SPECIAL MATHEMATICS COLLOQUIUM
Speaker: Kenneth Duru
Abstract. High order accurate and robust (provably stable) numerical methods for time-domain propagating waves are critical for progress in many fields of engineering and physical sciences. Although frequency-domain calculations still dominate much of the applied work, time-domain simulations will become increasingly important to study broadband problems and nonlinear scatterers and sources. With the advent of exascale machines, the development of reliable high order accurate and energy aware (compute bound with limited data movement) numerical schemes becomes even more imperative, since it will enable optimal solutions for many wave propagation problems. Effective time-domain solvers must include domain truncation schemes which provide arbitrary accuracy at small cost and high order accurate and time stable volume discretizations applicable to heterogeneous media with complex geometries. Furthermore, propagating waves are described by hyperbolic partial differential equations (PDEs), and because of the complexities of real geometries, internal interfaces, nonlinear boundary/interface conditions and the presence of disparate spatial and temporal scales in real media and sources, discontinuities and sharp wave fronts become fundamental features of the solutions. These introduce several theoretical and numerical challenges since we must resolve sharp wave fronts and accurately simulate discontinuous solutions.In this presentation, I will talk about:
1. A systematic way to derive high resolution and strictly stable finite difference and discontinuous Galerkin approximations for systems of hyperbolic PDEs on conforming and non-conforming curvilinear meshes;
2. New theories and practical aspects of perfectly matched layers to efficiently truncate large computational domains;
3. Numerical simulations of seismic waves and dynamic earthquake ruptures on nonplanar faults embedded in geometrically complex 3D earth models.