Abstract: Embedded boundary (also known as “cut cell”) methods for solving partial differential equations can significantly reduce costs for grid generation and computation in complex and moving domains. However, they have additional challenges around achieving high accuracy, numerical stability, and other important discretization qualities. I'll describe our methodology for higher-order cut cell discretizations for PDE’s on scales ranging from electronics to global climate simulations. Near the embedded boundary we use a stencil generation procedure that achieves higher-order convergence rates and good stability, even when there are boundary kinks or topology changes, or arbitrarily small cells. I will present how this is accomplished using a least squares reconstruction using continuous higher-order basis functions, which prevents instability for small cells. We are developing a large class of discretizations and applications using a parallel GPU software implementation with novel data structures that make it easier to manage these complex discretizations, fast solvers, and multi-physics simulations. 

Bio: Dr. Hans Johansen is a computational researcher at Lawrence Berkeley National Laboratory, specializing in numerical discretizations and algorithms for large-scale scientific computing. He focuses on computational science for biology, electronics, and climate, as well as HPC software technologies, and application performance and portability. He has over 30 years of experience in applied math, computational research, IT consulting, startups, and financial services technology. 

Host: Xinfeng Gao