Related papers: A quantitative performance analysis for Stokes sol…
We present a matrix-free flow solver for high-order finite element discretizations of the incompressible Navier-Stokes and Stokes equations with GPU acceleration. For high polynomial degrees, assembling the matrix for the linear systems…
The goal of this work is to construct and study hybrid and multiplicative two-level overlapping Schwarz algorithms with standard coarse spaces for the almost incompressible linear elasticity and Stokes systems, discretized by mixed finite…
Current trends in parallel processors call for the design of efficient massively parallel algorithms for scientific computing. Parallel algorithms for Monte Carlo simulations of thermodynamic ensembles of particles have received little…
Combinatorial decision problems arise in many different domains such as scheduling, routing, packing, bioinformatics, and many more. Despite recent advances in developing scalable solvers, there are still many problems which are often very…
Linear Programs (LPs) appear in a large number of applications and offloading them to the GPU is viable to gain performance. Existing work on offloading and solving an LP on GPU suggests that performance is gained from large sized LPs…
Iterative methods for solving large sparse systems of linear equations are widely used in many HPC applications. Extreme scaling of these methods can be difficult, however, since global communication to form dot products is typically…
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…
The goal of this work is to parallelize the multistep scheme for the numerical approximation of the backward stochastic differential equations (BSDEs) in order to achieve both, a high accuracy and a reduction of the computation time as…
Based on the Uzawa algorithm, we consider an adaptive finite element method for the Stokes system. We prove linear convergence with optimal algebraic rates for the residual estimator (which is equivalent to the total error), if the arising…
This paper presents a comparative optimization framework for smart charging of electrified vehicle fleets. Using heuristic sequential dynamic programming (SeqDP), the framework minimizes electricity costs while adhering to constraints…
Performance tests and analyses are critical to effective HPC software development and are central components in the design and implementation of computational algorithms for achieving faster simulations on existing and future computing…
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…
Unfitted finite element methods have emerged as a popular alternative to classical finite element methods for the solution of partial differential equations and allow modeling arbitrary geometries without the need for a boundary-conforming…
This paper reports large-scale direct numerical simulations of homogeneous-isotropic fluid turbulence, achieving sustained performance of 1.08 petaflop/s on gpu hardware using single precision. The simulations use a vortex particle method…
The design of fast solvers for isogeometric analysis is receiving a lot of attention due to the challenge that offers to find an algorithm with a robust convergence with respect to the spline degree. Here, we analyze the application of…
The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular…
Accurately simulating long-time dynamics of many-body systems is a challenge in both classical and quantum computing due to the accumulation of Trotter errors. While low-order Trotter-Suzuki decompositions are straightforward to implement,…
B-spline based orbital representations are widely used in Quantum Monte Carlo (QMC) simulations of solids, historically taking as much as 50% of the total run time. Random accesses to a large four-dimensional array make it challenging to…
In recent years, solvers for finite-element discretizations of linear or linearized saddle-point problems, like the Stokes and Oseen equations, have become well established. There are two main classes of preconditioners for such systems:…
Block-tridiagonal systems are prevalent in state estimation and optimal control, and solving these systems is often the computational bottleneck. Improving the underlying solvers therefore has a direct impact on the real-time performance of…