Related papers: Fast Computation of the Direct Scattering Transfor…
We present improved algorithms for fast calculation of the inverse square root for single-precision floating-point numbers. The algorithms are much more accurate than the famous fast inverse square root algorithm and have the same or…
The manuscript presents a new technique for computing the exponential of skew-Hermitian operators. Principal advantages of the proposed method include: stability even for large time-steps, the possibility to parallelize in time over many…
Standard explicit schemes for parabolic equations are not very convenient for computing practice due to the fact that they have strong restrictions on a time step. More promising explicit schemes are associated with explicit-implicit…
The derivation of combined prefactored compact schemes for first and second order derivatives is described here, relying on the Fourier analysis of the original prefactored compact schemes. By this approach, the order of accuracy of the…
In this work, in order to obtain higher-order schemes for solving forward backward stochastic differential equations, we adopt the high-order multi-step method in [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput., 36(4) (2014),…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
We show that the classical fourth order accurate compact finite difference scheme with high order strong stability preserving time discretizations for convection diffusion problems satisfies a weak monotonicity property, which implies that…
We describe an accelerated direct solver for the integral equations which model acoustic scattering from curved surfaces. Surfaces are specified via a collection of smooth parameterizations given on triangles, a setting which generalizes…
A fast algorithm (linear in the degrees of freedom) for the solution of linear variable-coefficient rational-order fractional integral and differential equations is described. The approach is related to the ultraspherical method for…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
In this work we present spectral algorithms for the numerical scattering for the defocusing Davey-Stewartson (DS) II equation with initial data having compact support on a disk, i.e., for the solution of d-bar problems. Our algorithms use…
In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of $O(N_{\text{iter.}}N\log…
Different ways of implementing dimension-by-dimension CWENO reconstruction are discussed and the most efficient method is applied to develop a fourth order central scheme for multi-dimensional hyperbolic problems. Fourth order accuracy and…
In this paper, a numerical method is proposed to calculate the eigenvalues of the Zakharov-Shabat system based on Chebyshev polynomials. A mapping in the form of tanh(ax) is constructed according to the asymptotic of the potential function…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
An integral equation based scheme is presented for the fast and accurate computation of effective conductivities of two-component checkerboard-like composites with complicated unit cells at very high contrast ratios. The scheme extends…
This work presents a fast direct solver strategy for electromagnetic integral equations in the high-frequency regime. The new scheme relies on a suitably preconditioned combined field formulation and results in a single skeleton form plus…
We explore the class of exponential integrators known as exponential time differencing (ETD) method in this letter to design low complexity nonlinear Fourier transform (NFT) algorithms that compute discrete approximations of the scattering…
We consider high-order splitting schemes for large-scale differential Riccati equations. Such equations arise in many different areas and are especially important within the field of optimal control. In the large-scale case, it is critical…
This paper presents a fast high-order method for the solution of two-dimensional problems of scattering by penetrable inhomogeneous media, with application to high-frequency configurations containing (possibly) discontinuous refractivities.…