Related papers: Accelerating Geometric Multigrid Preconditioning w…
In this work we exploit agglomeration based $h$-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature $h$-coarsened mesh…
In marine offshore engineering, cost-efficient simulation of unsteady water waves and their nonlinear interaction with bodies are important to address a broad range of engineering applications at increasing fidelity and scale. We consider a…
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
In this manuscript, we present a collective multigrid algorithm to solve efficiently the large saddle-point systems of equations that typically arise in PDE-constrained optimization under uncertainty, and develop a novel convergence…
As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…
Sketching-based preconditioners have been shown to accelerate the solution of dense least-squares problems with coefficient matrices having substantially more rows than columns. The cost of generating these preconditioners can be reduced by…
Large scale-free graphs are famously difficult to process efficiently: the skewed vertex degree distribution makes it difficult to obtain balanced partitioning. Our research instead aims to turn this into an advantage by partitioning the…
In order to compensate for the higher cost of double double and quad double arithmetic when solving large polynomial systems, we investigate the application of NVIDIA Tesla K20C general purpose graphics processing unit. The focus on this…
It is shown how various ideas that are well established for the solution of Poisson's equation using plane wave and multigrid methods can be combined with wavelet concepts. The combination of wavelet concepts and multigrid techniques turns…
The performance of finite element solvers on modern computer architectures is typically memory bound for sufficiently large problems. The main cause for this is that loading matrix elements from RAM into CPU cache is significantly slower…
Due to its optimal complexity, the multigrid (MG) method is one of the most popular approaches for solving large-scale linear systems arising from the discretization of partial differential equations. However, the parallel implementation of…
We present a mixed-precision implementation of the high-order discontinuous Galerkin method with ADER time stepping (ADER-DG) for solving hyperbolic systems of partial differential equations (PDEs) in the hyperbolic PDE engine ExaHyPE. The…
Graphics Processing Units allow for running massively parallel applications offloading the CPU from computationally intensive resources, however GPUs have a limited amount of memory. In this paper a trie compression algorithm for massively…
This paper establishes the first theoretical framework for analyzing the rounding-error effects on multigrid methods using mixed-precision iterative-refinement solvers. While motivated by the sparse symmetric positive definite (SPD) matrix…
Hardware trends have motivated the development of mixed precision algo-rithms in numerical linear algebra, which aim to decrease runtime while maintaining acceptable accuracy. One recent development is the development of an adaptive…
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…
We discuss the ill conditioning of the matrix for the discretised Poisson equation in the small aspect ratio limit, and motivate this problem in the context of nonhydrostatic ocean modelling. Efficient iterative solvers for the Poisson…
In order to obtain more accurate solutions of polynomial systems with numerical continuation methods we use multiprecision arithmetic. Our goal is to offset the overhead of double double arithmetic accelerating the path trackers and in…
We develop an algorithm to solve tridiagonal systems of linear equations, which appear in implicit finite-difference schemes of partial differential equations (PDEs), being the time-dependent Schr\"{o}dinger equation (TDSE) an ideal…
Multilevel quadrature methods for parametric operator equations such as the multilevel (quasi-) Monte Carlo method are closely related to the sparse tensor product approximation between the spatial variable and the parameter. In this…