Related papers: Space-Time Multigrid Methods Suitable for Topology…
A numerical algorithm for solving mantle convection problems with strongly variable viscosity is presented. Equations for conservation of mass and momentum for highly viscous and incompressible fluids are solved iteratively by a multigrid…
It is known that the solution of a conservative steady-state two-sided fractional diffusion problem can exhibit singularities near the boundaries. As consequence of this, and due to the conservative nature of the problem, we adopt a finite…
Many iterative parallel-in-time algorithms have been shown to be highly efficient for diffusion-dominated partial differential equations (PDEs), but are inefficient or even divergent when applied to advection-dominated PDEs. We consider the…
We propose a robust, adaptive coarse-grid correction scheme for matrix-free geometric multigrid targeting PDEs with strongly varying coefficients. The method combines uniform geometric coarsening of the underlying grid with heterogeneous…
Distributed stochastic gradient descent (SGD) with gradient compression has become a popular communication-efficient solution for accelerating distributed learning. One commonly used method for gradient compression is Top-K sparsification,…
In this paper, we propose new geometrically unfitted space-time Finite Element methods for partial differential equations posed on moving domains of higher order accuracy in space and time. As a model problem, the convection-diffusion…
Efficient thermal management in high-power electronic devices requires cooling channel designs that provide high heat removal while satisfying strict spatial and manufacturing constraints. This study presents a two-stage hierarchical…
Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…
Optimizing the transient control of gas networks is a highly challenging task. The corresponding model incorporates the combinatorial complexity of determining the settings for the many active elements as well as the non-linear and…
We present the Stagger-grid, a comprehensive grid of time-dependent, 3D hydrodynamic model atmospheres for late-type stars with realistic treatment of radiative transfer, covering a wide range in stellar parameters. This grid of 3D models…
We consider geometric multigrid methods for the solution of linear systems arising from isogeometric discretizations of elliptic partial differential equations. For classical finite elements, such methods are well known to be fast solvers…
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…
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…
In this study, we present an $hp$-multigrid preconditioner for a divergence-conforming HDG scheme for the generalized Stokes and the Navier-Stokes equations using an augmented Lagrangian formulation. Our method relies on conforming…
Algebraic multigrid (AMG) is conventionally applied in a black-box fashion, agnostic to the underlying geometry. In this work, we propose that using geometric information -- when available -- to assist with setting up the AMG hierarchy is…
Multiple time scale molecular dynamics enhances computational efficiency by updating slow motions less frequently than fast motions. However, in practice the largest outer time step possible is limited not by the physical forces but by…
Coarse Grid Projection (CGP) methodology is used to accelerate the computations of sets of decoupled nonlinear evolutionary and linear static equations. In CGP, the linear equations are solved on a coarsened mesh compared to the nonlinear…
In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
We investigate the problem of minimizing the expectation of smooth nonconvex functions in a distributed setting with multiple parallel workers that are able to compute stochastic gradients. A significant challenge in this context is the…