Related papers: Parareal Algorithm Implementation and Simulation i…
In-silico investigation of skin permeation is an important but also computationally demanding problem. To resolve all scales involved in full detail will not only require exascale computing capacities but also suitable parallel algorithms.…
A class of abstract nonlinear time-periodic evolution problems is considered which arise in electrical engineering and other scientific disciplines. An efficient solver is proposed for the systems arising after discretization in time based…
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…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
We present an efficient approach for writing architecture-agnostic parallel high-performance stencil computations in Julia, which is instantiated in the package ParallelStencil.jl. Powerful metaprogramming, costless abstractions and…
Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent differential equations by parallelizing the temporal domain. Among them, Parareal computes the solution sequentially using an inaccurate (fast) solver,…
With the advent of supercomputers, multi-processor environments and parallel-in-time (PinT) algorithms offer ways to solve initial value problems for ordinary and partial differential equations (ODEs and PDEs) over long time intervals, a…
The multi-resolution approximation (MRA) of Gaussian processes was recently proposed to conduct likelihood-based inference for massive spatial data sets. An advantage of the methodology is that it can be parallelized. We implemented the MRA…
We introduce Prob-GParareal, a probabilistic extension of the GParareal algorithm designed to provide uncertainty quantification for the Parallel-in-Time (PinT) solution of (ordinary and partial) differential equations (ODEs, PDEs). The…
Estimating parameters of Partial Differential Equations (PDEs) from noisy and indirect measurements often requires solving ill-posed inverse problems. These so called parameter estimation or inverse medium problems arise in a variety of…
We describe the development of a multi-purpose software for Bayesian statistical inference, BAT.jl, written in the Julia language. The major design considerations and implemented algorithms are summarized here, together with a test suite…
We present FractionalDiffEq.jl, a comprehensive solver suite for solving fractional differential equations, featuring high-performance numerical algorithms in the Julia programming language. FractionalDiffEq.jl is designed to be…
Dynamic languages have become popular for scientific computing. They are generally considered highly productive, but lacking in performance. This paper presents Julia, a new dynamic language for technical computing, designed for performance…
We present a new algorithm for solving the reduction problem in the context of holonomic integrals, which in turn provides an approach to integration with parameters. Our method extends the Griffiths--Dwork reduction technique to holonomic…
We present an open source computational framework geared towards the efficient numerical investigation of open quantum systems written in the Julia programming language. Built exclusively in Julia and based on standard quantum optics…
The Julia programming language has evolved into a modern alternative to fill existing gaps in scientific computing and data science applications. Julia leverages a unified and coordinated single-language and ecosystem paradigm and has a…
This paper presents a new algorithm for the parallel in time (PiT) numerical simulation of time dependent partial/ordinary differential equations. We propose a reliable alternative to the well know parareal in time algorithm, by formulating…
We introduce a time-parallel algorithm for solving numerically almost integrable Hamiltonian systems in action-angle coordinates. This algorithm is a refinement of that introduced by Saha, Stadel and Tremaine in 1997 (SST97) for the same…
This year marks the consolidation of Julia (https://julialang.org/), a programming language designed for scientific computing, as the first stable version (1.0) has been released, in August 2018. Among its main features, expressiveness and…
In this paper, we present a method that enables to solve in parallel the Euler-Lagrange system associated with the optimal control of a parabolic equation. Our approach is based on an iterative update of a sequence of intermediate targets…