Related papers: An Algorithmic Framework for Efficient Large-Scale…
The integrating factor and exponential time differencing methods are implemented and tested for solving the time-dependent Kohn--Sham equations. Popular time propagation methods used in physics, as well as other robust numerical approaches,…
To analyze complex and heterogeneous real-time embedded systems, recent works have proposed interface techniques between real-time calculus (RTC) and timed automata (TA), in order to take advantage of the strengths of each technique for…
To analyze complex and heterogeneous real-time embedded systems, recent works have proposed interface techniques between real-time calculus (RTC) and timed automata (TA), in order to take advantage of the strengths of each technique for…
In this paper, we consider the application of exponential integrators to problems that are advection dominated, either on the entire or on a subset of the domain. In this context, we compare Leja and Krylov based methods to compute the…
This paper provides an algorithm for simulating improper (or noncircular) complex-valued stationary Gaussian processes. The technique utilizes recently developed methods for multivariate Gaussian processes from the circulant embedding…
To integrate large systems of nonlinear differential equations in time, we consider a variant of nonlinear waveform relaxation (also known as dynamic iteration or Picard-Lindel\"of iteration), where at each iteration a linear inhomogeneous…
An effective means for analyzing the impact of novel operating schemes on power systems is time domain simulation, for example for investigating optimization-based curtailment of renewables to alleviate voltage violations. Traditionally,…
This article deals with the numerical integration in time of nonlinear Schr\"odinger equations. The main application is the numerical simulation of rotating Bose-Einstein condensates. The authors perform a change of unknown so that the…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
We develop robust and scalable fully implicit nonlinear finite element solvers for the simulations of biological transportation networks driven by the gradient flow minimization of a non-convex energy cost functional. Our approach employs a…
Suitable discretizations through tensor product formulas of popular multidimensional operators (diffusion or diffusion--advection, for instance) lead to matrices with $d$-dimensional Kronecker sum structure. For evolutionary Partial…
An iterative coupling algorithm based on restricted additive Schwarz domain decomposition is investigated to co-simulate electrical circuits with hybrid electromagnetic (EMT) and transient stability (TS) modeled using dynamic phasors. This…
We propose a computationally efficient and systematically convergent approach for elastodynamics simulations. We recast the second-order dynamical equation of elastodynamics into an equivalent first-order system of coupled equations, so as…
Many real-world systems are governed by the time-dependent, nonlinear differential equations. Dynamics of an electrical system are also best described using the very equations. Being one of the preferred machines when using advanced control…
Splitting algorithms are well-established in convex optimization and are designed to solve large-scale problems. Using such algorithms to simulate the behavior of nonlinear circuit networks provides scalable methods for the simulation and…
Obreshkov-like numerical integrators have been widely applied to power system transient simulation. Misuse of the numerical integrators as numerical differentiators may lead to numerical oscillation or bias. Criteria for Obreshkov-like…
Exponential integrators are special time discretization methods where the traditional linear system solves used by implicit schemes are replaced with computing the action of matrix exponential-like functions on a vector. A very general…
The importance of simulating pinning arrays in superconducting samples for the increase of critical currents has been increasing in the last few years. Since the Time Dependent Ginzburg Landau (TDGL) can be more accurate than alternative…
The machine learning explosion has created a prominent trend in modern computer hardware towards low precision floating-point operations. In response, there have been growing efforts to use low and mixed precision in general scientific…
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector…