Adaptive Discontinuous Galerkin Methods Applied to Multiscale & Multiphysics Problems towards Large-scale Modeling & Joint Imaging

Abstract

Advanced numerical algorithms should be amenable to the scalability in the increasingly powerful supercomputer architectures, the adaptivity in the intricately multi-scale engineering problems, the efficiency in the extremely large-scale wave simulations, and the stability in the dynamically multi-phase coupling interfaces. In this study, I will present a multi-scale \& multi-physics 3D wave propagation simulator to tackle these grand scientific challenges. This simulator is based on a unified high-order discontinuous Galerkin (DG) method, with adaptive nonconformal meshes, for efficient wave propagation modeling. This algorithm is compatible with a diverse portfolio of real-world geophysical/biomedical applications, ranging from longstanding tough problems: such as arbitrary anisotropic elastic/electromagnetic materials, viscoelastic materials, poroelastic materials, piezoelectric materials, and fluid-solid coupling, to recent challenging topics: such as fracture-wave interactions. Meanwhile, I will also present some important theoretical improvements. Especially, I will show innovative Riemann solvers, inspired by physical meanings, in a unified mathematical framework, which are the key to guaranteeing the stability and accuracy of the DG methods and domain decomposition methods.