Discontinuous Galerkin Spectral Element Approximations for the Reflection and Transmission of Waves from Moving Material Interfaces

• Other Authors: Winters, Andrew R. (authoraut)
• Format: Others
• Language: English; English
• Published: Florida State University
• Subjects: Mathematics
• Online Access: http://purl.flvc.org/fsu/fd/FSU_migr_etd-8916

This dissertation develops and evaluates a computationally efficient and high-order numerical method to compute wave reflection and transmission from moving material boundaries. We use a discontinuous Galerkin spectral element approximation with an arbitrary Lagrangian-Eulerian mapping and derive the exact upwind numerical fluxes to model the physics of wave reflection and transmission at jumps in material properties. Spectral accuracy is obtained by placing moving material interfaces at element boundaries and solving the appropriate Riemann problem. We also derive and evaluate an explicit local time stepping (LTS) integration for the DGSEM on moving meshes. The LTS procedure is derived from Adams-Bashforth multirate time integration methods. We present speedup and memory estimates, which show that the explicit LTS integration scales well with problem size. The LTS time integrator is also highly parallelizable. The manuscript also gathers, derives and analyzes several analytical solutions for the problem of wave reflection and transmission from a plane moving material interface. We present time-step refinement studies and numerical examples to show the approximations for wave reflection and transmission at dielectric and acoustic interfaces are spectrally accurate in space and have design temporal accuracy. The numerical tests also validate theoretical estimates that the LTS procedure can reduce computational cost by as much as an order of magnitude for time accurate problems. Finally, we investigate the parallel speedup of the LTS integrator and compare it to a standard, low-storage Runge-Kutta method. === A Dissertation submitted to the Department of Mathematics in partial fulfillment of the requirements for the degree of Doctor of Philosophy. === Spring Semester, 2014. === February 20, 2014. === Discontinuous Galerkin, Multirate Time Intergration, Spectral Method, Wave Reflection/Transmission === Includes bibliographical references. === David Kopriva, Professor Directing Dissertation; Jorge Piekarewicz, University Representative; M. Yousuff Hussaini, Committee Member; Kyle Gallivan, Committee Member; Nick Cogan, Committee Member; Bettye Anne Case, Committee Member.