Related papers: On parallel solution of ordinary differential equa…
Explicit integrating factor Runge-Kutta methods are attractive and popular in developing high-order maximum bound principle preserving time-stepping schemes for Allen-Cahn type gradient flows. However, they always suffer from the…
Using (a,b)-trees as an example, we show how to perform a parallel split with logarithmic latency and parallel join, bulk updates, intersection, union (or merge), and (symmetric) set difference with logarithmic latency and with information…
Parareal is a widely studied parallel-in-time method that can achieve meaningful speedup on certain problems. However, it is well known that the method typically performs poorly on non-diffusive equations. This paper analyzes linear…
In simulating physical systems, conservation of the total energy is often essential, especially when energy conversion between different forms of energy occurs frequently. Recently, a new fourth order energy-preserving integrator named MB4…
For many users of Satisfiability Modulo Theories (SMT) solvers, the solver's performance is the main bottleneck in their application. One promising approach for improving performance is to leverage the increasing availability of parallel…
In the realm of big data and machine learning, data-parallel, distributed stochastic algorithms have drawn significant attention in the present days.~While the synchronous versions of these algorithms are well understood in terms of their…
Arrival of multicore systems has enforced a new scenario in computing, the parallel and distributed algorithms are fast replacing the older sequential algorithms, with many challenges of these techniques. The distributed algorithms provide…
A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach…
We present a full implementation of the parareal algorithm---an integration technique to solve differential equations in parallel---in the Julia programming language for a fully general, first-order, initial-value problem. We provide a…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…
We investigate the parallel performance of Parallel Spectral Deferred corrections, a numerical approach that provides small-scale parallelism for the numerical solution of initial value problems. The scheme is applied to the shallow-water…
Computer simulations in QCD are based on the discretization of the theory on a Euclidean lattice. To compute the mean value of an observable, usually the Hybrid Monte Carlo method is applied. Here equations of motion, derived from an…
An approach is treated for numerical integration of ordinary differential equations systems of the first order with choice of a computation scheme, ensuring the required local precision. The treatment is made on the basis of schemes of…
The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…
First-order methods based on the PDHG algorithm have recently emerged as a viable option for efficiently solving large-scale linear programming problems. One highly desirable property of these methods is that they can make effective use of…
Sampling-based planning has become a de facto standard for complex robots given its superior ability to rapidly explore high-dimensional configuration spaces. Most existing optimal sampling-based planning algorithms are sequential in nature…
Mixed-precision methods combine low and high precision arithmetics to exploit low precision computational speed and high precision accuracy. Large ODE systems that contain many heterogeneous interactions lead to a high computational cost…
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…
Parallelization is a popular strategy for improving the performance of iterative algorithms. Optimization methods are no exception: design of efficient parallel optimization methods and tight analysis of their theoretical properties are…
In this article, a family of two- and three-stage explicit multiquadric (MQ) and inverse multiquadric (IMQ) radial basis functions (RBFs) Runge-Kutta methods are introduced for solving ordinary differential equations. These methods are…