Three-dimensional free surface modelling in an unstructured mesh environment for metal processing applications

In the casting of metals, tundish flow, welding, converters, and other metal processing applications, the behaviour of the fluid surface is important. In aluminium alloys, for example, oxides formed on the surface may be drawn into the body of the melt where they act as faults in the solidified product affecting cast quality. For this reason, accurate description of wave behaviour, air entrapment, and other effects need to be modelled, in the presence of heat transfer and possibly phase change. The authors have developed a single-phase algorithm for modelling this problem. The Scalar Equation Algorithm (SEA) (see Refs. 1 and 2), enables the transport of the property discontinuity representing the free surface through a fixed grid. An extension of this method to unstructured mesh codes is presented here, together with validation. The new method employs a TVD flux limiter in conjunction with a ray-tracing algorithm, to ensure a sharp bound interface. Applications of the method are in the filling and emptying of mould cavities, with heat transfer and phase change.

Converting best manual practice into generic automatable strategies for unstructured mesh parallelisation

The manual effort required to convert sequential computational mechanics programs into a useful, scalable parallel form is considerable. Tools that can assist in the conversion process are clearly required. Computer aided parallelisation tools (CAPTools) have been developed to generate efficient parallel code for real world structured grid application codes such as Computational Fluid Dynamics. Automatable single-program multi-data (SPMD) overlapping domain decomposition (DD) techniques established for structured grid codes have been adapted by the authors to manually parallelise unstructured mesh applications. Inspector loops have been used to provide generic techniques for the run-time support necessary to extend the capabilities of CAPTools to automatic implementation of SPMD DD techniques in the parallelisation of unstructured mesh codes. Copyright © 1999 John Wiley & Sons, Ltd.

Multilevel mesh partitioning for optimizing domain shape

Multilevel algorithms are a successful class of optimization techniques that address the mesh partitioning problem for mapping meshes onto parallel computers. They usually combine a graph contraction algorithm together with a local optimization method that refines the partition at each graph level. To date, these algorithms have been used almost exclusively to minimize the cut-edge weight in the graph with the aim of minimizing the parallel communication overhead. However, it has been shown that for certain classes of problems, the convergence of the underlying solution algorithm is strongly influenced by the shape or aspect ratio of the subdomains. Therefore, in this paper, the authors modify the multilevel algorithms to optimize a cost function based on the aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Staggered-mesh computation for aerodynamic sound

For the numerical solution of the linearized Euler equations, an optimized computational scheme is considered. It is based on fully staggered (in space and time) regular meshes and on a simple mirroring procedure at the stepwise solid walls. There is no need to define ghost points into the solid ohjects that reflect the sound waves. Test results demonstrate the accuracy of the method that may be used for aeroacoustic problems with complex geometries.

A scalable strategy for the parallelization of multiphysics unstructured mesh-iterative codes on distributed-memory systems

Realizing scalable performance on high performance computing systems is not straightforward for single-phenomenon codes (such as computational fluid dynamics [CFD]). This task is magnified considerably when the target software involves the interactions of a range of phenomena that have distinctive solution procedures involving different discretization methods. The problems of addressing the key issues of retaining data integrity and the ordering of the calculation procedures are significant. A strategy for parallelizing this multiphysics family of codes is described for software exploiting finite-volume discretization methods on unstructured meshes using iterative solution procedures. A mesh partitioning-based SPMD approach is used. However, since different variables use distinct discretization schemes, this means that distinct partitions are required; techniques for addressing this issue are described using the mesh-partitioning tool, JOSTLE. In this contribution, the strategy is tested for a variety of test cases under a wide range of conditions (e.g., problem size, number of processors, asynchronous / synchronous communications, etc.) using a variety of strategies for mapping the mesh partition onto the processor topology.

An automatable generic strategy for dynamic load balancing in parallel structured mesh CFD codes

Parallel computing is now widely used in numerical simulation, particularly for application codes based on finite difference and finite element methods. A popular and successful technique employed to parallelize such codes onto large distributed memory systems is to partition the mesh into sub-domains that are then allocated to processors. The code then executes in parallel, using the SPMD methodology, with message passing for inter-processor interactions. In order to improve the parallel efficiency of an imbalanced structured mesh CFD code, a new dynamic load balancing (DLB) strategy has been developed in which the processor partition range limits of just one of the partitioned dimensions uses non-coincidental limits, as opposed to coincidental limits. The ‘local’ partition limit change allows greater flexibility in obtaining a balanced load distribution, as the workload increase, or decrease, on a processor is no longer restricted by the ‘global’ (coincidental) limit change. The automatic implementation of this generic DLB strategy within an existing parallel code is presented in this chapter, along with some preliminary results.

Automatic and effective multi-dimensional parallelisation of structured mesh based codes

The most common parallelisation strategy for many Computational Mechanics (CM) (typified by Computational Fluid Dynamics (CFD) applications) which use structured meshes, involves a 1D partition based upon slabs of cells. However, many CFD codes employ pipeline operations in their solution procedure. For parallelised versions of such codes to scale well they must employ two (or more) dimensional partitions. This paper describes an algorithmic approach to the multi-dimensional mesh partitioning in code parallelisation, its implementation in a toolkit for almost automatically transforming scalar codes to parallel form, and its testing on a range of ‘real-world’ FORTRAN codes. The concept of multi-dimensional partitioning is straightforward, but non-trivial to represent as a sufficiently generic algorithm so that it can be embedded in a code transformation tool. The results of the tests on fine real-world codes demonstrate clear improvements in parallel performance and scalability (over a 1D partition). This is matched by a huge reduction in the time required to develop the parallel versions when hand coded – from weeks/months down to hours/days.

Multilevel mesh partitioning for optimising aspect ratio

Multilevel algorithms are a successful class of optimisation techniques which address the mesh partitioning problem. 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, however it has been shown that for certain classes of solution algorithm, the convergence of the solver is strongly influenced by the subdomain aspect ratio. In this paper therefore, we modify the multilevel algorithms in order to optimise a cost function based on aspect ratio. Several variants of the algorithms are tested and shown to provide excellent results.

Mesh partitioning: a multilevel balancing and refinement algorithm

Multilevel algorithms are a successful class of optimization techniques which addresses the mesh partitioning problem. They usually combine a graph contraction algorithm together with a local optimization method which refines the partition at each graph level. In this paper we present an enhancement of the technique which uses imbalance to achieve higher quality partitions. We also present a formulation of the Kernighan-Lin partition optimization algorithm which incorporates load-balancing. The resulting algorithm is tested against a different but related state-of-the-art partitioner and shown to provide improved results.

Shape-optimized mesh partitioning and load balancing for parallel adaptive FEM

We present a dynamic distributed load balancing algorithm for parallel, adaptive Finite Element simulations in which we use preconditioned Conjugate Gradient solvers based on domain-decomposition. The load balancing is designed to maintain good partition aspect ratio and we show that cut size is not always the appropriate measure in load balancing. Furthermore, we attempt to answer the question why the aspect ratio of partitions plays an important role for certain solvers. We define and rate different kinds of aspect ratio and present a new center-based partitioning method of calculating the initial distribution which implicitly optimizes this measure. During the adaptive simulation, the load balancer calculates a balancing flow using different versions of the diffusion algorithm and a variant of breadth first search. Elements to be migrated are chosen according to a cost function aiming at the optimization of subdomain shapes. Experimental results for Bramble's preconditioner and comparisons to state-of-the-art load balancers show the benefits of the construction.

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.

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.