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

It is well known that the choice of the iterative method is crucial in determining the speed of the converged solution. This article presents a detailed comparison between several iterative techniques for solving incmopressible…

This report presents the GPU acceleration of implicit kinetic meshfree methods using modified LU-SGS algorithms. The meshfree scheme is based on the least squares kinetic upwind method (LSKUM). In the existing matrix-free LU-SGS approaches…

In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the…

In recent years, GPU-accelerated optimization solvers based on second-order methods (e.g., interior-point methods) have gained momentum with the advent of mature and efficient GPU-accelerated direct sparse linear solvers, such as cuDSS.…

The Riemann problem for first-order hyperbolic systems of partial differential equations is of fundamental importance for both theoretical and numerical purposes. Many approximate solvers have been developed for such systems; exact solution…

This paper presents a heterogeneous adaptive mesh refinement (AMR) framework for efficient simulation of moderately stiff reactive problems. This framework features an elaborate subcycling-in-time algorithm along with a specialized…

ILU(k) is a commonly used preconditioner for iterative linear solvers for sparse, non-symmetric systems. It is often preferred for the sake of its stability. We present TPILU(k), the first efficiently parallelized ILU(k) preconditioner that…

This paper deals with linear algebra operations on Graphics Processing Unit (GPU) with complex number arithmetic using double precision. An analysis of their uses within iterative Krylov methods is presented to solve acoustic problems.…

We design and investigate efficient multigrid solvers for multiphase Stokes problems discretised via mixed-degree local discontinuous Galerkin methods. Using the template of a standard multigrid V-cycle, we develop a smoother analogous to…

In geometry processing, numerical optimization methods often involve solving sparse linear systems of equations. These linear systems have a structure that strongly resembles to adjacency graphs of the underlying mesh. We observe how…

Within the framework of $ p $-adaptive flux reconstruction, we aim to construct efficient polynomial multigrid ($p$MG) preconditioners for implicit time integration of the Navier--Stokes equations using Jacobian-free Newton--Krylov (JFNK)…

The paper compares standard iterative methods for solving the generalized Stokes problem arising from the time and space approximation of the time-dependent incompressible Navier-Stokes equations. Various preconditioning techniques are…

We study the solution of block-structured linear algebra systems arising in optimization by using iterative solution techniques. These systems are the core computational bottleneck of many problems of interest such as parameter estimation,…

Low precision arithmetic, in particular half precision floating point arithmetic, is now available in commercial hardware. Using lower precision can offer significant savings in computation and communication costs with proportional savings…

Recent advances in the field of machine learning open a new era in high performance computing. Applications of machine learning algorithms for the development of accurate and cost-efficient surrogates of complex problems have already…

In this paper, we develop a new parallel auxiliary grid algebraic multigrid (AMG) method to leverage the power of graphic processing units (GPUs). In the construction of the hierarchical coarse grid, we use a simple and fixed coarsening…

This paper presents an experimental evaluation of parallel-in-time Kalman filters and smoothers using graphics processing units (GPUs). In particular, the paper evaluates different all-prefix-sum algorithms, that is, parallel scan…

In this work we present a multilayer shallow model to approximate the Navier-Stokes equations with hydrostatic pressure and the $\mu(I)$-rheology. The main advantages of this approximation are (i) the low cost associated with the numerical…

We present a scalability study of Golub-Kahan bidiagonalization for the parallel iterative solution of symmetric indefinite linear systems with a 2x2 block structure. The algorithms have been implemented within the parallel numerical…

Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…