Geometric Multigrid (GMG) methods are widely used in numerical analysis to accelerate the convergence of partial differential equations solvers using a hierarchy of grid discretizations. These solvers find plenty of applications in various fields in engineering and scientific domains, where solving PDEs is of fundamental importance. Using multigrid methods, the pace at which the solvers arrive at the solution can be improved at an algorithmic level. With the advance in modern computer architecture, solving problems with higher complexity and sizes is feasible - this is also the case with multigrid methods. However, since hardware support alone cannot achieve high performance in execution time, there is a need for good software that help programmers in doing so. Multiple grid sizes and recursive expression of multigrid cycles make the task of manual program optimization tedious and error-prone. A high-level language that aids domain experts to quickly express complex algorithms in a compact way using dedicated constructs for multigrid methods and with good optimization support is thus valuable. Typical computation patterns in a GMG algorithm includes stencils, point-wise accesses, restriction and interpolation of a grid. These computations can be optimized for performance on modern architectures using standard parallelization and locality enhancement techniques. Several past works have addressed the problem of automatic optimizations of computations in various scientific domains using a domain-specific language (DSL) approach. A DSL is a language with features to express domain-specific computations and compiler support to enable optimizations specific to these computations. Halide and PolyMage are two of the recent works in this direction, that aim to optimize image processing pipelines. Many computations like upsampling and downsampling an image are similar to interpolation and restriction in geometric multigrid methods. In this thesis, we demonstrate how high performance can be achieved on GMG algorithms written in the PolyMage domain-specific language with new optimizations we added to the compiler. We also discuss the implementation of non-trivial optimizations, on PolyMage compiler, necessary to achieve high parallel performance for multigrid methods on modern architectures. We realize these goals by: • introducing multigrid domain-specific constructs to minimize the verbosity of the algorithm specification; • storage remapping to reduce the memory footprint of the program and improve cache locality exploitation; • mitigating execution time spent in data handling operations like memory allocation and freeing, using a pool of memory, across multiple multigrid cycles; and • incorporating other well-known techniques to leverage performance, like exploiting multi-dimensional parallelism and minimizing the lifetime of storage buffers. We evaluate our optimizations on a modern multicore system using five different benchmarks varying in multigrid cycle structure, complexity and size, for two-and three-dimensional data grids. Experimental results show that our optimizations: • improve performance of existing PolyMage optimizer by 1.31x; • are better than straight-forward parallel and vector implementations by 3.2x; • are better than hand-optimized versions in conjunction with optimizations by Pluto, a state-of-the-art polyhedral source-to-source optimizer, by 1.23x; and • achieve up to 1.5$\times$ speedup over NAS MG benchmark from the NAS Parallel Benchmarks. (The speedup numbers are Geometric means over all benchmarks)

Le bâtiment devient de plus en plus un système complexe où les flux énergétiques doivent être gérés en fonction des usages : on parle de bâtiments intelligents. Il s'ensuit une complexité croissante pour les concepteurs, qui doivent s'intéresser autant au bâtiment lui-même (plusieurs sources électriques et multiplication des charges) qu'à ses équipements, sa gestion énergétique mais aussi aux interactions avec l'environnement extérieur (flux d'informations exogènes sur le marché d'énergie, prix d'achat et de revente, subventions à l'auto-consommation, etc...). Il est désormais nécessaire de coupler la phase de conception avec celle de gestion énergétique du bâtiment. Les travaux de cette thèse visent à proposer une démarche méthodologique permettant de formuler automatiquement les problèmes d'optimisation exploitables autant en conception qu'en exploitation du système bâtiment. La démarche est basée sur les concepts issus de l'ingénierie dirigée par les modèles (IDM). / The building is becoming increasingly a complex system where energy flows must be managed according to consumption: we talk about intelligent buildings. This means increasing complexity for designers who need to focus as much on building itself (several power sources and multiplication of charges) in its equipment, and in its energy management but also to interactions with the external environment (exogenous flow of information on the energy market, the purchase price and resale, subsidies for self-consumption, etc. ...). It is now necessary to tie the design phase with that of building energy management. The work of this thesis aims at proposing a methodological approach to automatically formulate optimization problems at design stage and under operation of building. The approach is based on concepts from the model-driven engineering (MDE).