Parallel unstructured solvers for linear partial differential equations

This thesis presents the development of a parallel algorithm to solve symmetric systems of linear equations and the computational implementation of a parallel partial differential equations solver for unstructured meshes. The proposed method, called distributive conjugate gradient - DCG, is based on a single-level domain decomposition method and the conjugate gradient method to obtain a highly scalable parallel algorithm. An overview on methods for the discretization of domains and partial differential equations is given. The partition and refinement of meshes is discussed and the formulation of the weighted residual method for two- and three-dimensions presented. Some of the methods to solve systems of linear equations are introduced, highlighting the conjugate gradient method and domain decomposition methods. A parallel unstructured PDE solver is proposed and its actual implementation presented. Emphasis is given to the data partition adopted and the scheme used for communication among adjacent subdomains is explained. A series of experiments in processor scalability is also reported. The derivation and parallelization of DCG are presented and the method validated throughout numerical experiments. The method capabilities and limitations were investigated by the solution of the Poisson equation with various source terms. The experimental results obtained using the parallel solver developed as part of this work show that the algorithm presented is accurate and highly scalable, achieving roughly linear parallel speed-up in many of the cases tested

Parallel unstructured solvers for linear partial differential equations

This thesis presents the development of a parallel algorithm to solve symmetric systems of linear equations and the computational implementation of a parallel partial differential equations solver for unstructured meshes. The proposed method, called distributive conjugate gradient - DCG, is based on a single-level domain decomposition method and the conjugate gradient method to obtain a highly scalable parallel algorithm. An overview on methods for the discretization of domains and partial differential equations is given. The partition and refinement of meshes is discussed and the formulation of the weighted residual method for two- and three-dimensions presented. Some of the methods to solve systems of linear equations are introduced, highlighting the conjugate gradient method and domain decomposition methods. A parallel unstructured PDE solver is proposed and its actual implementation presented. Emphasis is given to the data partition adopted and the scheme used for communication among adjacent subdomains is explained. A series of experiments in processor scalability is also reported. The derivation and parallelization of DCG are presented and the method validated throughout numerical experiments. The method capabilities and limitations were investigated by the solution of the Poisson equation with various source terms. The experimental results obtained using the parallel solver developed as part of this work show that the algorithm presented is accurate and highly scalable, achieving roughly linear parallel speed-up in many of the cases tested.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Accounting and Statistical Analyses for Sustainable Development

In this Open Access publication Claudia Lemke develops a comprehensive Multi-Level Sustainable Development Index (MLSDI) that is applicable to micro, meso, and macro objects by conducting methodological and empirical research. Multi-level comparability is crucial because the Sustainable Development Goals (SDGs) at macro level can only be achieved if micro and meso objects contribute. The author shows that a novel information-theoretic algorithm outperforms established multivariate statistical weighting methods such as the principal component analysis (PCA). Overcoming further methodological shortcomings of previous sustainable development indices, the MLSDI avoids misled managerial and political decision making

Efficient, concurrent Bayesian analysis of full waveform LaDAR data

Bayesian analysis of full waveform laser detection and ranging (LaDAR) signals using reversible jump Markov chain Monte Carlo (RJMCMC) algorithms have shown higher estimation accuracy, resolution and sensitivity to detect weak signatures for 3D surface profiling, and construct multiple layer images with varying number of surface returns. However, it is computational expensive. Although parallel computing has the potential to reduce both the processing time and the requirement for persistent memory storage, parallelizing the serial sampling procedure in RJMCMC is a significant challenge in both statistical and computing domains. While several strategies have been developed for Markov chain Monte Carlo (MCMC) parallelization, these are usually restricted to fixed dimensional parameter estimates, and not obviously applicable to RJMCMC for varying dimensional signal analysis. In the statistical domain, we propose an effective, concurrent RJMCMC algorithm, state space decomposition RJMCMC (SSD-RJMCMC), which divides the entire state space into groups and assign to each an independent RJMCMC chain with restricted variation of model dimensions. It intrinsically has a parallel structure, a form of model-level parallelization. Applying the convergence diagnostic, we can adaptively assess the convergence of the Markov chain on-the-fly and so dynamically terminate the chain generation. Evaluations on both synthetic and real data demonstrate that the concurrent chains have shorter convergence length and hence improved sampling efficiency. Parallel exploration of the candidate models, in conjunction with an error detection and correction scheme, improves the reliability of surface detection. By adaptively generating a complimentary MCMC sequence for the determined model, it enhances the accuracy for surface profiling. In the computing domain, we develop a data parallel SSD-RJMCMC (DP SSD-RJMCMCU) to achieve efficient parallel implementation on a distributed computer cluster. Adding data-level parallelization on top of the model-level parallelization, it formalizes a task queue and introduces an automatic scheduler for dynamic task allocation. These two strategies successfully diminish the load imbalance that occurred in SSD-RJMCMC. Thanks to the coarse granularity, the processors communicate at a very low frequency. The MPIbased implementation on a Beowulf cluster demonstrates that compared with RJMCMC, DP SSD-RJMCMCU has further reduced problem size and computation complexity. Therefore, it can achieve a super linear speedup if the number of data segments and processors are chosen wisely