spatial and temporal degrees of freedom in the analysis, then this computational complexity scales as O (Ns 2 Nt 2. Recently, it has been theoretically demonstrated that if classical MOT schemes are augmented with 2D plane wave time domain (PWTD) algorithms, their computational complexity can be reduced to O(NsNt log Nt). This article elucidates key steps in implementing such a scheme within the context of 2D transient TMz and TEz electromagnetic scattering analysis. Several numerical examples that demonstrate the efficacy of the proposed schemes and also confirm the aforementioned computational complexity are presented.

A fast BIEM for three-dimensional elastodynamics in time domain

A fast boundary integral equation method for three-dimensional (3D) elastodynamics in time domain is proposed. We discuss in detail the plane wave time domain (PWTD) algorithm in 3D elastodynamics, whose complexity is O(N s log 2N s N t ) or O( N s 3/2 N t), depending on the choice of the algorithms for the Legendre transform, where N s and N t are the spatial and temporal degrees of freedom, respectively. An O( N s 3/2 N t) implementation is made, whose efficiency is demonstrated in problems of the size of N s=O(10 4).

Fast analysis of transient electromagnetic scattering phenomena using the multilevel plane wave time domain algorithm

The computational complexity of classical marching-on-in-time (MOT) methods for solving time domain integral equations (TDIEs) pertinent to the analysis of transient scattering phenomena involving perfectly conducting targets grows as O(N/sub t/N/sub s//sup 2/) (N/sub t/ and N/sub s/ denote the number of temporal and spatial degrees of freedom (DOF) of the electric current on the target). This scaling law impedes the application of these schemes to the analysis of large-scale scattering phenomena. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient wave fields generated by temporally bandlimited sources and hence the acceleration of marching on in time based TDIE solvers. Previously, we described a two-level PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting targets; the computational complexity of this algorithm scales as O(N/sub t/N/sub s//sup 1.5/logN/sub s/). Here, a multilevel PWTD scheme for rapidly evaluating electric fields due to temporally bandlimited electric current sources is described. In addition, a multilevel PWTD enhanced TDIE solver for analyzing electromagnetic scattering from perfectly conducting scatterers using O(N/sub t/N/sub s/log/sup 2/N/sub s/) CPU resources is outlined. Last, the accuracy and CPU/memory efficiency of this solver are demonstrated by analyzing transient scattering from electrically large bodies.

A fast higher-order time-domain finite element-boundary integral method for 3-D electromagnetic scattering analysis

A novel hybrid time-domain finite element-boundary integral method for analyzing three-dimensional (3-D) electromagnetic scattering phenomena is presented. The method couples finite element and boundary integral field representations in a way that results in a sparse system matrix and solutions that are devoid of spurious modes. To accurately represent the unknown fields, the scheme employs higher-order vector basis functions defined on curvilinear tetrahedral elements. To handle problems involving electrically large objects, the multilevel plane-wave time-domain algorithm is used to accelerate the evaluation of the boundary integrals. Numerical results demonstrate the accuracy and versatility of the proposed scheme.

A two-level plane wave time-domain algorithm for fast analysis of EMC/EMI problems

A fast time-domain integral equation (TE)-based scheme for analyzing transient electromagnetic compatibility and interference (EMC/EMI) problems involving printed circuit boards and cables/connectors that reside in shielding enclosures, is presented. The proposed algorithm hybridizes a classical marching-on-in-time (MOT) solver for analyzing radiation from perfect electrically conducting (PEC) surface/wire geometries with the previously introduced two-level plane wave time-domain (PWTD) algorithm. The accuracy and efficacy of the resulting MOT-PWTD algorithm are validated via analysis of the radiation characteristics of a number of structures including a loaded motherboard that resides in a chassis. For a problem with N/sub s/ spatial and N/sub T/ temporal unknowns, the computational complexity of the two-level MOT-PWTD algorithm scales as O(N/sub T/N/sub S//sup 1.5/ log N/sub S/) as opposed to O(N/sub T/N/sub S//sup 2/) for a classical MOT scheme.

Errata to "analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm"

Errata to "analysis of transient electromagnetic scattering phenomena using a two-level plane wave time domain algorithm"

A fast time-domain finite element-boundary integral method for electromagnetic analysis

A time-domain, finite element-boundary integral (FE-BI) method is presented for analyzing electromagnetic (EM) scattering from two-dimensional (2-D) inhomogeneous objects. The scheme's finite-element component expands transverse fields in terms of a pair of orthogonal vector basis functions and is coupled to its boundary integral component in such a way that the resultant finite element mass matrix is diagonal, and more importantly, the method delivers solutions that are free of spurious modes. The boundary integrals are computed using the multilevel plane-wave time-domain algorithm to enable the simulation of large-scale scattering phenomena. Numerical results demonstrate the capabilities and accuracy of the proposed hybrid scheme.

