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A New High-Order Fourier Continuation-Based Elasticity Solver for Complex Three-Dimensional Geometries


Amlani, Faisal (2014) A New High-Order Fourier Continuation-Based Elasticity Solver for Complex Three-Dimensional Geometries. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/V9DQ-P103.


This thesis presents a new approach for the numerical solution of three-dimensional problems in elastodynamics. The new methodology, which is based on a recently introduced Fourier continuation (FC) algorithm for the solution of Partial Differential Equations on the basis of accurate Fourier expansions of possibly non-periodic functions, enables fast, high-order solutions of the time-dependent elastic wave equation in a nearly dispersionless manner, and it requires use of CFL constraints that scale only linearly with spatial discretizations. A new FC operator is introduced to treat Neumann and traction boundary conditions, and a block-decomposed (sub-patch) overset strategy is presented for implementation of general, complex geometries in distributed-memory parallel computing environments. Our treatment of the elastic wave equation, which is formulated as a complex system of variable-coefficient PDEs that includes possibly heterogeneous and spatially varying material constants, represents the first fully-realized three-dimensional extension of FC-based solvers to date. Challenges for three-dimensional elastodynamics simulations such as treatment of corners and edges in three-dimensional geometries, the existence of variable coefficients arising from physical configurations and/or use of curvilinear coordinate systems and treatment of boundary conditions, are all addressed. The broad applicability of our new FC elasticity solver is demonstrated through application to realistic problems concerning seismic wave motion on three-dimensional topographies as well as applications to non-destructive evaluation where, for the first time, we present three-dimensional simulations for comparison to experimental studies of guided-wave scattering by through-thickness holes in thin plates.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Applied mathematics; elastic wave equation; Fourier continuation; numerical partial differential equations
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Awards:W.P. Carey & Co., Inc., Prize in Applied Mathematics, 2014. Demetriades - Tsafka - Kokkalis Prize in Seismo-Engineering, Prediction and Protection, 2014.
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Bruno, Oscar P.
Thesis Committee:
  • Bruno, Oscar P. (chair)
  • Meiron, Daniel I.
  • Owhadi, Houman
  • Blanquart, Guillaume
Defense Date:27 September 2013
Non-Caltech Author Email:fpamlani (AT)
Record Number:CaltechTHESIS:10082013-093825165
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7974
Deposited By: Faisal Amlani
Deposited On:14 May 2014 16:09
Last Modified:04 Oct 2019 00:02

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