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The proliferation of floating anthropogenic debris in rivers has emerged as a pressing environmental concern, exerting a detrimental influence on biodiversity, water quality, and human activities such as navigation and recreation. The…

Spectral methods of moments provide a powerful tool for learning the parameters of latent variable models. Despite their theoretical appeal, the applicability of these methods to real data is still limited due to a lack of robustness to…

Coordinate-based neural networks parameterizing implicit surfaces have emerged as efficient representations of geometry. They effectively act as parametric level sets with the zero-level set defining the surface of interest. We present a…

Anisotropic mesh quality measures and anisotropic mesh adaptation are studied for polygonal meshes. Three sets of alignment and equidistribution measures are developed, one based on least squares fitting, one based on generalized…

We propose a numerical method for solving block-structured mesh partitioning problems based on the variational level-set method of (Zhao et al., J Comput Phys 127, 1996) which has been widely used in many partitioning problems such as image…

Image segmentation is an essential component in many image processing and computer vision tasks. The primary goal of image segmentation is to simplify an image for easier analysis, and there are two broad approaches for achieving this: edge…

In this paper, we study the stability and convergence of a decoupled and linearized mixed finite element method (FEM) for incompressible miscible displacement in a porous media whose permeability and porosity are discontinuous across some…

Two methods of level set type are proposed for solving the Cauchy problem for an elliptic equation. Convergence and stability results for both methods are proven, characterizing the iterative methods as regularization methods for this…

A defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous two-time levels. In the defect…

We explore anisotropic regularisation methods in the spirit of [Holler & Kunisch, 14]. Based on ground truth data, we propose a bilevel optimisation strategy to compute the optimal regularisation parameters of such a model for the…

A range of optimization cases of two-dimensional Stefan problems, solved using a tracking-type cost-functional, is presented. A level set method is used to capture the interface between the liquid and solid phases and an immersed boundary…

We propose a level-set method for a mean curvature flow whose boundary is prescribed by interpreting the boundary as an obstacle. Since the corresponding obstacle problem is globally solvable, our method gives a global-in-time level-set…

We developed a sharp interface level-set approach for two-phase immiscible flow with moving contact lines. The Cox-Voinov model is used to describe the moving contact line. A piecewise linear interface method is used to construct the signed…

We study wetting droplets formed of active Brownian particles in contact with a repulsive potential barrier, in a wedge geometry. Our numerical results demonstrate a transition between partially wet and completely wet states, as a function…

In spite of its overall efficiency and robustness for capturing the interface in multiphase fluid dynamics simulations, the well-known shortcoming of the level-set method is associated with the lack of a systematic approach for preserving…

Microstructured surfaces that control the direction of liquid transport are not only ubiquitous in nature, but they are also central to technological processes such as fog/water harvesting, oil-water separation, and surface lubrication.…

Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces…

In this paper, we propose a novel machine learning method based on an adaptive tensor neural network subspace for solving quasiperiodic elliptic problems. To this end, we first provide a theoretical analysis of the associated quasiperiodic…

A new semi-discrete finite element scheme for the evolution of three parametrized curves by curvature flow that are connected by a triple junction is presented and analyzed. In this triple junction, conditions are imposed on the angles at…

The recent introduction of synchrophasor technology into power distribution systems has given impetus to various monitoring, diagnostic, and control applications, such as system identification and event detection, which are crucial for…