David J. Smith

Meurig T. Gallagher, Debajyoti Choudhuri, David J. Smith

The method of regularized stokeslets is a powerful numerical method to solve the Stokes flow equations for problems in biological fluid mechanics. A recent variation of this method incorporates a nearest-neighbor discretization to improve accuracy and efficiency while maintaining the ease-of-implementation of the original meshless method. This method contains three sources of numerical error, the regularization error associated from using the regularized form of the boundary integral equations (with parameter $\varepsilon$), and two sources of discretization error associated with the force and quadrature discretizations (with lengthscales $h_f$ and $h_q$). A key issue to address is the quadrature error: initial work has not fully explained observed numerical convergence phenomena. In the present manuscript we construct sharp quadrature error bounds for the nearest-neighbor discretisation, noting that the error for a single evaluation of the kernel depends on the smallest distance ($δ$) between these discretization sets. The quadrature error bounds are described for two cases: with disjoint sets ($δ>0$) being close to linear in $h_q$ and insensitive to $\varepsilon$, and contained sets ($δ=0$) being quadratic in $h_q$ with inverse dependence on $\varepsilon$. The practical implications of these error bounds are discussed with reference to the condition number of the matrix system for the nearest-neighbor method, with the analysis revealing that the condition number is insensitive to $\varepsilon$ for disjoint sets, and grows linearly with $\varepsilon$ for contained sets. Error bounds for the general case ($δ\geq 0$) are revealed to be proportional to the sum of the errors for each case.

Anja Sheppard, Tyler Smithline, Andrew Scheffer et al.

In this paper, we introduce ShipwreckFinder, an open-source QGIS plugin that detects shipwrecks from multibeam sonar data. Shipwrecks are an important historical marker of maritime history, and can be discovered through manual inspection of bathymetric data. However, this is a time-consuming process and often requires expert analysis. Our proposed tool allows users to automatically preprocess bathymetry data, perform deep learning inference, threshold model outputs, and produce either pixel-wise segmentation masks or bounding boxes of predicted shipwrecks. The backbone of this open-source tool is a deep learning model, which is trained on a variety of shipwreck data from the Great Lakes and the coasts of Ireland. Additionally, we employ synthetic data generation in order to increase the size and diversity of our dataset. We demonstrate superior segmentation performance with our open-source tool and training pipeline as compared to a deep learning-based ArcGIS toolkit and a more classical inverse sinkhole detection method. The open-source tool can be found at https://github.com/umfieldrobotics/ShipwreckFinderQGISPlugin.