Contribution to high-performance simulation and highly scalable numerical schemes

My contributions concern the improvement of computational methods from the point of view of parallelization, the design of optimized algorithms and implementations for specific machines, but also on the upgrade of some numerical schemes. In the various simulation codes on which I have been involved, it has been required to adapt or renovate calculation schemes for efficient execution on machines with a large number of cores. My inputs contribute throughout the entire chain, from modeling, to efficient implementation on large supercomputers. The studies I carried out were done in close interaction with the designers and users of the simulation codes so that the results are effective and usable in production. The document is composed of three main chapters plus a final one enclosing conclusions and perspectives. Although my scientific work is not limited to Gysela, I chose here to focus a large part of the document on this application in order to simplify the contextual setting and to allow me to get into some of the details. Chapter 2 concerns various studies carried out to make the best use of the today's supercomputers. After a short description of the physical problem in Gysela, the numerical methods are described, and then I discuss the improvements required to exploit the biggest academic calculators in Europe. Chapter 3 summarizes works in closer connection with the field of applied mathematics. The implementation of specific test cases within Gysela and the adaptation of numerical methods in the Vlasov and Poisson solvers make it possible to better preserve certain invariants and improve the precision of the code. Chapter 4 focuses on work on the development of parallel algorithms and the implementation of optimization techniques dedicated to new architectures. Studies on various applications are highlighted. I draw some insights from lessons learned on these new computing devices. The very last chapter 5 gives a conclusion of the previous chapters, and outlines some of the research projects I plan for the years to come