Hariri Institute for Computing Colloquium joint with CCS & Mechanical Engineering: “Compatible meshfree discretization”–Nathaniel Trask, Center for Computing Research at Sandia National Laboratories

Spatially compatible discretization broadly encapsulates discretizations of PDEs possessing mimetic properties of continuum operators, such as conservation, maximum principles, H(div)/H(curl) - conformity, or discrete preservation of an exact sequence. Due to the lack of topological information classically provided by a mesh, meshfree methods have struggled to obtain these properties which have proven critical to modern solution of PDEs. In this talk, we will present an overview of meshfree work being done at SNL before intoducing two recent projects. In the first, we show how a graph may be used as a surrogate for a mesh to obtain a meshfree discretization of conservation laws possessing discrete local conservation principles that have historically eluded meshfree techniques. In the second, we demonstrate recent work using meshfree discretizations of nonlocal models for mechanics and transport, illustrating their ability to naturally handle transport and mechanics problems involving fracture and heterogeneous microstructure.