Related papers: An adaptive finite element multigrid solver using …
We present a highly general implementation of fast multipole methods on graphics processing units (GPUs). Our two-dimensional double precision code features an asymmetric type of adaptive space discretization leading to a particularly…
This work presents the GPU acceleration of the open-source code CaNS for very fast massively-parallel simulations of canonical fluid flows. The distinct feature of the many-CPU Navier-Stokes solver in CaNS is its fast direct solver for the…
In this paper, we aim to introduce a new perspective when comparing highly parallelized algorithms on GPU: the energy consumption of the GPU. We give an analysis of the performance of linear algebra operations, including addition of…
Earth system models (ESM) demand significant hardware resources and energy consumption to solve atmospheric chemistry processes. Recent studies have shown improved performance from running these models on GPU accelerators. Nonetheless,…
Linear solvers are major computational bottlenecks in a wide range of decision support and optimization computations. The challenges become even more pronounced on heterogeneous hardware, where traditional sparse numerical linear algebra…
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…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
We propose a CPU-GPU heterogeneous computing method for solving time-evolution partial differential equation problems many times with guaranteed accuracy, in short time-to-solution and low energy-to-solution. On a single-GH200 node, the…
This paper proposes a GPU-accelerated optimization framework for collision avoidance problems where the controlled objects and the obstacles can be modeled as the finite union of convex polyhedra. A novel collision avoidance constraint is…
We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be…
We propose a GPU-accelerated distributed optimization algorithm for controlling multi-phase optimal power flow in active distribution systems with dynamically changing topologies. To handle varying network configurations and enable…
We propose a generic algorithmic building block to accelerate training of machine learning models on heterogeneous compute systems. Our scheme allows to efficiently employ compute accelerators such as GPUs and FPGAs for the training of…
In this paper, we present algorithms and implementations for the end-to-end GPU acceleration of matrix-free low-order-refined preconditioning of high-order finite element problems. The methods described here allow for the construction of…
With the hardware support for half-precision arithmetic on NVIDIA V100 GPUs, high-performance computing applications can benefit from lower precision at appropriate spots to speed up the overall execution time. In this paper, we investigate…
The efficient solution of large sparse saddle point systems is very important in computational fluid mechanics. The discontinuous Galerkin finite element methods have become increasingly popular for incompressible flow problems but their…
In this article, we solve the Stokes and Navier-Stokes equations with the deal$.$II finite-element library. In particular, we use its multigrid, adaptive-mesh, and matrix-free infrastructures to design efficient linear and nonlinear…
We accelerated an ab-initio molecular QMC calculation by using GPGPU. Only the bottle-neck part of the calculation is replaced by CUDA subroutine and performed on GPU. The performance on a (single core CPU + GPU) is compared with that on a…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
We consider differential Lyapunov and Riccati equations, and generalized versions thereof. Such equations arise in many different areas and are especially important within the field of optimal control. In order to approximate their…
An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on…