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A fully discrete finite element method, based on a new weak formulation and a new time-stepping scheme, is proposed for the surface diffusion flow of closed curves in the two-dimensional plane. It is proved that the proposed method can…
The concept of representative volume element or RVE is invoked to develop an algorithm for numerical homogenization of fluid filled porous solids. RVE based methods decouple analysis of a composite material into analyses at the local and…
Accurate triangulation of the domain plays a pivotal role in computing the numerical approximation of the differential operators. A good triangulation is the one which aids in reducing discretization errors. In a standard collocation…
The stability of most surface-tension-driven interfacial flow simulations is governed by the capillary time-step constraint. This concerns particularly small-scale flows and, more generally, highly-resolved liquid-gas simulations with…
In the calculation of thermodynamic properties and three dimensional structures of macromolecules, such as proteins, it is important to have a good algorithm for computing solvent accessible surface area of macromolecules. Here we propose a…
A novel interface reconstruction strategy for volume of fluid (VOF) methods is introduced that represents the liquid-gas interface as two planes that co-exist within a single computational cell. In comparison to the piecewise linear…
This paper describes the main features of a pioneering unsteady solver for simulating ideal two-fluid plasmas on unstructured grids, taking profit of GPGPU (General-purpose computing on graphics processing units). The code, which has been…
We present a numerical method for interface-resolved simulations of evaporating two-fluid flows based on the volume-of-fluid (VoF) method. The method has been implemented in an efficient FFT-based two-fluid Navier-Stokes solver, using an…
A simple and efficient algorithm to numerically compute the genus of surfaces of three-dimensional objects using the Euler characteristic formula is presented. The algorithm applies to objects obtained by thresholding a scalar field in a…
In this work we present an extension of the Virtual Element Method with curved edges for the numerical approximation of the second order wave equation in a bidimensional setting. Curved elements are used to describe the domain boundary, as…
We propose an efficient finite-element analysis of the vector wave equation in a class of relatively general curved polygons. The proposed method is suitable for an accurate and efficient calculation of the propagation constants of…
Encoding geospatial objects is fundamental for geospatial artificial intelligence (GeoAI) applications, which leverage machine learning (ML) models to analyze spatial information. Common approaches transform each object into known formats,…
The article discusses an algorithm for recognizing the contour of fragments of a honeycomb block. The inapplicability of ready-made functions of the OpenCV library is shown. Two proposed algorithms are considered. The direct scanning…
The gVOF package includes a complete and self-contained set of routines for volume of fluid initialization, interface reconstruction and fluid advection, which are used to implement several accurate and efficient geometric volume of fluid…
We provide two algorithms for computing the volume of a convex polytope with half-space representation {x>=0; Ax <=b} for some (m,n) matrix A and some m-vector b. Both algorithms have a O(n^m) computational complexity which makes them…
Foveated imaging provides a better tradeoff between situational awareness (field of view) and resolution and is critical in long-wavelength infrared regimes because of the size, weight, power, and cost of thermal sensors. We demonstrate…
This paper presents a finite volume method for simulating two-phase flows using a level set approach coupled with volume of fluid method capable of simulating sharp fluid interfaces. The efficiency of the method is a result of the fact that…
Current quantum computing devices have different strengths and weaknesses depending on their architectures. This means that flexible approaches to circuit design are necessary. We address this task by introducing a novel space-efficient…
In this paper, we present a new method for computing the f-vector of a marked order polytope. Namely, given an arbitrary (polyhedral) subdivision of an arbitrary convex polytope, we construct a cochain complex (over the two-element field…
We report on the computation of invariants, covariants, and contravariants of cubic surfaces. All algorithms are implemented in the computer algebra system magma.