Related papers: Parareal Algorithm Implementation and Simulation i…
We present an algorithm for the solution of a simultaneous space-time discretization of linear parabolic evolution equations with a symmetric differential operator in space. Building on earlier work, we recast this discretization into a…
This report provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines. To illustrate the basic concepts and key issues,…
In this article we present a parallel algorithm for simulation of the heat conduction process inside the so-called pulse cryogenic cell. This simulation is important for designing the device for portion injection of working gases into…
This article presents a strongly polynomial-time algorithm for the general linear programming problem. This algorithm is an implicit reduction procedure that works as follows. Primal and dual problems are combined into a special system of…
We present StochasticPrograms.jl, a user-friendly and powerful open-source framework for stochastic programming written in the Julia language. The framework includes both modeling tools and structure-exploiting optimization algorithms.…
Multi-objective integer optimization problems are hard to solve, mainly because the number of nondominated images is often extremely large. We present the first exact algorithm, called PEA, that fully utilizes the multicore architecture of…
We introduce Metatheory.jl: a lightweight and performant general purpose symbolics and metaprogramming framework meant to simplify the act of writing complex Julia metaprograms and to significantly enhance Julia with a native term rewriting…
The Parareal algorithm was invented in 2001 in order to parallelize the solution of evolution problems in the time direction. It is based on parallel fine time propagators called F and sequential coarse time propagators called G, which…
Dynamic systems have a fundamental relevance in the description of physical phenomena. The search for more accurate and faster numerical integration methods for the resolution of such systems is, therefore, an important topic of research.…
We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including…
With the growing complexity and capability of contemporary robotic systems, the necessity of sophisticated computing solutions to efficiently handle tasks such as real-time processing, sensor integration, decision-making, and control…
This paper proposes an efficient parallelised computation of field/circuit coupled systems co-simulated with the Waveform Relaxation (WR) technique. The main idea of the introduced approach lies in application of the parallel-in-time method…
The high cost of sequential time integration is one major constraint that limits the speedup of a time-parallel algorithm like the Parareal algorithm due to the difficulty of coarsening time steps in a stiff numerical problem. To address…
For quantum computers to become useful tools to physicists, engineers and computational scientists, quantum algorithms for solving nonlinear differential equations need to be developed. Despite recent advances, the quest for a solver that…
Numerical solutions of partial differential equations enable a broad range of scientific research. The Dedalus Project is a flexible, open-source, parallelized computational framework for solving general partial differential equations using…
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 this work the parallel-in-time algorithm Parareal was applied to the ocean-circulation and sea-ice model FESOM2 developed by the Alfred-Wegener Institut (AWI). The climate model provides one time integration method and hence, the coarse…
We report a detailed analysis of the optical realization [1, 3, 2, 4] of the analogue algorithm described in the first paper of this series [5] for the simultaneous factorization of an exponential number of integers. Such an analogue…
The ParaDiag family of algorithms solves differential equations by using preconditioners that can be inverted in parallel through diagonalization. In the context of optimal control of linear parabolic PDEs, the state-of-the-art ParaDiag…
Imaging Mueller polarimetry has already proved its potential for metrology, remote sensing and biomedicine. The real-time applications of this modality require both video rate image acquisition and fast data post-processing algorithms.…