Related papers: Parareal Algorithm Implementation and Simulation i…
The purpose of this article is to propose ODE based approaches for the numerical evaluation of matrix functions $f(A)$, a question of major interest in the numerical linear algebra. To this end, we model $f(A)$ as the solution at a finite…
A random search algorithm intended to solve discrete optimization problems is considered. We outline the main components of the algorithm, and then describe it in more detail. We show how the algorithm can be implemented on parallel…
Mathematica is a powerful application package for doing mathematics and is used almost in all branches of science. It has widespread applications ranging from quantum computation, statistical analysis, number theory, zoology, astronomy, and…
Classical methods to simulate quantum systems are not only a key element of the physicist's toolkit for studying many-body models but are also increasingly important for verifying and challenging upcoming quantum computers. Pauli…
In this paper, we investigate the strong convergence analysis of parareal algorithms for stochastic Maxwell equations with the damping term driven by additive noise. The proposed parareal algorithms proceed as two-level temporal…
This paper considers one of the fundamental parallel-in-time methods for the solution of ordinary differential equations, Parareal, and extends it by adopting a neural network as a coarse propagator. We provide a theoretical analysis of the…
A key component of many robotics model-based planning and control algorithms is physics predictions, that is, forecasting a sequence of states given an initial state and a sequence of controls. This process is slow and a major computational…
The paper presents a novel modular hybrid parallel robot for pancreatic surgery and its higher-order kinematics derived based on various formalisms. The classical vector, homogeneous transformation matrices and dual quaternion approaches…
The parareal algorithm represents an important class of parallel-in-time algorithms for solving evolution equations and has been widely applied in practice. To achieve effective speedup, the choice of the coarse propagator in the algorithm…
Large molecular dynamics simulations (millions of atoms, tens of microseconds, thousands of processors) hit the strong scalability wall: simulation on twice as many processors does not take half the time. Inspired by large N-body space…
GPUs and other accelerators are popular devices for accelerating compute-intensive, parallelizable applications. However, programming these devices is a difficult task. Writing efficient device code is challenging, and is typically done in…
In this paper, we are concerned with the micro-macro Parareal algorithm for the simulation of initial-value problems. In this algorithm, a coarse (fast) solver is applied sequentially over the time domain, and a fine (time-consuming) solver…
The ParaOpt algorithm was recently introduced as a time-parallel solver for optimal-control problems with a terminal-cost objective, and convergence results have been presented for the linear diffusive case with implicit-Euler time…
This paper demonstrates how certified computational tools can be used to address various problems in control theory. In particular, we introduce PACE.jl, a Julia package that implements symbolic elimination techniques, including (among…
We describe a package realized in the Julia programming language which performs symbolic manipulations applied to nonlinear evolution equations, their flows, and commutators of such objects. This tool was employed to perform contrived…
In this papers, we couple the parareal algorithm with projection methods of the trajectory on a specific manifold, defined by the preservation of some conserved quantities of the differential equations. First, projection methods are…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
This paper presents a highly-parallelizable parallel-in-time algorithm for efficient solution of nonlinear time-periodic problems. It is based on the time-periodic extension of the Parareal method, known to accelerate sequential…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We present an implementation of algorithms for the symbolic integration of hyperlogarithms multiplied by rational functions in the computer algebra system FORM. This implementation encompasses cases where hyperlogarithms have rational…