Towards exascale BEM simulations: hybrid parallelisation strategies for boundary element methods

Many fields of engineering benefit from an accurate and reliable solver for the Laplace equation. Such an equation is able to model many different phenomena, and is at the base of several multi-physics solvers. For example, in nautical engineering, since the Navier{Stokes system has an extremely high computational cost, many reduced order models are often used to predict ship performance. Under the assumption of incompressible fluid and irrotational flow it is possible to recover a flow field by simply imposing mass conservation, which simplifies to a Laplace equation. Morevore, the deep theoretical background that surrounds this equation, makes it ideal as a benchmark to test new numerical softwares. Over the last decades such equation has often been solved through its Boundary integral formulation, leading to Boundary Element Methods. What makes such methods appealing with respect to a classical Finite Element Method is the fact that they only require discretisation of the boundary. The purpose of the present work is to develop an effcient and optimize BEM for the Laplace equation, designed around the architecture of modern CPUs.