Modelling binary alloy solidification with adaptive mesh refinement

The solidification of a binary alloy results in the formation of a porous mushy layer, within which spontaneous localisation of fluid flow can lead to the emergence of features over a range of spatial scales. We describe a finite volume method for simulating binary alloy solidification in two dimensions with local mesh refinement in space and time. The coupled heat, solute, and mass transport is described using an enthalpy method with flow described by a Darcy-Brinkman equation for flow across porous and liquid regions. The resulting equations are solved on a hierarchy of block-structured adaptive grids. A projection method is used to compute the fluid velocity, whilst the viscous and nonlinear diffusive terms are calculated using a semi-implicit scheme. A series of synchronization steps ensure that the scheme is flux-conservative and correct for errors that arise at the boundaries between different levels of refinement. We also develop a corresponding method using Darcy's law for flow in a porous medium/narrow Hele-Shaw cell. We demonstrate the accuracy and efficiency of our method using established benchmarks for solidification without flow and convection in a fixed porous medium, along with convergence tests for the fully coupled code. Finally, we demonstrate the ability of our method to simulate transient mushy layer growth with narrow liquid channels which evolve over time

Parallel Processes in HPX: Designing an Infrastructure for Adaptive Resource Management

Advancement in cutting edge technologies have enabled better energy efficiency as well as scaling computational power for the latest High Performance Computing(HPC) systems. However, complexity, due to hybrid architectures as well as emerging classes of applications, have shown poor computational scalability using conventional execution models. Thus alternative means of computation, that addresses the bottlenecks in computation, is warranted. More precisely, dynamic adaptive resource management feature, both from systems as well as application\u27s perspective, is essential for better computational scalability and efficiency. This research presents and expands the notion of Parallel Processes as a placeholder for procedure definitions, targeted at one or more synchronous domains, meta data for computation and resource management as well as infrastructure for dynamic policy deployment. In addition to this, the research presents additional guidelines for a framework for resource management in HPX runtime system. Further, this research also lists design principles for scalability of Active Global Address Space (AGAS), a necessary feature for Parallel Processes. Also, to verify the usefulness of Parallel Processes, a preliminary performance evaluation of different task scheduling policies is carried out using two different applications. The applications used are: Unbalanced Tree Search, a reference dynamic graph application, implemented by this research in HPX and MiniGhost, a reference stencil based application using bulk synchronous parallel model. The results show that different scheduling policies provide better performance for different classes of applications; and for the same application class, in certain instances, one policy fared better than the others, while vice versa in other instances, hence supporting the hypothesis of the need of dynamic adaptive resource management infrastructure, for deploying different policies and task granularities, for scalable distributed computing

Doctor of Philosophy

dissertationSolutions to Partial Di erential Equations (PDEs) are often computed by discretizing the domain into a collection of computational elements referred to as a mesh. This solution is an approximation with an error that decreases as the mesh spacing decreases. However, decreasing the mesh spacing also increases the computational requirements. Adaptive mesh re nement (AMR) attempts to reduce the error while limiting the increase in computational requirements by re ning the mesh locally in regions of the domain that have large error while maintaining a coarse mesh in other portions of the domain. This approach often provides a solution that is as accurate as that obtained from a much larger xed mesh simulation, thus saving on both computational time and memory. However, historically, these AMR operations often limit the overall scalability of the application. Adapting the mesh at runtime necessitates scalable regridding and load balancing algorithms. This dissertation analyzes the performance bottlenecks for a widely used regridding algorithm and presents two new algorithms which exhibit ideal scalability. In addition, a scalable space- lling curve generation algorithm for dynamic load balancing is also presented. The performance of these algorithms is analyzed by determining their theoretical complexity, deriving performance models, and comparing the observed performance to those performance models. The models are then used to predict performance on larger numbers of processors. This analysis demonstrates the necessity of these algorithms at larger numbers of processors. This dissertation also investigates methods to more accurately predict workloads based on measurements taken at runtime. While the methods used are not new, the application of these methods to the load balancing process is. These methods are shown to be highly accurate and able to predict the workload within 3% error. By improving the accuracy of these estimations, the load imbalance of the simulation can be reduced, thereby increasing the overall performance

Enhancing productivity and performance portability of opencl applications on heterogeneous systems using runtime optimizations

Initially driven by a strong need for increased computational performance in science and engineering, heterogeneous systems have become ubiquitous and they are getting increasingly complex. The single processor era has been replaced with multi-core processors, which have quickly been surrounded by satellite devices aiming to increase the throughput of the entire system. These auxiliary devices, such as Graphics Processing Units, Field Programmable Gate Arrays or other specialized processors have very different architectures. This puts an enormous strain on programming models and software developers to take full advantage of the computing power at hand. Because of this diversity and the unachievable flexibility and portability necessary to optimize for each target individually, heterogeneous systems remain typically vastly under-utilized. In this thesis, we explore two distinct ways to tackle this problem. Providing automated, non intrusive methods in the form of compiler tools and implementing efficient abstractions to automatically tune parameters for a restricted domain are two complementary approaches investigated to better utilize compute resources in heterogeneous systems. First, we explore a fully automated compiler based approach, where a runtime system analyzes the computation flow of an OpenCL application and optimizes it across multiple compute kernels. This method can be deployed on any existing application transparently and replaces significant software engineering effort spent to tune application for a particular system. We show that this technique achieves speedups of up to 3x over unoptimized code and an average of 1.4x over manually optimized code for highly dynamic applications. Second, a library based approach is designed to provide a high level abstraction for complex problems in a specific domain, stencil computation. Using domain specific techniques, the underlying framework optimizes the code aggressively. We show that even in a restricted domain, automatic tuning mechanisms and robust architectural abstraction are necessary to improve performance. Using the abstraction layer, we demonstrate strong scaling of various applications to multiple GPUs with a speedup of up to 1.9x on two GPUs and 3.6x on four