A very common and relevant concern in the most disparate applications in Computer Science, scientific and engineering modelling, is to have robust, reliable tools for fast computations. Two main factors contribute to this purpose: algorithms having low computational and communication costs, and the availability of architectures for high performance computing. A wide set of problems relies more or less explicitly on computational Linear Algebra in order to simplify problems whose symbolic solution would be prohibitively time requiring for computers. For this reason computational Linear Algebra is continuously evoked in numerical Calculus in order to solve scientific and engineering problems as fast as possible. At the same time, the algorithms involved need to be adapted frequently to the growing industry of computers and clusters architectures.
This project focuses on both aspects: devising novel computational Linear Algebra algorithms to be implemented in avant-garde parallel architectures that include clusters of multi-threaded processors and GPUs. In particular, we will concentrate on those fields of computational Linear Algebra that concern basic matrix operations and linear solvers, as they appear as intermediate steps within more complex frameworks in systems modelling and simulation. Depending on the nature of the input data, we aim to investigate the best parallel paradigms to use, also integrating state-of-the-art libraries for Linear Algebra.
Modelling and simulating scientific and engineering phenomena involves many stages: system observation and measurement, model derivation, application of numerical methods and their implementation, possibly optimization and parallelization, validation and verification of the model. Many experts are devoted to a specific step of this chain, whose links though often suffer from lack of communication. As a consequence, scientists and engineers that master model derivation and numerical calculus end up dedicating themselves to writing code and running experiments. In this context, we propose an intermediate link between different parties, and in particular between the design of numerical algorithms and their parallel implementation. Depending on the nature of the problem under study, the goal of this project is to explore what are the most suitable Linear Algebra algorithms to use in wider frameworks that aim to study the solution and the properties of the model. Against this background, we will investigate what are the most convenient parallel architectures to use for the implementation of such algorithms. This is done also by integrating routines of state-of-the-art Linear Algebra libraries in more specific contexts, thus optimizing the code and having a robust evaluation of the parallel paradigm to use, including hybrid approaches whenever they are convenient. Parallel Linear Algebra libraries are also going to be used in the validation phase. Hence, we aim to export Linear Algebra parallel, validated, reliable software that may be easily imported by scientists and engineers that need to test the model under study and to run simulations, guaranteeing high performances.