A Chebyshev Spectral Method for Normal Mode and Parabolic Equation Models in Underwater Acoustics

<div><svg height="8.80315pt" id="M118" style="vertical-align:-0.04981041pt" version="1.1" viewbox="-0.0498162 -8.75334 15.1709 8.80315" width="15.1709pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M592 498C586 556 582 629 581 675H560C545 656 537 650 510 650H115C87 650 74 652 60 675H40C38 620 33 555 28 495H57C69 539 77 568 89 585C102 607 122 616 205 616H267V123C267 44 259 34 168 28V0H454V28C360 34 352 44 352 123V616H422C498 616 514 608 531 584C542 568 552 543 562 495L592 498Z"></path></g><g transform="matrix(.013,0,0,-0.013,8.021,0)"><path d="M495 163C480 117 462 85 444 65C421 39 387 34 332 34C290 34 256 36 236 47C218 57 213 77 213 131V526C213 612 222 616 301 622V650H40V622C122 616 128 611 128 526V126C128 41 120 34 36 28V0H489C498 31 519 126 525 157L495 163Z"></path></g></svg> deviations of the analytical solution calculated by the virtual source method, Kraken, and CSM at the receiver depth.</div>

Mathematical Problems in Engineering

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Figure 3

Figure 3: A Chebyshev Spectral Method for Normal Mode and Parabolic Equation Models in Underwater Acoustics 