The parallel edge-based solution of 3D incompressible Navier-Stokes equations is presented. The governing partial differential equations are discretized using the SUPG/PSPG stabilized finite element method [5] on unstructured grids. The resulting fully coupled nonlinear system of equations is solved by the inexact Newton-Krylov method [1]. Matrix-vector products within GMRES are computed edge-b...

In this paper a novel Boundary Element (BE) formulation for sensitivity analysis of local active noise control in a three-dimensional field is presented. The formulation is based on the Helmholtz differential equation and it is valid for internal as well as for scattering wave propagation problems. The primary noise is attenuated within an enclosure, called control volume, by adding a control s...

Many computational algorithms in science and engineering give rise to large sparse linear systems of equations which need to be solved as efficiently as possible. As the size of the problems of interest increases, it becomes necessary to consider exploiting multiprocessors to solve these systems. This paper reports on the implementation of a parallel solver for sparse linear systems of equation...

We demonstrate algorithm-based fault tolerance for silent, transient data corruption in “black-box” preconditioners. We consider both additive Schwarz domain decomposition with an ILU(k) subdomain solver, and algebraic multigrid, both implemented in the Trilinos library. We evaluate faults that corrupt preconditioner results in both single and multiple MPI ranks. We then analyze how our approac...

The present paper describes the development and the performance of parallel FEM software for solving various CFD problems. Domain decomposition strategy and parallel iterative GMRES solver have been adapted to the universal space-time FEM code FEMTOOL, which allows implementation of any partial differential equation with minor expenses. The developed data structures, the static load balancing a...

This paper introduces the recursive sweeping preconditioner for the numerical solu4 tion of the Helmholtz equation in 3D. This is based on the earlier work of the sweeping preconditioner 5 with the moving perfectly matched layers (PMLs). The key idea is to apply the sweeping precondi6 tioner recursively to the quasi-2D auxiliary problems introduced in the 3D sweeping preconditioner. 7 Compared ...

A simulator, which includes a full three dimensional, multi-component and three phase model for secondary oil migration is used to study ow through fractured and faulted regions. A control volume discretization is used to discretize the strongly coupled system of partial diierential equations the model creates. Non-regular and non-matching local grid reenement (LGR) is used in critical areas to...

Abstract In this paper, we will report our recent efforts to apply a Schur complement method for nonlinear hyperbolic problems. We use the finite volume method and an implicit version of the Roe approximate Riemann solver. With the interface variable introduced in [4] in the context of single phase flows, we are able to simulate twofluid models ([12]) with various schemes such as upwind, center...

In this paper, we extend our work for the heat equation in [4] and for the Stokes equations in [5] to the nonstationary Navier-Stokes equations in two dimensions. We examine continuous Galerkin-Petrov (cGP) time discretization schemes for nonstationary incompressible flow. In particular, we implement and analyze numerically the higher order cGP(2)-method. For the space discretization, we use th...

The paper introduces the sweeping preconditioner, which is highly efficient for iterative solutions of the variable-coefficient Helmholtz equation including veryhigh-frequency problems. The first central idea of this novel approach is to construct an approximate factorization of the discretized Helmholtz equation by sweeping the domain layer by layer, starting from an absorbing layer or boundar...