A fast algorithm for particle simulations
Journal of Computational Physics
A parallel hashed Oct-Tree N-body algorithm
Proceedings of the 1993 ACM/IEEE conference on Supercomputing
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Accelerating Fast Multipole Methods for the Helmholtz Equation at Low Frequencies
IEEE Computational Science & Engineering
Efficient fast multipole method for low-frequency scattering
Journal of Computational Physics
A wideband fast multipole method for the Helmholtz equation in three dimensions
Journal of Computational Physics
Fast evaluation of Helmholtz potential on graphics processing units (GPUs)
Journal of Computational Physics
A multilevel Cartesian non-uniform grid time domain algorithm
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.47 |
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.