SCAIM Seminar: Emily Walsh

Solutions of partial differential equations are often highly anisotropic and have strongly directional features. Examples include PDES which have shocks and interfaces in the solution. When calculating the solutions to these PDEs it is important to use computational meshes which align themselves with features in the solution. Many adaptive mesh methods explicitly and implicitly use equidistribution and alignment, and a metric tensor M is typically used to define the desired level of anisotropy. In this talk I will describe a mesh method which combines equidistribution with optimal transport that does not require the explicit construction of a metric tensor M, although such an M always exists. I will show that this method is very effective at aligning elements along solution features including linear shocks and radially symmetric structures. Furthermore, I will provide numerical results to show this method is cheap and robust to implement, and allows solutions to be very well approximated.