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We present novel algorithmic solutions together with implementation details utilizing non-Abelian symmetries in order to boost the current limits of tensor network state algorithms on high performance computing infrastructure. In our…
This paper is to give an overview of AMG methods for solving large scale systems of equations such as those from the discretization of partial differential equations. AMG is often understood as the acronym of "Algebraic Multi-Grid", but it…
Improving the computational efficiency of quantum many-body calculations from a hardware perspective remains a critical challenge. Although field-programmable gate arrays (FPGAs) have recently been exploited to improve the computational…
Algebraic multigrid (AMG) is a widely used scalable solver and preconditioner for large-scale linear systems resulting from the discretization of a wide class of elliptic PDEs. While AMG has optimal computational complexity, the cost of…
In the present paper we propose a coupled multigrid method for generalized Stokes flow problems. Such problems occur as subproblems in implicit time-stepping approaches for time-dependent Stokes problems. The discretized Stokes system is a…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We…
We investigate the energy efficiency of a library designed for parallel computations with sparse matrices. The library leverages high-performance, energy-efficient Graphics Processing Unit (GPU) accelerators to enable large-scale scientific…
Efficient solution of 3D elasticity problems is an important part of many industrial and scientific applications. Smoothed aggregation algebraic multigrid using rigid body modes for the tentative prolongation operator construction is an…
This study presents novel strategies for improving the node-level performance of matrix-free evaluation of continuous and discontinuous Galerkin spatial discretizations on unstructured tetrahedral grids. In our approach the underlying…
Although multigrid is asymptotically optimal for solving many important partial differential equations, its efficiency relies heavily on the careful selection of the individual algorithmic components. In contrast to recent approaches that…
In this paper, we present a novel local and parallel two-grid finite element scheme for solving the Stokes equations, and rigorously establish its a priori error estimates. The scheme admits simultaneously small scales of subproblems and…
The paper studies a higher order unfitted finite element method for the Stokes system posed on a surface in three-dimensional space. The method employs generalized Taylor-Hood finite element pairs on tetrahedral bulk mesh to discretize the…
In this article, a new generic higher-order finite-element framework for massively parallel simulations is presented. The modular software architecture is carefully designed to exploit the resources of modern and future supercomputers.…
Achieving efficient task parallelism on many-core architectures is an important challenge. The widely used GNU OpenMP implementation of the popular OpenMP parallel programming model incurs high overhead for fine-grained, short-running tasks…
The computational complexity of naive, sampling-based uncertainty quantification for 3D partial differential equations is extremely high. Multilevel approaches, such as multilevel Monte Carlo (MLMC), can reduce the complexity significantly,…
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…
We present a monolithic geometric multigrid preconditioner for solving fluid-solid interaction problems in Stokes limit. The problems are discretized by a spatially adaptive high-order meshless method, the generalized moving least squares…
The multimesh finite element method enables the solution of partial differential equations on a computational mesh composed by multiple arbitrarily overlapping meshes. The discretization is based on a continuous--discontinuous function…
Stencil computations consume a major part of runtime in many scientific simulation codes. As prototypes for this class of algorithms we consider the iterative Jacobi and Gauss-Seidel smoothers and aim at highly efficient parallel…