Related papers: A new ParaDiag time-parallel time integration meth…
While many ideas and proofs of concept for parallel-in-time integration methods exists, the number of large-scale, accessible time-parallel codes is rather small. This is often due to the apparent or subtle complexity of the algorithms and…
We present original time-parallel algorithms for the solution of the implicit Euler discretization of general linear parabolic evolution equations with time-dependent self-adjoint spatial operators. Motivated by the inf-sup theory of…
As CPU clock speeds have stagnated, and high performance computers continue to have ever higher core counts, increased parallelism is needed to take advantage of these new architectures. Traditional serial time-marching schemes are a…
We propose a parareal based time parallelization scheme in the phase-space for the particle-in-Fourier (PIF) discretization of the Vlasov-Poisson system used in kinetic plasma simulations. We use PIF with a coarse tolerance for the…
Simulation of the monodomain equation, crucial for modeling the heart's electrical activity, faces scalability limits when traditional numerical methods only parallelize in space. To optimize the use of large multi-processor computers by…
The time parallel solution of optimality systems arising in PDE constraint optimization could be achieved by simply applying any time parallel algorithm, such as Parareal, to solve the forward and backward evolution problems arising in the…
In this article, we present a parallel discretization and solution method for parabolic problems with a higher number of space dimensions. It consists of a parallel-in-time approach using the multigrid reduction-in-time algorithm MGRIT with…
Time parallelization, also known as PinT (Parallel-in-Time) is a new research direction for the development of algorithms used for solving very large scale evolution problems on highly parallel computing architectures. Despite the fact that…
Modern high performance computers are massively parallel; for many PDE applications spatial parallelism saturates long before the computer's capability is reached. Parallel-in-time methods enable further speedup beyond spatial saturation by…
We construct a space-time parallel method for solving parabolic partial differential equations by coupling the Parareal algorithm in time with overlapping domain decomposition in space. The goal is to obtain a discretization consisting of…
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…
This paper presents a novel parallel-in-time algorithm able to compute time-periodic solutions of problems where the period is not given. Exploiting the idea of the multiple shooting method, the proposed approach calculates the initial…
We propose a new parallel-in-time algorithm for solving optimal control problems constrained by discretized partial differential equations. Our approach, which is based on a deeper understanding of ParaExp, considers an overlapping…
The precise mechanisms responsible for the natural dynamos in the Earth and Sun are still not fully understood. Numerical simulations of natural dynamos are extremely computationally intensive, and are carried out in parameter regimes many…
This paper presents a parallel-in-time multilevel iterative method for solving differential algebraic equation, arising from a discretization of linear time-dependent partial differential equation. The core of the method is the multilevel…
The time domain analysis of eddy current problems often requires the simulation of long time intervals, e.g. until a steady state is reached. Fast-switching excitations e.g. in pulsedwidth modulated signals require in addition very small…
We introduce a micro-macro parareal algorithm for the time-parallel integration of multiscale-in-time systems. The algorithm first computes a cheap, but inaccurate, solution using a coarse propagator (simulating an approximate slow…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
The numerical simulation of the time-dependent Schr\"odinger equation for quantum systems is a very active research topic. Yet, resolving the solution sufficiently in space and time is challenging and mandates the use of modern…
Parallel-in-time methods are developed to accelerate the direct-adjoint looping procedure. Particularly, we utilize the Paraexp algorithm, previously developed to integrate equations forward in time, to accelerate the direct-adjoint looping…