Multilevel Plane Wave Time Domain Research Articles

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.

Multilevel plane wave time domain–based global boundary kernels for two‐dimensional finite difference time domain simulations

Time domain boundary integrals are used to impose global transparent boundary conditions in two‐dimensional finite difference time domain solvers. Augmenting classical methods for imposing these conditions with the multilevel plane wave time domain scheme reduces the computational cost of enforcing a global transparent boundary condition from O() to O(st log s log t); here s and t denote the number of equivalent source boundary nodes and their time samples used to integrate external fields, respectively. Numerical results demonstrate that for thin and concave material objects, plane wave time domain‐accelerated global transparent boundary kernels outperform perfectly matched layer‐based absorbing boundary schemes without loss of accuracy.

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 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.

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.

Acceleration of integral equation based transient analysis of acoustic scattering phenomena using the plane wave time domain algorithm

The numerical analysis of transient scattering from homogeneous bodies residing in an unbounded medium is often performed using integral equation (IE) based methods. The major advantages of these methods over differential equation based techniques are that (i) the radiation condition is implicitly imposed in the formulation, and that (ii) the number of spatial unknowns, Ns, scales as the surface area of the scatterer. However, IE techniques are notoriously costly as their computational complexity scales as O(N2s) per time step. This complexity can be reduced considerably by using the recently introduced plane wave time domain (PWTD) algorithm [A. A. Ergin et al., J. Comput. Phys. 146, 157–180 (1998)]. In this presentation, the PWTD algorithm will be briefly reviewed and its incorporation into an IE-based transient solver for analyzing scattering from rigid bodies will be elucidated. It will be shown that the computational cost of a transient analysis using two-level and multilevel PWTD enhanced solvers scales as O(Ns1.5<th>log<th>Ns) and O(Ns<th>log2<th>Ns) per time step, respectively. Numerical examples that validate these complexity estimates and demonstrate the efficacy of the proposed methods in analyzing scattering from realistic structures will be presented.

Fast Evaluation of Three-Dimensional Transient Wave Fields Using Diagonal Translation Operators

This paper presents novel plane wave time domain (PWTD) algorithms which accelerate the computational analysis of transient surface scattering phenomena. The proposed PWTD algorithms permit the fast evaluation of transient fields satisfying the wave equation. The cost associated with the computation of fields atNsobservers produced by a surface bound source density represented in terms ofNsspatial samples forNttime steps scales asO(NtN2s) if classical time domain integral-equation-based methods are used. It is shown that this cost can be reduced toO(NtN4/3slogNs) andO(NtNslogNs) using two-level and multilevel PWTD schemes, respectively. These algorithms are the time domain counterparts of frequency domain fast multipole methods and make feasible the practical broadband analysis of scattering from large and complex bodies.