Adaptive Discontinuous Galerkin Methods Applied to Multiscale & Multiphysics Problems towards Large-scale Modeling & Joint Imaging
Repository Usage Stats
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.
Zhan, Qiwei (2019). Adaptive Discontinuous Galerkin Methods Applied to Multiscale & Multiphysics Problems towards Large-scale Modeling & Joint Imaging. Dissertation, Duke University. Retrieved from https://hdl.handle.net/10161/18679.
Dukes student scholarship is made available to the public using a Creative Commons Attribution / Non-commercial / No derivative (CC-BY-NC-ND) license.