Boundary Integral Equation Solver for Flexural-Gravity Wave Scattering by Variable-Thickness Ice
A fast, high-order numerical method for the scattering of time-harmonic flexural-gravity waves by a thin elastic plate of spatially varying thickness (a model of sea ice or an ice shelf with ridges and rolls) floating on a fluid of infinite depth. The coupled potential-flow / thin-plate boundary-value problem, whose plate flexure adds a fourth-order biharmonic term, is reformulated under natural thickness assumptions as a Fredholm second-kind boundary integral equation; the paper analyzes its solvability and mapping properties, then discretizes it with a high-order-accurate Nystrom scheme whose kernel sums are FFT-accelerated, yielding a scalable, high-order-convergent solver.
Integral equations for flexural-gravity waves: analysis and numerical methods T. Askham∗ J.G.
This numerical-analysis paper treats the scattering of flexural-gravity waves - the waves that propagate when an elastic sheet such as sea ice or an ice shelf floats on water - by a thin plate of spa…