Related papers: Convergence analysis for parallel-in-time solution…
For the time-parallel Parareal method, there exists both numerical and analytical proof that it converges very well for diffusive problems like the heat equation. Many applications, however, do not lead to simple homogeneous diffusive…
This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise…
Time-parallel algorithms, such as Parareal, are well-understood for linear problems, but their convergence analysis for nonlinear, chaotic systems remains limited. This paper introduces a new theoretical framework for analysing…
In this paper the Micro-Macro Parareal algorithm was adapted to PDEs. The parallel-in-time approach requires two meshes of different spatial resolution in order to compute approximations in an iterative way to a predefined reference…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
The aim of this paper is to develop an algebraic multigrid method to solve eigenvalue problems based on the combination of the multilevel correction scheme and the algebraic multigrid method for linear equations. Our approach uses the…
We describe a parallel algorithm for solving the time-independent 3d Schrodinger equation using the finite difference time domain (FDTD) method. We introduce an optimized parallelization scheme that reduces communication overhead between…
We derive global estimates for the error in solutions of linear hyperbolic systems due to inaccurate boundary geometry. We show that the error is bounded by data and bounded in time when the solutions in the true and approximate domains are…
Models with dominant advection always posed a difficult challenge for projection-based reduced order modelling. Many methodologies that have recently been proposed are based on the pre-processing of the full-order solutions to accelerate…
We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the…
The multigrid-reduction-in-time (MGRIT) technique has proven to be successful in achieving higher run-time speedup by exploiting parallelism in time. The goal of this article is to develop and analyze a MGRIT algorithm, using FCF-relaxation…
Multigrid methods have been a popular approach for solving linear systems arising from the discretization of partial differential equations (PDEs) for several decades. They are particularly effective for accelerating convergence rates with…
As the number of processor cores on supercomputers becomes larger and larger, algorithms with high degree of parallelism attract more attention. In this work, we propose a novel space-time coupled algorithm for solving an inverse problem…
Current algorithms for large-scale industrial optimization problems typically face a trade-off: they either require exponential time to reach optimal solutions, or employ problem-specific heuristics. To overcome these limitations, we…
We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
In this paper a local Fourier analysis for multigrid methods on tetrahedral grids is presented. Different smoothers for the discretization of the Laplace operator by linear finite elements on such grids are analyzed. A four-color smoother…
An adaptive method for parabolic partial differential equations that combines sparse wavelet expansions in time with adaptive low-rank approximations in the spatial variables is constructed and analyzed. The method is shown to converge and…
The Parareal algorithm is used to solve time-dependent problems considering multiple solvers that may work in parallel. The key feature is a initial rough approximation of the solution that is iteratively refined by the parallel solvers. We…
Multiscale analysis of a degenerate pseudoparabolic variational inequality, modelling the two-phase flow with dynamical capillary pressure in a perforated domain, is the main topic of this work. Regularisation and penalty operator methods…