Low-storage, explicit Runge-Kutta schemes for the compressible Navier-Stokes equations
Applied Numerical Mathematics
Journal of Computational Physics
Numerical treatment of two-dimensional interfaces for acoustic and elastic waves
Journal of Computational Physics
Dispersive and dissipative behaviour of high order discontinuous Galerkin finite element methods
Journal of Computational Physics
Metric Identities and the Discontinuous Spectral Element Method on Curvilinear Meshes
Journal of Scientific Computing
Journal of Scientific Computing
Optimal Discontinuous Galerkin Methods for Wave Propagation
SIAM Journal on Numerical Analysis
A Pseudospectral Penalty Scheme for 2D Isotropic Elastic Wave Computations
Journal of Scientific Computing
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Scalable adaptive mantle convection simulation on petascale supercomputers
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Nodal Discontinuous Galerkin Methods: Algorithms, Analysis, and Applications
Implementing Spectral Methods for Partial Differential Equations: Algorithms for Scientists and Engineers
Journal of Scientific Computing
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
Proceedings of the 2010 ACM/IEEE International Conference for High Performance Computing, Networking, Storage and Analysis
p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
SIAM Journal on Scientific Computing
Deforming composite grids for solving fluid structure problems
Journal of Computational Physics
Journal of Scientific Computing
Numerical methods for solid mechanics on overlapping grids: Linear elasticity
Journal of Computational Physics
Journal of Computational Physics
Extreme-scale UQ for Bayesian inverse problems governed by PDEs
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Parallel geometric-algebraic multigrid on unstructured forests of octrees
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
Journal of Computational Physics
Hi-index | 31.47 |
We introduce a high-order discontinuous Galerkin (dG) scheme for the numerical solution of three-dimensional (3D) wave propagation problems in coupled elastic-acoustic media. A velocity-strain formulation is used, which allows for the solution of the acoustic and elastic wave equations within the same unified framework. Careful attention is directed at the derivation of a numerical flux that preserves high-order accuracy in the presence of material discontinuities, including elastic-acoustic interfaces. Explicit expressions for the 3D upwind numerical flux, derived as an exact solution for the relevant Riemann problem, are provided. The method supports h-non-conforming meshes, which are particularly effective at allowing local adaptation of the mesh size to resolve strong contrasts in the local wavelength, as well as dynamic adaptivity to track solution features. The use of high-order elements controls numerical dispersion, enabling propagation over many wave periods. We prove consistency and stability of the proposed dG scheme. To study the numerical accuracy and convergence of the proposed method, we compare against analytical solutions for wave propagation problems with interfaces, including Rayleigh, Lamb, Scholte, and Stoneley waves as well as plane waves impinging on an elastic-acoustic interface. Spectral rates of convergence are demonstrated for these problems, which include a non-conforming mesh case. Finally, we present scalability results for a parallel implementation of the proposed high-order dG scheme for large-scale seismic wave propagation in a simplified earth model, demonstrating high parallel efficiency for strong scaling to the full size of the Jaguar Cray XT5 supercomputer.