Analysis of transient electromagnetic scattering from closed surfaces using a combined field integral equation

In the past, both the time-domain electric and magnetic field integral equations have been applied to the analysis of transient scattering from closed structures. Unfortunately, the solutions to both these equations are often corrupted by the presence of spurious interior cavity modes. In this article, a time-domain combined field integral equation is derived and shown to offer solutions devoid of any resonant components. It is anticipated that stable marching-on-in-time schemes for solving this combined field integral equation supplemented by fast transient evaluation schemes such as the plane wave time-domain algorithm will enable the analysis of scattering from electrically large closed bodies capable of supporting resonant modes.

Analysis of transient electromagnetic scattering phenomena using a two-level plane wave time-domain algorithm

A fast algorithm is presented for solving electric, magnetic, and combined field time-domain integral equations pertinent to the analysis of surface scattering phenomena. The proposed two-level plane wave time-domain (PWTD) algorithm permits a numerically rigorous reconstruction of transient near-fields from their far-field expansion and augments classical marching-on in-time (MOT) based solvers. The computational cost of analyzing surface scattering phenomena using PWTD-enhanced MOT schemes scales as O(N/sub i/N/sub s//sup 2/3/ log N/sub s/) as opposed to /spl Oscr/(N/sub t/N/sub s//sup 2/) for classical MOT methods, where N/sub t/ and N/sub s/ are the numbers of temporal and spatial basis functions discretizing the scatterer current. Numerical results that demonstrate the efficacy of the proposed solver in analyzing transient scattering from electrically large structures and that confirm the above complexity estimate are presented.

Fast analysis of transient acoustic wave scattering from rigid bodies using the multilevel plane wave time domain algorithm

The analysis of transient wave scattering from rigid bodies using integral equation-based techniques is computationally intensive: if carried out using classical schemes, the evaluation of the velocity potential on the surface of a three-dimensional scatterer, represented in terms of Ns spatial basis functions for Nt time steps, requires O(NtNs2) operations. The recently developed plane wave time domain (PWTD) algorithm permits the rapid evaluation of transient fields that are generated by bandlimited source distributions. It has been shown that incorporation of the PWTD algorithm into integral equation-based solvers in a two-level setting reduces the computational complexity of a transient analysis to O(NtNs1.5 logNs). In this paper, it is shown that casting the PWTD scheme into a multilevel framework permits the analysis of transient acoustic surface scattering phenomena in O(NtNslog2Ns) operations using O(NtNs) memory. Numerical examples that demonstrate the efficacy of the multilevel implementation are also presented.

Fast Evaluation of Two-Dimensional Transient Wave Fields

This paper presents a novel scheme to efficiently evaluate transient linear wave fields that are generated by two-dimensional (2D) source configurations. The scheme, termed the plane wave time domain algorithm (PWTD), realizes a diagonal translation operator for 2D transient wave fields through their representation in terms of Hilbert transformed plane wave expansions. Numerical results are presented that validate the algorithm and demonstrate its convergence properties. The proposed PWTD algorithm can be coupled to classical 2D time domain integral equation solvers in a two-level and multilevel setting. It is shown that analysis of a 2D surface scattering phenomenon, in which sources are represented in terms of Ns spatial and Nt temporal samples, based on two-level and multilevel PWTD augmented integral equation solvers, requires O(N1.5sNt log Nt) and O(NsNt log Ns log Nt) computational resources, respectively (as opposed to O(N2sNt2) for a classical solver). Therefore, these PWTD schemes render feasible the rapid integral equation based analysis of 2D transient scattering phenomena involving large surfaces.

Fast transient analysis of acoustic wave scattering from rigid bodies using a two-level plane wave time domain algorithm

It is well known that the computational cost associated with the application of classical time domain integral equation methods to the analysis of scattering from acoustical targets scales unfavorably with problem size. Indeed, performing a three-dimensional scattering analysis using these methods requires O(NtNs2) operations, where Ns denotes the number of basis functions that model the spatial field distribution over the surface of the scatterer and Nt is the number of time steps in the analysis. Recently, novel plane wave time domain algorithms that augment these classical methods and thereby reduce their high computational cost have been introduced. This paper describes such a plane wave time domain algorithm within the context of the analysis of acoustic scattering from rigid bodies and outlines its incorporation into a time domain integral equation solver in a two-level setting. It is shown that the resulting scheme has a computational complexity of O(NtNs1.5 log Ns). Examples comparing the accuracy and computational efficiency of the conventional and accelerated methods are presented. The proposed two-level scheme renders feasible the broadband analysis of scattering from large and complex bodies.