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The generalized winding number is an essential part of the geometry processing toolkit, allowing to quantify how much a given point is inside a surface, even when the surface has boundaries and noise. We propose a new universal method to…
This paper develops a computational framework with unfitted meshes to solve linear piezoelectricity and flexoelectricity electromechanical boundary value problems including strain gradient elasticity at infinitesimal strains. The high-order…
We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on…
The isometric embedding of surfaces in three-dimensional space is fundamental to various physical systems, from elastic sheets to programmable materials. While continuous surfaces typically admit unique solutions under suitable boundary…
The intersection of two orthogonal cylinders represents a classical problem in computational geometry with direct applications to engineering design, manufacturing, and numerical simulation. While analytical solutions exist for the fully…
The atmospheric and water turbulence mitigation problems have emerged as challenging inverse problems in computer vision and optics communities over the years. However, current methods either rely heavily on the quality of the training…
Models that involve coupled dynamics in a mixed-dimensional geometry are of increasing interest in several applications. Here, we describe the development of a simulation model for flow in fractured porous media, where the fractures and…
To design a method to solve the issues of handling 'dirty' and highly complex geometries, the topology-free method combined with the immersed boundary method is presented for viscous and incompressible flows at a high Reynolds number. The…
Recent studies of wetting in a two-component square-gradient model of interfaces in a fluid mixture, showing three-phase bulk coexistence, have revealed some highly surprising features. Numerical results show that the density profile paths,…
This paper presents a general and robust method for the fluid-structure interaction of membranes and shells undergoing large displacement and large added-mass effects by coupling an immersed-boundary method with a shell finite-element…
This paper proposes a simple technique of curve and surface construction with B-splines. Given a control polygon or a control mesh together with node ordinates corresponding to all control points, a rational curve or surface is obtained by…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
This work proposes four novel hybrid quadrature schemes for the efficient and accurate evaluation of weakly singular boundary integrals (1/r kernel) on arbitrary smooth surfaces. Such integrals appear in boundary element analysis for…
We present a methodology for simulating three-dimensional flow of incompressible viscoplastic fluids modelled by generalised Newtonian rheological equations. It is implemented in a highly efficient framework for massively parallelisable…
The goal of this study is to provide a method for computing the following: Given a network of curves in 3d (satisfying a condition at the intersection points), compute efficiently a smooth surface such that the curves are geodesics on it.…
Obstacle detection by semantic segmentation shows a great promise for autonomous navigation in unmanned surface vehicles (USV). However, existing methods suffer from poor estimation of the water edge in the presence of visual ambiguities,…
Intersection algorithms are very important in computation of geometrical problems. Algorithms for a line intersection with linear or quadratic surfaces are quite efficient. However, algorithms for a line intersection with other surfaces are…
Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the interior and on the boundary of the domain. However, generally…
In this work, we propose a detailed computational framework for modelling the envelope of the swept volume, that is the boundary of the volume obtained by sweeping an input solid along a trajectory of rigid motions. Our framework is adapted…
Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann…