A new analytical method for parallel, diffusion-type load balancing

We propose a new proof technique which can be used to analyze many parallel load balancing algorithms. The technique is designed to handle concurrent load balancing actions, which are often the main obstacle in the analysis. We demonstrate the usefulness of the approach by analyzing various natural diffusion-type protocols. Our results are similar to, or better than, previously existing ones, while our proofs are much easier. The key idea is to first sequentialize the original, concurrent load transfers, analyze this new, sequential system, and then to bound the gap between both.

Accurate Reaction-Diffusion Operator Splitting on Tetrahedral Meshes for Parallel Stochastic Molecular Simulations

Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, meaning that the serial limit has already been reached in sub-cellular models. This calls for parallel simulations that can take advantage of the power of modern supercomputers; however exact methods are known to be inherently serial. We introduce an operator splitting implementation for irregular grids with a novel method to improve accuracy, and demonstrate potential for scalable parallel simulations in an initial MPI version. We foresee that this groundwork will enable larger scale, whole-cell stochastic simulations in the near future.Comment: 33 pages, 10 figure

Parallel and Distributed Simulation from Many Cores to the Public Cloud (Extended Version)

In this tutorial paper, we will firstly review some basic simulation concepts and then introduce the parallel and distributed simulation techniques in view of some new challenges of today and tomorrow. More in particular, in the last years there has been a wide diffusion of many cores architectures and we can expect this trend to continue. On the other hand, the success of cloud computing is strongly promoting the everything as a service paradigm. Is parallel and distributed simulation ready for these new challenges? The current approaches present many limitations in terms of usability and adaptivity: there is a strong need for new evaluation metrics and for revising the currently implemented mechanisms. In the last part of the paper, we propose a new approach based on multi-agent systems for the simulation of complex systems. It is possible to implement advanced techniques such as the migration of simulated entities in order to build mechanisms that are both adaptive and very easy to use. Adaptive mechanisms are able to significantly reduce the communication cost in the parallel/distributed architectures, to implement load-balance techniques and to cope with execution environments that are both variable and dynamic. Finally, such mechanisms will be used to build simulations on top of unreliable cloud services.Comment: Tutorial paper published in the Proceedings of the International Conference on High Performance Computing and Simulation (HPCS 2011). Istanbul (Turkey), IEEE, July 2011. ISBN 978-1-61284-382-

DisPar Methods and Their Implementation on a Heterogeneous PC Cluster

Esta dissertação avalia duas áreas cruciais da simulação de advecção- difusão. A primeira parte é dedicada a estudos numéricos. Foi comprovado que existe uma relação directa entre os momentos de deslocamento de uma partícula de poluente e os erros de truncatura. Esta relação criou os fundamentos teóricos para criar uma nova família de métodos numéricos, DisPar. Foram introduzidos e avaliados três métodos. O primeiro é um método semi-Lagrangeano 2D baseado nos momentos de deslocamento de uma partícula para malhas regulares, DisPar-k. Com este método é possível controlar explicitamente o erro de truncatura desejado. O segundo método também se baseia nos momentos de deslocamento de uma partícula, sendo, contudo, desenvolvido para malhas uniformes não regulares, DisParV. Este método também apresentou uma forte robustez numérica. Ao contrário dos métodos DisPar-K e DisParV, o terceiro segue uma aproximação Eulereana com três regiões de destino da partícula. O método foi desenvolvido de forma a manter um perfil de concentração inicial homogéneo independentemente dos parâmetros usados. A comparação com o método DisPar-k em situações não lineares realçou as fortes limitações associadas aos métodos de advecção-difusão em cenários reais. A segunda parte da tese é dedicada à implementação destes métodos num Cluster de PCs heterogéneo. Para o fazer, foi desenvolvido um novo esquema de partição, AORDA. A aplicação, Scalable DisPar, foi implementada com a plataforma da Microsoft .Net, tendo sido totalmente escrita em C#. A aplicação foi testada no estuário do Tejo que se localiza perto de Lisboa, Portugal. Para superar os problemas de balanceamento de cargas provocados pelas marés, foram implementados diversos esquemas de partição: “Scatter Partitioning”, balanceamento dinâmico de cargas e uma mistura de ambos. Pelos testes elaborados, foi possível verificar que o número de máquinas vizinhas se apresentou como o mais limitativo em termos de escalabilidade, mesmo utilizando comunicações assíncronas. As ferramentas utilizadas para as comunicações foram a principal causa deste fenómeno. Aparentemente, o Microsoft .Net remoting 1.0 não funciona de forma apropriada nos ambientes de concorrência criados pelas comunicações assíncronas. Este facto não permitiu a obtenção de conclusões acerca dos níveis relativos de escalabilidade das diferentes estratégias de partição utilizadas. No entanto, é fortemente sugerido que a melhor estratégia irá ser “Scatter Partitioning” associada a balanceamento dinâmico de cargas e a comunicações assíncronas. A técnica de “Scatter Partitioning” mitiga os problemas de desbalanceamentos de cargas provocados pelas marés. Por outro lado, o balanceamento dinâmico será essencialmente activado no inicio da simulação para corrigir possíveis problemas nas previsões dos poderes de cada processador.This thesis assesses two main areas of the advection-diffusion simulation. The first part is dedicated to the numerical studies. It has been proved that there is a direct relation between pollutant particle displacement moments and truncation errors. This relation raised the theoretical foundations to create a new family of numerical methods, DisPar. Three methods have been introduced and appraised. The first is a 2D semi- Lagrangian method based on particle displacement moments for regular grids, DisPar-k. With this method one can explicitly control the desired truncation error. The second method is also based on particle displacement moments but it is targeted to regular/non-uniform grids, DisParV. The method has also shown a strong numerical capacity. Unlike DisPar-k and DisParV, the third method is a Eulerian approximation for three particle destination units. The method was developed so that an initial concentration profile will be kept homogeneous independently of the used parameters. The comparison with DisPar-k in non-linear situations has emphasized the strong shortcomings associated with numerical methods for advection-diffusion in real scenarios. The second part of the dissertation is dedicated to the implementation of these methods in a heterogeneous PC Cluster. To do so, a new partitioning method has been developed, AORDA. The application, Scalable DisPar, was implemented with the Microsoft .Net framework and was totally written in C#. The application was tested on the Tagus Estuary, near Lisbon (Portugal). To overcome the load imbalances caused by tides scatter partitioning was implemented, dynamic load balancing and a mix of both. By the tests made, it was possible to verify that the number of neighboring machines was the main factor affecting the application scalability, even with asynchronous communications. The tools used for communications mainly caused this. Microsoft .Net remoting 1.0 does not seem to properly work in environments with concurrency associated with the asynchronous communications. This did not allow taking conclusions about the relative efficiency between the partitioning strategies used. However, it is strongly suggested that the best approach will be to scatter partitioning with dynamic load balancing and with asynchronous communications. Scatter partitioning mitigates load imbalances caused by tides and dynamic load balancing is basically trigged at the begging of the simulation to correct possible problems in processor power predictions

