Solution of the three-dimensional Helmholtz equation using ... - cerfacs
Solution of the three-dimensional Helmholtz equation using ... - cerfacs
Solution of the three-dimensional Helmholtz equation using ... - cerfacs
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Motivations<br />
Wave propagation modelling<br />
<strong>Solution</strong> method components: Iterative method and multigrid<br />
<strong>Solution</strong> strategy<br />
Numerical experiments<br />
Perspectives and conclusions<br />
<strong>Helmholtz</strong> problem<br />
Continuous problem<br />
Discrete problem<br />
Continuous problem<br />
<strong>Helmholtz</strong> <strong>equation</strong> in <strong>the</strong> frequency domain [k = ω v :<br />
wavenumber]:<br />
−∆u − ω2<br />
v 2 u = g in Ω<br />
with Perfectly Matched Layer (PML) [Berenger, 1994]<br />
Notations<br />
ω = 2π f is <strong>the</strong> angular frequency, v <strong>the</strong> velocity <strong>of</strong> <strong>the</strong> wave, u <strong>the</strong><br />
pressure <strong>of</strong> <strong>the</strong> wave, g represents <strong>the</strong> source term<br />
8/27 Multigrid for geophysics applications
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