Related papers: Parallel in time partially explicit splitting sche…
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…
In this paper, contrast-independent partially explicit time discretization for wave equations in heterogeneous high-contrast media via mass lumping is concerned. By employing a mass lumping scheme to diagonalize the mass matrix, the matrix…
The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…
The modeling of atmospheric processes in the context of weather and climate simulations is an important and computationally expensive challenge. The temporal integration of the underlying PDEs requires a very large number of time steps,…
For time-dependent partial differential equations, parallel-in-time integration using the "parallel full approximation scheme in space and time" (PFASST) is a promising way to accelerate existing space-parallel approaches beyond their…
We propose a parallel adaptive constraint-tightening approach to solve a linear model predictive control problem for discrete-time systems, based on inexact numerical optimization algorithms and operator splitting methods. The underlying…
The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give…
With steadily increasing parallelism for high-performance architectures, simulations requiring a good strong scalability are prone to be limited in scalability with standard spatial-decomposition strategies at a certain amount of parallel…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
This paper introduces a new method of partitioning the solution space of a multi-objective optimisation problem for parallel processing, called Efficient Projection Partitioning. This method projects solutions down into a single dimension,…
Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…
In this paper we combine the Parareal parallel-in-time method together with spatial parallelization and investigate this space-time parallel scheme by means of solving the three-dimensional incompressible Navier-Stokes equations.…
The efficient solution of sparse, linear systems resulting from the discretization of partial differential equations is crucial to the performance of many physics-based simulations. The algorithmic optimality of multilevel approaches for…
The paper investigates a non-intrusive parallel time integration with multigrid for space-fractional diffusion equations in two spatial dimensions. We firstly obtain a fully discrete scheme via using the linear finite element method to…
The paper deals with the developing of the methodological backgrounds for the modeling and simulation of complex dynamical objects. Such backgrounds allow us to perform coordinate transformation and formulate the algorithm of its usage for…
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…
Optimal multiple sequence alignment by dynamic programming, like many highly dimensional scientific computing problems, has failed to benefit from the improvements in computing performance brought about by multi-processor systems, due to…
For the numerical solution of time-dependent partial differential equations, time-parallel methods have recently shown to provide a promising way to extend prevailing strong-scaling limits of numerical codes. One of the most complex methods…
In this paper, we propose a parallel space-time domain decomposition method for solving an unsteady source identification problem governed by the linear convection-diffusion equation. Traditional approaches require to solve repeatedly a…
To extend prevailing scaling limits when solving time-dependent partial differential equations, the parallel full approximation scheme in space and time (PFASST) has been shown to be a promising parallel-in-time integrator. Similar to a…