High Performance solvers (HPC) for problems governed by partial differential equations in large domains and/or with complex geometry
Modern engineering needs tools for solving partial differential equations (PDE) in large domains that often contain highly complex geometries. These domains are difficult to deal with standard techniques, due to the high computational cost that they require. To this end, the group carries out research on the construction of simulation tools for High Performance Computing (HPC), which offer characteristics of accuracy, efficiency, reliability and scalability on the latest generation of exascale machines. Success in the construction of these tools can only be guaranteed by a process which, in an integrated way, extends from the theoretical concepts to the implementation on the computer of appropriate numerical schemes. For this reason, the group is committed to combining the tools of numerical mathematics with those of information technology, given the complexity of modern computational systems. Accuracy is guaranteed by the discretization techniques that the group investigates: they range from the classic ones, such as the finite element method (FEM), to the latest generation ones, such as the virtual element method (VEM) or Hybrid High- Order (HHO). VEM and HHO allow you to manage geometries with elements of arbitrary shape without difficulty. Calculation efficiency is ensured not only by the appropriate theoretical construction of the numerical methods but also by their implementation on the computer. The latter is subjected to adequate profiling, aimed at establishing the rate of use of the underlying hardware to guide any optimizations of the code. The reliability of the instruments produced is certified through extensive use of unit tests. Finally, scalability is a fundamental aspect on which the group is active, as the size of the problems to be solved requires a high degree of parallelism. Scalability is ensured by designing numerical methods that take into account the characteristics of the hardware on which they will be executed. In particular, we carry out research on methods suitable for distributed memory architectures (MPI) and GPU architectures.