AI & ML
Boundary integral methods and shape reconstruction for periodic fluid--solid interfaces
arXiv cs.NA0 views
arXiv:2611.09201v1 Announce Type: new Abstract: This paper studies direct scattering by periodic fluid--solid interfaces and interface reconstruction from multifrequency near-field data. Using Helmholtz decomposition and quasi-periodic single-layer potentials, we formulate a coupled boundary integral system with the standard stress traction, establish its equivalence to the original fluid--solid transmission problem under suitable assumptions, and construct a corresponding Nystr\"om discretization. For near-field observations at finitely many measurement points, we establish local Fr\'echet differentiability of the observation map with a quadratic remainder estimate. In the smooth setting, the derivative transmission problem and its boundary integral formulation are used to compute the observation Jacobian required for interface reconstruction. The interface is reconstructed by regularized Gauss--Newton iteration in a Fourier space that is progressively enriched as the frequency increases. Numerical experiments assess direct-solver accuracy and reconstruction performance for different interfaces, material configurations, and noise levels.
Source:https://arxiv.org/abs/2611.09201PreviousConstruction of DAE solver Rodas4PW and numerical test examples with Rosenbrock and W-methods in OrdinaryDiffEqRosenbrock.jlNextOn the convergence of Lattice Boltzmann method for advection-diffusion equation with intermediate scaling
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