Physics – Computational Physics
Scientific paper
2011-12-02
Physics
Computational Physics
Submitted to J. Comput. Phys.; 30 pages, 11 figures
Scientific paper
We develop mathematical framework and computational tools for calculating frequency responses of linear time-invariant PDEs in which an independent spatial variable belongs to a compact interval. In conventional studies this computation is done numerically using spatial discretization of differential operators in the evolution equation. In this paper, we introduce an alternative method that avoids the need for finite-dimensional approximation of the underlying operators. This method recasts the frequency response operator as a two point boundary value problem and uses state-of-the-art automatic spectral collocation techniques for solving the resulting boundary value problems with accuracy comparable to machine precision. Our approach has two advantages over currently available schemes: first, it avoids numerical instabilities encountered in systems with differential operators of high order and, second, it alleviates difficulty in implementing boundary conditions. We provide examples from Newtonian and viscoelastic fluid dynamics to illustrate utility of the proposed method.
Jovanović Mihailo R.
Lieu Binh K.
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