Designing a scalable dynamic load -balancing algorithm for pipelined single program multiple data applications on a non-dedicated heterogeneous network of workstations

Dynamic load balancing strategies have been shown to be the most critical part of an efficient implementation of various applications on large distributed computing systems. The need for dynamic load balancing strategies increases when the underlying hardware is a non-dedicated heterogeneous network of workstations (HNOW). This research focuses on the single program multiple data (SPMD) programming model as it has been extensively used in parallel programming for its simplicity and scalability in terms of computational power and memory size.;This dissertation formally defines and addresses the problem of designing a scalable dynamic load-balancing algorithm for pipelined SPMD applications on non-dedicated HNOW. During this process, the HNOW parameters, SPMD application characteristics, and load-balancing performance parameters are identified.;The dissertation presents a taxonomy that categorizes general load balancing algorithms and a methodology that facilitates creating new algorithms that can harness the HNOW computing power and still preserve the scalability of the SPMD application.;The dissertation devises a new algorithm, DLAH (Dynamic Load-balancing Algorithm for HNOW). DLAH is based on a modified diffusion technique, which incorporates the HNOW parameters. Analytical performance bound for the worst-case scenario of the diffusion technique has been derived.;The dissertation develops and utilizes an HNOW simulation model to conduct extensive simulations. These simulations were used to validate DLAH and compare its performance to related dynamic algorithms. The simulations results show that DLAH algorithm is scalable and performs well for both homogeneous and heterogeneous networks. Detailed sensitivity analysis was conducted to study the effects of key parameters on performance

A method for molecular dynamics on curved surfaces

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in the field of diffusive transport have focussed on solving the diffusion equation on curved surfaces, for which it is not tractable to incorporate particle interactions even though these play a crucial role in crowded systems. We show here that it is possible to combine standard constraint algorithms with the classical velocity Verlet scheme to perform molecular dynamics simulations of particles constrained to an arbitrarily curved surface, in which such interactions can be taken into account. Furthermore, unlike Brownian dynamics schemes in local coordinates, our method is based on Cartesian coordinates allowing for the reuse of many other standard tools without modifications, including parallelisation through domain decomposition. We show that by applying the schemes to the Langevin equation for various surfaces, confined Brownian motion is obtained, which has direct applications to many biological and physical problems. Finally we present two practical examples that highlight the applicability of the method: (i) the influence of crowding and shape on the lateral diffusion of proteins in curved membranes and (ii) the self-assembly of a coarse-grained virus capsid protein model.Comment: 30 pages, 5 figure