Related papers: Numerical Methods for Fast Nonlinear Fourier Trans…
A novel class of high-order linearly implicit energy-preserving integrating factor Runge-Kutta methods are proposed for the nonlinear Schr\"odinger equation. Based on the idea of the scalar auxiliary variable approach, the original equation…
We develop continuous-stage Runge-Kutta methods based on weighted orthogonal polynomials in this paper. There are two main highlighted merits for developing such methods: Firstly, we do not need to study the tedious solution of…
Multiphysics systems are driven by multiple processes acting simultaneously, and their simulation leads to partitioned systems of differential equations. This paper studies the solution of partitioned systems of differential equations using…
We propose a family of integrators, Flow-Composed Implicit Runge-Kutta (FCIRK) methods, for perturbations of nonlinear ordinary differential equations, consisting of the composition of flows of the unperturbed part alternated with one step…
The Fast Fourier Transform (FFT) over a finite field $\mathbb{F}_q$ computes evaluations of a given polynomial of degree less than $n$ at a specifically chosen set of $n$ distinct evaluation points in $\mathbb{F}_q$. If $q$ or $q-1$ is a…
The Number Theoretic Transform (NTT) is an indispensable tool for computing efficient polynomial multiplications in post-quantum lattice-based cryptography. It has strong resemblance with the Fast Fourier Transform (FFT), which is the most…
In a previous paper, a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions. In this paper, we…
We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK) methods applied to systems of (non-necessarily Hamiltonian) ordinary differential equations by means of Newton-like iterations. We pay particular…
In order to solve continuous-time optimal control problems, direct methods transcribe the infinite-dimensional problem to a nonlinear program (NLP) using numerical integration methods. In cases where the integration error can be manipulated…
Complex dynamical networks appear in a wide range of physical, biological, and engineering systems. The coupling of subsystems with varying time scales often results in multirate behavior. During the simulation of highly integrated…
Although Fourier series approximation is ubiquitous in computational physics owing to the Fast Fourier Transform (FFT) algorithm, efficient techniques for the fast evaluation of a three-dimensional truncated Fourier series at a set of…
One of the main computational bottlenecks when working with kernel based learning is dealing with the large and typically dense kernel matrix. Techniques dealing with fast approximations of the matrix vector product for these kernel…
The convergence of a family of AMF-Runge-Kutta methods (in short AMF-RK) for the time integration of evolutionary Partial Differential Equations (PDEs) of Advection Diffusion Reaction type semi-discretized in space is considered. The…
We have shown previously that functionally fitted Runge-Kutta (FRK) methods can be studied using a convenient collocation framework. Here, we extend that framework to functionally fitted Runge-Kutta-Nystr\"om (FRKN) methods, shedding…
Parareal is a well-known parallel-in-time algorithm that combines a coarse and fine propagator within a parallel iteration. It allows for large-scale parallelism that leads to significantly reduced computational time compared to serial…
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier…
This work deals with two groups of spectral analysis results for matrices arising in fully implicit Runge-Kutta methods used for linear time-dependent partial differential equations. These were applied for different formulations of the same…
In this paper, we use multithreaded fast Fourier transforms provided in three highly optimized packages, FFTW-2.1.5, FFTW-3.3.7, and Intel MKL FFT, to present a novel model-based parallel computing technique as a very effective and portable…
The well-known discrete Fourier transform (DFT) can easily be generalized to arbitrary nodes in the spatial domain. The fast procedure for this generalization is referred to as nonequispaced fast Fourier transform (NFFT). Various…
In recent years there has been a renewed interest in finding fast algorithms to compute accurately the linear canonical transform (LCT) of a given function. This is driven by the large number of applications of the LCT in optics and signal…