Coarse grain parallel finite element simulations for incompressible flows

Abstract

Parallel simulation of incompressible uid ows is considered on networks of homogeneous workstations. Coarse-grain parallelization of a Taylor-Galerkin=pressure-correction ÿnite element algorithm are discussed, taking into account network communication costs. The main issues include the parallelization of system assembly, and iterative and direct solvers, that are of common interest to ÿnite element and general numerical computation. The parallelization strategies are implemented on a Sun workstation cluster using the Parallel Virtual Machine (PVM) message passing library. Test results are obtained with a maximum of nineteen workstations and various PVM conÿgurations are exhibited. Parallel e ciency close to ideal has been achieved for some strategies adopted. It is suggested that load balancing may not always be beneÿcial on distributed platforms with broadcasting communication connection. ? 1998 John Wiley & Sons, Ltd.

Sub-cell approximations for viscoelastic flows—filament stretching

“…This efficient element-by-element procedure is space optimal, reflecting overall linear space complexity in nodal degrees of freedom, and linear time-complexity per time-step. The Jacobi scheme is an appropriate choice, being wellsuited for parallelisation (see Grant et al [7]) and for these mass-matrix equations, along with their suitable conditioning properties. In contrast, a direct scheme Choleski reduction is employed at stage two, to compute the pressure-difference over the time-step.…”

Distributed parallel computation for complex rotational flows of non‐Newtonian fluids

“…Here, this involves a parallelised timemarching finite element algorithm. This algorithm follows a so-called fractionalstaged semi-implicit Taylor-Galerkin/pressure-correction scheme, par-TGPC [3,5,10,11]. In this algorithm temporal domain discretisation is achieved adopting a Taylor series expansion in time, prior to spatial discretisation.…”

“…It is upon this basis that the present parallel performance characteristics are achieved. A comprehensive description on the parallelisation of par-TGPC and the algebraic solution procedures is given in [11]. Briefly, both direct and iterative procedures necessitate an assembly and solution phase, involving finite element loop construction of right-hand-side vectors and matrix components.…”

“…The discrete problem may be posed in either coupled form, leading to large system matrices, or alternatively, in decoupled mode which may be handled iteratively. In the viscoelastic domain, examples of using PVM for parallelising numerical codes are described in [8][9][10][11]. In [8], two-dimensional steady-state solutions for entry flow and stick-slip flow problems were obtained employing POLYFLOW code with a finite element algorithm.…”

“…In [10,11], we described the parallel implementation of the present TGPC algorithm for inelastic fluids and flow past a rigid sphere in a tube employing unstructured meshes. Parallelisation was achieved via FORTRAN 77 code, using PVM on a cluster of diskless Sun Sparc-1 workstations, based upon paradigms of domain decomposition and a degree-of-freedom approach.…”