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Full-Text Articles in Physical Sciences and Mathematics
Bloch Spectra For High Contrast Elastic Media, Jayasinghage Ruchira Nirmali Perera
Bloch Spectra For High Contrast Elastic Media, Jayasinghage Ruchira Nirmali Perera
LSU Doctoral Dissertations
The primary goal of this dissertation is to develop analytic representation formulas and power series to describe the band structure inside periodic elastic crystals made from high contrast inclusions. We use source free modes associated with structural spectra to represent the solution operator of the Lame' system inside phononic crystals. Then we obtain convergent power series for the Bloch wave spectrum using the representation formulas. An explicit bound on the convergence radius is given through the structural spectra of the inclusion array and the Dirichlet spectra of the inclusions. Sufficient conditions for the separation of spectral branches of the dispersion …
Sparse Spectral-Tau Method For The Two-Dimensional Helmholtz Problem Posed On A Rectangular Domain, Gabriella M. Dalton
Sparse Spectral-Tau Method For The Two-Dimensional Helmholtz Problem Posed On A Rectangular Domain, Gabriella M. Dalton
Mathematics & Statistics ETDs
Within recent decades, spectral methods have become an important technique in numerical computing for solving partial differential equations. This is due to their superior accuracy when compared to finite difference and finite element methods. For such spectral approximations, the convergence rate is solely dependent on the smoothness of the solution yielding the potential to achieve spectral accuracy. We present an iterative approach for solving the two-dimensional Helmholtz problem posed on a rectangular domain subject to Dirichlet boundary conditions that is well-conditioned, low in memory, and of sub-quadratic complexity. The proposed approach spectrally approximates the partial differential equation by means of …