Parallel optimisation algorithms for multilevel mesh partitioning

Three parallel optimisation algorithms, for use in the context of multilevel graph partitioning of unstructured meshes, are described. The first, interface optimisation, reduces the computation to a set of independent optimisation problems in interface regions. The next, alternating optimisation, is a restriction of this technique in which mesh entities are only allowed to migrate between subdomains in one direction. The third treats the gain as a potential field and uses the concept of relative gain for selecting appropriate vertices to migrate. The results are compared and seen to produce very high global quality partitions, very rapidly. The results are also compared with another partitioning tool and shown to be of higher quality although taking longer to compute.

Multiphase mesh partitioning

We consider the load-balancing problems which arise from parallel scientific codes containing multiple computational phases, or loops over subsets of the data, which are separated by global synchronisation points. We motivate, derive and describe the implementation of an approach which we refer to as the multiphase mesh partitioning strategy to address such issues. The technique is tested on several examples of meshes, both real and artificial, containing multiple computational phases and it is demonstrated that our method can achieve high quality partitions where a standard mesh partitioning approach fails.

SMARTFIRE: an integrated computational fluid dynamics code and expert system for fire field modelling

SMARTFIRE, an open architecture integrated CFD code and knowledge based system attempts to make fire field modeling accessible to non-experts in Computational Fluid Dynamics (CFD) such as fire fighters, architects and fire safety engineers. This is achieved by embedding expert knowledge into CFD software. This enables the 'black-art' associated with the CFD analysis such as selection of solvers, relaxation parameters, convergence criteria, time steps, grid and boundary condition specification to be guided by expert advice from the software. The user is however given the option of overriding these decisions, thus retaining ultimate control. SMARTFIRE also makes use of recent developments in CFD technology such as unstructured meshes and group solvers in order to make the CFD analysis more efficient. This paper describes the incorporation within SMARTFIRE of the expert fire modeling knowledge required for automatic problem setup and mesh generation as well as the concept and use of group solvers for automatic and manual dynamic control of the CFD code.

Load-balancing for mesh-based applications on heterogeneous cluster computers

This paper discusses load-balancing issues when using heterogeneous cluster computers. There is a growing trend towards the use of commodity microprocessor clusters. Although today's microprocessors have reached a theoretical peak performance in the range of one GFLOPS/s, heterogeneous clusters of commodity processors are amongst the most challenging parallel systems to programme efficiently. We will outline an approach for optimising the performance of parallel mesh-based applications for heterogeneous cluster computers and present case studies with the GeoFEM code. The focus is on application cost monitoring and load balancing using the DRAMA library.

Multilevel mesh partitioning for heterogeneous communication networks

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem for distributing unstructured meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimisation method which refines the partition at each graph level. To date these algorithms have been used almost exclusively to minimise the cut edge weight in the graph with the aim of minimising the parallel communication overhead, but recently there has been a perceived need to take into account the communications network of the parallel machine. For example the increasing use of SMP clusters (systems of multiprocessor compute nodes with very fast intra-node communications but relatively slow inter-node networks) suggest the use of hierarchical network models. Indeed this requirement is exacerbated in the early experiments with meta-computers (multiple supercomputers combined together, in extreme cases over inter-continental networks). In this paper therefore, we modify a multilevel algorithm in order to minimise a cost function based on a model of the communications network. Several network models and variants of the algorithm are tested and we establish that it is possible to successfully guide the optimisation to reflect the chosen architecture.

Multiphase mesh partitioning for parallel computational mechanics codes

We consider the load-balancing problems which arise from parallel scientific codes containing multiple computational phases, or loops over subsets of the data, which are separated by global synchronisation points. We motivate, derive and describe the implementation of an approach which we refer to as the multiphase mesh partitioning strategy to address such issues. The technique is tested on example meshes containing multiple computational phases and it is demonstrated that our method can achieve high quality partitions where a standard mesh partitioning approach fails.

Characterisation of weldpool shapes in the laser welding of thick plates

We consider the problem of finding the heat distribution and the shape of the liquid fraction during laser welding of a thick steel plate using the finite volume CFD package PHYSICA. Since the shape of the keyhole is not known in advance, the following two-step approach to handling this problem has been employed. In the first stage, we determine the geometry of the keyhole for the steady-state case and form an appropriate mesh that includes both the workpiece and the keyhole. In the second stage, we impose the boundary conditions by assigning temperature to the walls of the keyhole and find the heat distribution and the shape of the liquid fraction for a given welding speed and material properties. We construct a fairly accurate approximation of the keyhole as a sequence of include sliced cones. A formula for finding the initial radius of the keyhole is derived by determining the radius of the vaporisation isotherm for the line heat source. We report on the results of a series of computational experiments for various heat input values and welding velocities.

Three-phase computations of the continuous casting process

In this paper, the continuous casting process for steel slab production is modelled using a mult-physics approach. For this purpose, a Finite Volume (FV) numerical model was constructed in 3D, with the following characteristics: Time dependent, turbulent fluid flow and heat transfer in the molten steel and flux regions, solidification of the skin layer, under prescribed heat loss boundary conditions, particle tracking simulation of argon bubbles injected with the metal into the mould, full coupling between bubbles and liquid through buoyancy and interfacial forces using a novel gas accumulation technique, and a full transient simulation of flux-metal interface behaviour under the influence of gravity and fluid inertial forces and bubble plume buoyancy. The unstructure mesh FV code PHYSICA developed at Greenwich was used for carry out the simulations with physical process data and properties supplied by IRSID SA.

