Lecture 32: 29 November 2010Lecture 33: 29 November 2010 Resonances for the frequency-domain Helmholtz problem in a finite domain. Impact of losses. Representation of dissipation loss via complex coefficients in the PDE, and the necessity of frequency dependence in loss. Brief mention of the time-domain representation as a convolution, and Kramers-Kronig relations that come from causality constraints. Discussed how "absorbing boundaries" are implemented in the frequency domain via complex coordinate stretching, leading to the idea of perfectly matched layers (PML); discussed section 3.1-3.3 of the notes, and showed some animations of wave propagation showing the effect of the boundaries and the impact of PML.MIT OpenCourseWarehttp://ocw.mit.edu 18.303 Linear Partial Differential Equations: Analysis and NumericsFall 2010 For information about citing these materials or our Terms of Use, visit:
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