相关论文: ILU Smoothers for Low Mach Navier-Stokes Pressure …

Immersed boundary methods (IBMs) facilitate the simulation of flows around stationary, moving, and deforming bodies on Cartesian grids. However, extending these simulations to the large grid sizes required for realistic flow problems…

In this paper, we consider the iterative solution of linear algebraic equations under the condition that matrix-vector products with the coefficient matrix are computed only partially. At the same time, non-computed entries are set to…

We provide the first global model recovery results for the IRLS (iteratively reweighted least squares) heuristic for robust regression problems. IRLS is known to offer excellent performance, despite bad initializations and data corruption,…

The acceleration of sparse matrix computations on modern many-core processors, such as the graphics processing units (GPUs), has been recognized and studied over a decade. Significant performance enhancements have been achieved for many…

Recent enhancements to the Primal-Dual Hybrid Gradient (PDHG) algorithm have enabled GPUs to efficiently solve large linear programming problems, often faster than the long-dominant simplex and interior-point methods. The solutions found by…

Distributed machine learning workloads use data and tensor parallelism for training and inference, both of which rely on the AllReduce collective to synchronize gradients or activations. However, AllReduce algorithms are delayed by the…

We consider multigrid methods for finite volume discretizations of the Reynolds Averaged Navier-Stokes (RANS) equations for both steady and unsteady flows. We analyze the effect of different smoothers based on pseudo time iterations, such…

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider…

We present the design and optimization of a linear solver on General Purpose GPUs for the efficient and high-throughput evaluation of the marginalized graph kernel between pairs of labeled graphs. The solver implements a preconditioned…

Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…

In the finite volume framework, a Lax-Wendrof type second-order flux solver for the compressible Navier-Stokes equations is proposed by utilizing a hyperbolic relaxation model. The flux solver is developed by applying the generalized…

We present an efficient, robust and fully GPU-accelerated aggregation-based algebraic multigrid preconditioning technique for the solution of large sparse linear systems. These linear systems arise from the discretization of elliptic PDEs.…

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…

We present the GPU implementation of the general-purpose interior-point solver Clarabel for convex optimization problems with conic constraints. We introduce a mixed parallel computing strategy that processes linear constraints first, then…

3D Gaussian Splatting (3DGS) is widely used for novel view synthesis due to its high rendering quality and fast inference time. However, 3DGS predominantly relies on first-order optimizers such as Adam, which leads to long training times.…

Numerical climate- and weather-prediction requires the fast solution of the equations of fluid dynamics. Discontinuous Galerkin (DG) discretisations have several advantageous properties. They can be used for arbitrary domains and support a…

The compositional model is often used to describe multicomponent multiphase porous media flows in the petroleum industry. The fully implicit method with strong stability and weak constraints on time-step sizes is commonly used in the…

We introduce the "inverse square root linear unit" (ISRLU) to speed up learning in deep neural networks. ISRLU has better performance than ELU but has many of the same benefits. ISRLU and ELU have similar curves and characteristics. Both…

As part of the development of a Poisson solver for the spectral element discretization used in the GeoFluid Object Workbench (GeoFLOW) code, we propose a solver for the linear system arising from a Gauss-Legendre-Lobatto global spectral…