SIAM Journal on Scientific and Statistical Computing
Fast adaptive methods for the free-space heat equation
SIAM Journal on Scientific Computing
Computing rank-revealing QR factorizations of dense matrices
ACM Transactions on Mathematical Software (TOMS)
Fast evaluation of three-dimensional transient wave fields using diagonal translation operators
Journal of Computational Physics
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
A fast adaptive multipole algorithm in three dimensions
Journal of Computational Physics
Fast evaluation of two-dimensional transient wave fields
Journal of Computational Physics
IES3: Efficient Electrostatic and Electromagnetic Simulation
IEEE Computational Science & Engineering
A fast method for solving the heat equation by layer potentials
Journal of Computational Physics
On the numerical solution of the heat equation I: Fast solvers in free space
Journal of Computational Physics
Journal of Computational Physics
Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications
Numerical Simulation in Molecular Dynamics: Numerics, Algorithms, Parallelization, Applications
A Cartesian non-uniform grid interpolation method for fast field evaluation on elongated domains
International Journal of Numerical Modelling: Electronic Networks, Devices and Fields
Hi-index | 31.45 |
Diffusion, lossy wave, and Klein-Gordon equations find numerous applications in practical problems across a range of diverse disciplines. The temporal dependence of all three Green's functions are characterized by an infinite tail. This implies that the cost complexity of the spatio-temporal convolutions, associated with evaluating the potentials, scales as ON"s^2N"t^2, where N"s and N"t are the number of spatial and temporal degrees of freedom, respectively. In this paper, we discuss two new methods to rapidly evaluate these spatio-temporal convolutions by exploiting their block-Toeplitz nature within the framework of accelerated Cartesian expansions (ACE). The first scheme identifies a convolution relation in time amongst ACE harmonics and the fast Fourier transform (FFT) is used for efficient evaluation of these convolutions. The second method exploits the rank deficiency of the ACE translation operators with respect to time and develops a recursive numerical compression scheme for the efficient representation and evaluation of temporal convolutions. It is shown that the cost of both methods scales as O(N"sN"tlog^2N"t). Several numerical results are presented for the diffusion equation to validate the accuracy and efficacy of the fast algorithms developed here.