An extension of the deterministic variational multiscale (VMS) approach with algebraic subgrid scale (SGS) modeling is considered for developing stabilized finite element formulations for the linear stochastic scalar advection-diffusion equation and the incompressible stochastic Navier-Stokes equations. The stabilized formulations are numerically implemented using the spectral stochastic formul...

A new ®nite element model has been developed to simulate two-dimensional free surface ̄ow in rivers and estuaries. The variables of the model are the speci®c discharge and the water level. The algorithm takes into account the natural boundaries of the ̄ow, de®ned by the contour lines of zero depth, with a new approach that accepts positive and negative values for the water depth. In this way, we...

The effective use of parallelized hardware is an important goal of today’s computer developments. Nvidia GPUs are an important footing in this context. While CUDA implemented algorithms focus on detailed optimized usage of GPU elements the pragma directive parallelization targets GPU computation for a broader community. In this paper we focus on the implementation of OpenACC and OpenMP 4.5 para...

We conduct simulations for the unsteady state anisotropic diffusion process in the human brain by discretizing the governing diffusion equation on a face-centered cubic grid and adopting a high performance differential-algebraic equation solver, IDA, to deal with the resulting large-scale system of DAEs. Incomplete LU preconditioning techniques are used with the GMRES method to accelerate the c...

We present a distributed parallel mesh curving method for virtual geometry. The main application is to generate large-scale curved meshes on complex geometry suitable analysis with unstructured high-order methods. Accordingly, we devise the technique geometrically accurate composed of high-quality elements. To this end, advocate degree continuation penalty-based second-order optimizer that uses...

We present a new solver for massively parallel simulations of fully three-dimensional multiphase flows. The solver runs on a variety of computer architectures from laptops to supercomputers and on 65536 threads or more (limited only by the availability to us of more threads). The code is wholly written by the authors in Fortran 2003 and uses a domain decomposition strategy for parallelization w...

The convergence of the restarted GMRES method can be significantly improved, for some problems, by using a weighted inner product that changes at each restart. How does this weighting affect convergence, and when is it useful? We show that weighted inner products can help in two distinct ways: when the coefficient matrix has localized eigenvectors, weighting can allow restarted GMRES to focus o...

We consider the solution of a linear system of equations using the GMRES iterative method. In [3], a strategy to relax the accuracy of the matrix-vector product is proposed for general systems and illustrated on a large set of numerical experiments. This work is based on some heuristic considerations and proposes a strategy that often enables a convergence of the GMRES iterates xk within a rela...

Linear systems are required to solve in many scientific applications and the solution of these systems often dominates the total running time. In this paper, we introduce our work on developing parallel linear solvers and preconditioners for solving large sparse linear systems using NVIDIA GPUs. We develop a new sparse matrix-vector multiplication kernel and a sparse BLAS library for GPUs. Base...

This paper presents a numerical study of the 3D ow around a cylinder which was de ned as a benchmark problem for the steady state Navier–Stokes equations within the DFG high-priority research program ow simulation with high-performance computers by Sch afer and Turek (Vol. 52, Vieweg: Braunschweig, 1996). The rst part of the study is a comparison of several nite element discretizations with res...