Dynamic fluid–structure interaction using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: • a single mesh covering the entire domain, • a Navier–Stokes flow, • a single FV-UM discretisation approach for both the flow and solid mechanics procedures, • an implicit predictor–corrector version of the Newmark algorithm, • a single code embedding the whole strategy.

A finite volume unstructured mesh approach to dynamic fluid-structure interaction: an assessment of the challenge of flutter analysis

Computational modelling of dynamic fluid-structure interaction (DFSI) is problematical since conventionally computational fluid dynamics (CFD) is solved using finite volume (FV) methods and computational structural mechanics (CSM) is based entirely on finite element (FE) methods. Hence, progress in modelling the emerging multi-physics problem of dynamic fluid-structure interaction in a consistent manner is frustrated and significant problems in computation convergence may be encountered in transferring and filtering data from one mesh and solution procedure to another, unless the fluid-structure coupling is either one way, very weak or both. This paper sets out the solution procedure for modelling the multi-physics dynamic fluid-structure interaction problem within a single software framework PHYSICA, using finite volume, unstructured mesh (FV-UM) procedures and will focus upon some of the problems and issues that have to be resolved for time accurate closely coupled dynamic fluid-structure flutter analysis.

Dynamic fluid-structure interactions using finite volume unstructured mesh procedures

A three-dimensional finite volume, unstructured mesh (FV-UM) method for dynamic fluid–structure interaction (DFSI) is described. Fluid structure interaction, as applied to flexible structures, has wide application in diverse areas such as flutter in aircraft, wind response of buildings, flows in elastic pipes and blood vessels. It involves the coupling of fluid flow and structural mechanics, two fields that are conventionally modelled using two dissimilar methods, thus a single comprehensive computational model of both phenomena is a considerable challenge. Until recently work in this area focused on one phenomenon and represented the behaviour of the other more simply. More recently, strategies for solving the full coupling between the fluid and solid mechanics behaviour have been developed. A key contribution has been made by Farhat et al. [Int. J. Numer. Meth. Fluids 21 (1995) 807] employing FV-UM methods for solving the Euler flow equations and a conventional finite element method for the elastic solid mechanics and the spring based mesh procedure of Batina [AIAA paper 0115, 1989] for mesh movement. In this paper, we describe an approach which broadly exploits the three field strategy described by Farhat for fluid flow, structural dynamics and mesh movement but, in the context of DFSI, contains a number of novel features: a single mesh covering the entire domain, a Navier–Stokes flow, a single FV-UM discretisation approach for both the flow and solid mechanics procedures, an implicit predictor–corrector version of the Newmark algorithm, a single code embedding the whole strategy.

Parallel mesh partitioning on distributed memory systems

The problem of deriving parallel mesh partitioning algorithms for mapping unstructured meshes to parallel computers is discussed in this chapter. In itself this raises a paradox - we seek to find a high quality partition of the mesh, but to compute it in parallel we require a partition of the mesh. In fact, we overcome this difficulty by deriving an optimisation strategy which can find a high quality partition even if the quality of the initial partition is very poor and then use a crude distribution scheme for the initial partition. The basis of this strategy is to use a multilevel approach combined with local refinement algorithms. Three such refinement algorithms are outlined and some example results presented which show that they can produce very high global quality partitions, very rapidly. The results are also compared with a similar multilevel serial partitioner and shown to be almost identical in quality. Finally we consider the impact of the initial partition on the results and demonstrate that the final partition quality is, modulo a certain amount of noise, independent of the initial partition.

Dynamic mesh partitioning and load-balancing for parallel computational mechanics codes

In this Chapter we discuss the load-balancing issues arising in parallel mesh based computational mechanics codes for which the processor loading changes during the run. We briefly touch on geometric repartitioning ideas and then focus on different ways of using a graph both to solve the load-balancing problem and the optimisation problem, both locally and globally. We also briefly discuss whether repartitioning is always valid. Sample illustrative results are presented and we conclude that repartitioning is an attractive option if the load changes are not too dramatic and that there is a certain trade-off between partition quality and volume of data that the underlying application needs to migrate.

Collaborating components in mesh-based electronic packaging

From the model geometry creation to the model analysis, the stages in between such as mesh generation are the most manpower intensive phase in a mesh-based computational mechanics simulation process. On the other hand the model analysis is the most computing intensive phase. Advanced computational hardware and software have significantly reduced the computing time - and more importantly the trend is downward. With the kind of models envisaged coming, which are larger, more complex in geometry and modelling, and multiphysics, there is no clear trend that the manpower intensive phase is to decrease significantly in time - in the present way of operation it is more likely to increase with model complexity. In this paper we address this dilemma in collaborating components for models in electronic packaging application.

A two dimensional unstructured staggered mesh method with special treatment of tangential velocity

A two dimensional staggered unstructured discretisation scheme for the solution of fluid flow problems has been developed. This scheme stores and solves the velocity vector resolutes normal and parallel to each cell face and other scalar variables (pressure, temperature) are stored at cell centres. The coupled momentum; continuity and energy equations are solved, using the well known pressure correction algorithm SIMPLE. The method is tested for accuracy and convergence behaviour against standard cell-centre solutions in a number of benchmark problems: The Lid-Driven Cavity, Natural Convection in a Cavity and the Melting of Gallium in a rectangular domain.