Abstract:

Wave propagation problems arise in a wide range of applications such as mitigation of seismic hazards, exploration of energy resources, and optimal design of acoustic devices. The mathematical models are second order hyperbolic partial differential equation on very large domains with heterogeneous material and complicated geometry. Solving the cutting-edge problems requires efficient numerical methods for wave propagation over long distance in 3D. The great challenge is to design numerical methods that are computationally efficient, geometrically flexible, and scale well on parallel computers.

Finite difference methods are computationally efficient for solving wave propagation problems but have difficulties in handling complicated geometry of domain boundaries and material interfaces. On the other hand, Galerkin methods can resolve geometrical features on unstructured grids but are less efficient than finite difference methods for large-scale problems. In this talk, I will present a numerical technique that is both computationally efficient and geometrically flexible. The essential idea is to discretise the governing equations in space by using high-order finite difference methods in a large part of the domain. In regions with complicated geometries or rapid variation in material properties, the equation is discretised by discontinuous Galerkin methods on unstructured grids. I will focus on the numerical treatment at the interface between the two methods and derive an overall discretisation that is stable and high-order accurate. 

Bio:

Siyang Wang is an assistant professor in computational mathematics at Umeå University in Sweden since 2021. Before joining Umeå, he was a lecturer in numerical analysis at Mälardalen University 2019-2020, and a postdoc fellow in computational mathematics at Chalmers University of Technology 2017-2019. Siyang got his PhD in scientific computing at Uppsala University in 2017. Siyang's research centres around the development, analysis and implementation of numerical methods for partial differential equations. The main application areas include wave propagation, heat conduction and fluid flows.