Partial differential equations (PDEs) are pervasive in engineering and science, and their numerical solutions are of paramount importance in understanding complex, natural, engineered, and societal systems. Many large-scale PDE systems need to be solved on irregularly shaped domains or have other geometric complications. In addition, spatial and temporal adaptivity is essential to keep the memory footprint small, especially on modern heterogeneous architectures where data-movement costs dominate. Adaptivity leads to irregular memory access, making it challenging to get good performance and scalability, especially  for larger problems.

In this talk, I will present algorithms for large-scale adaptive refinement that achieve high levels of spatial and temporal adaptivity on complex geometries without sacrificing scalability or efficiency. Additionally, by using a Domain  Specific Language (DSL) in conjunction with automatic code generators we are able to make application codes extensible and highly portable as well. I will present these methods in the context of two challenging applications, generating gravitational waveforms for binary black hole mergers and simulations of jet atomization in the context of aerospace combustors. I will also demonstrate the efficacy of the methods briefly or other applications, including the thermal management of miniaturized integrated circuits, investigating the effect of platooning on transportation efficiency, and analysis of COVID transmission in classrooms. 

Location: Maxwell Dworkin G125 and Zoom