Related papers: Asynchronous Parareal Algorithm Applied to Europea…
The need for scalable numerical solutions has motivated the development of asynchronous parallel algorithms, where a set of nodes run in parallel with little or no synchronization, thus computing with delayed information. This paper studies…
Parareal algorithms are studied for semilinear parabolic stochastic partial differential equations. These algorithms proceed as two-level integrators, with fine and coarse schemes, and have been designed to achieve a `parallel in real time'…
System performance for networks composed of interconnected subsystems can be increased if the traditionally separated subsystems are jointly optimized. Recently, parallel and distributed optimization methods have emerged as a powerful tool…
This paper proposes a general formulation for temporal parallelisation of dynamic programming for optimal control problems. We derive the elements and associative operators to be able to use parallel scans to solve these problems with…
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…
Recently, the ParaOpt algorithm was proposed as an extension of the time-parallel Parareal method to optimal control. ParaOpt uses quasi-Newton steps that each require solving a system of matching conditions iteratively. The…
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…
To enhance solution accuracy and training efficiency in neural network approximation to partial differential equations, partitioned neural networks can be used as a solution surrogate instead of a single large and deep neural network…
An algorithm is discussed for converting a class of recursive processes to a parallel system. It is argued that this algorithm can be superior to certain methods currently found in the literature for an important subset of problems. The…
The number of parameters in large-scale language models based on transformers is gradually increasing, and the scale of computing clusters is also growing. The technology of quickly mobilizing large amounts of computing resources for…
In this paper, we propose an iterative splitting method to solve the partial differential equations in option pricing problems. We focus on the Heston stochastic volatility model and the derived two-dimensional partial differential equation…
Convergence of classical parallel iterations is detected by performing a reduction operation at each iteration in order to compute a residual error relative to a potential solution vector. To efficiently run asynchronous iterations,…
Two characteristics that make convex decomposition algorithms attractive are simplicity of operations and generation of parallelizable structures. In principle, these schemes require that all coordinates update at the same time, i.e., they…
Discrete variational methods have shown an excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative method for discrete variational methods appropriate for boundary value…
The advent of asynchronous iterative scheme gives high efficiency to numerical computations. However, it is generally difficult to handle the problems of resource management and convergence detection. This paper uses JACK2, an asynchronous…
We present a novel approach to the parallelization of the parabolic fast multipole method for a space-time boundary element method for the heat equation. We exploit the special temporal structure of the involved operators to provide an…
For the parallel-in-time integration method Parareal, pipelining can be used to hide some of the cost of the serial correction step and improve its efficiency. The paper introduces a basic OpenMP implementation of pipelined Parareal and…
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…
We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…
The parareal algorithm is known to allow for a significant reduction in wall clock time for accurate numerical solutions by parallelising across the time dimension. We present and test a micro-macro version of parareal, in which the fine…