Related papers: Textbook efficiency: massively parallel matrix-fre…
In this work, we formulate and analyze a geometric multigrid method for the iterative solution of the discrete systems arising from the finite element discretization of symmetric second-order linear elliptic diffusion problems. We show that…
We present a monolithic hp space-time multigrid method (hp-STMG) for tensor-product space-time finite element discretizations of the incompressible Navier-Stokes equations. We employ mapped inf-sup stable pairs $\mathbb Q_{r+1}/\mathbb…
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…
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…
We propose the first optimal geometric multigrid solver for hybrid high-order discretizations that can handle arbitrary polytopal agglomeration hierarchies in both two and three dimensions. The key ingredient is the use of modified skeleton…
This paper presents a novel parallel splitting algorithm for solving quasi-static multiple-network poroelasticity (MPET) equations. By introducing a total pressure variable, the MPET system can be reformulated into a coupled…
Most of the prior work in massively parallel data processing assumes homogeneity, i.e., every computing unit has the same computational capability, and can communicate with every other unit with the same latency and bandwidth. However, this…
Algebraic multigrid (AMG) is one of the most efficient iterative methods for solving large sparse system of equations. However, how to build/check restriction and prolongation operators in practical of AMG methods for nonsymmetric {\em…
In the near future, massively parallel computing systems will be necessary to solve computation intensive applications. The key bottleneck in massively parallel implementation of numerical algorithms is the synchronization of data across…
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…
Large linear systems with sparse, non-symmetric matrices arise in the modeling of Markov chains or in the discretization of convection-diffusion problems. Due to their potential to solve sparse linear systems with an effort that is linear…
In this paper, a fully aggregation-based algebraic multigrid strategy is developed for nonlinear contact problems of saddle point type using a mortar finite element approach. While the idea of extending multigrid methods to saddle point…
The computation of stationary distributions of Markov chains is an important task in the simulation of stochastic models. The linear systems arising in such applications involve non-symmetric M-matrices, making algebraic multigrid methods a…
Designing the topology of three-dimensional structures is a challenging problem due to its memory and time consumption. In this paper, we present a robust and efficient algorithm for solving large-scale 3D topology optimization problems.…
Multilevel/multigrid methods is one of the most popular approaches for solving a large sparse linear system of equations, typically, arising from the discretization of partial differential equations. One critical step in the…
This paper presents the use of element-based algebraic multigrid (AMGe) hierarchies, implemented in the ParELAG (Parallel Element Agglomeration Algebraic Multigrid Upscaling and Solvers) library, to produce multilevel preconditioners and…
Multilevel techniques are efficient approaches for solving the large linear systems that arise from discretized partial differential equations and other problems. While geometric multigrid requires detailed knowledge about the underlying…
The growing demands of distributed learning on resource constrained edge devices underscore the importance of efficient on device model compression. Tensor Train Decomposition (TTD) offers high compression ratios with minimal accuracy loss,…
This paper discusses our recent generalized optimal algebraic multigrid (AMG) convergence theory applied to the steady-state Stokes equations discretized using Taylor-Hood elements ($\pmb{ \mathbb{P}}_2/\mathbb{P}_{1}$). The generalized…
The goal of this primer is to provide a relatively short exposition of the basics of multigrid methods, simplified by focusing on fundamental concepts in a variational setting. This is done by way of a quadratic energy minimization…