相关论文: A parallel space-time multigrid method for the edd…

A numerical approach for solving evolutionary partial differential equations in two and three space dimensions on block-based adaptive grids is presented. The numerical discretization is based on high-order, central finite-differences and…

Parallel-in-time methods for partial differential equations (PDEs) have been the subject of intense development over recent decades, particularly for diffusion-dominated problems. It has been widely reported in the literature, however, that…

Elliptic partial differential equations must be solved numerically for many problems in numerical relativity, such as initial data for every simulation of merging black holes and neutron stars. Existing elliptic solvers can take multiple…

This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…

We consider the parallel time integration of the linear advection equation with the Parareal and two-level multigrid-reduction-in-time (MGRIT) algorithms. Our aim is to develop a better understanding of the convergence behaviour of these…

This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…

We present an approach to solving problems in micromechanics that is amenable to massively parallel calculations through the use of graphical processing units and other accelerators. The problems lead to nonlinear differential equations…

With the stagnation of processor core performance, further reductions in the time-to-solution for geophysical fluid problems are becoming increasingly difficult with standard time integrators. Parallel-in-time exposes and exploits…

We propose and investigate new robust preconditioners for space-time Isogeometric Analysis of parabolic evolution problems. These preconditioners are based on a time parallel multigrid method. We consider a decomposition of the space-time…

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…

Targeting simulations on parallel hardware architectures, this paper presents computational kernels for efficient computations in mortar finite element methods. Mortar methods enable a variationally consistent imposition of coupling…

We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…

Highly heterogeneous, anisotropic coefficients, e.g. in the simulation of carbon-fibre composite components, can lead to extremely challenging finite element systems. Direct solvers for the resulting large and sparse linear systems suffer…

We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…

The demand for substantial increases in the spatial resolution of global weather- and climate- prediction models makes it necessary to use numerically efficient and highly scalable algorithms to solve the equations of large scale…

We consider the numerical solution of Poisson's equation on structured grids using geometric multigrid with nonstandard coarse grids and coarse level operators. We are motivated by the problem of developing high-order accurate numerical…

We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We focus on patch smoothers, which offer robust convergence…

For low-frequency electromagnetic problems, where wave-propagation effects can be neglected, eddy current formulations are commonly used as a simplification of the full Maxwell's equations. In this setup, time-domain simulations, needed to…

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…

We present an adaptive methodology for the solution of (linear and) non-linear time dependent problems that is especially tailored for massively parallel computations. The basic concept is to solve for large blocks of space-time unknowns…