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The main goal of this paper is to demonstrate the application of metric-based mesh adaptation to real gas problems and highlight the benefits particularly when complex geometries are considered. We use the Hessian of the temperature…
We study the roughening transition of an interface in an Ising system on a 3D simple cubic lattice using a finite size scaling method. The particular method has recently been proposed and successfully tested for various solid on solid…
Estimating correspondences between deformed shape instances is a long-standing problem in computer graphics; numerous applications, from texture transfer to statistical modelling, rely on recovering an accurate correspondence map. Many…
We present a projection-based numerical integration technique to deal with embedded interface in finite element (FE) framework. The element cut by an embedded interface is denoted as a cut cell. We recognize elemental matrices of a cut cell…
To definite and compute differential invariants, like curvatures, for triangular meshes (or polyhedral surfaces) is a key problem in CAGD and the computer vision. The Gaussian curvature and the mean curvature are determined by the…
We present careful numerical convergence studies, using parameterized curves to reach very high resolutions in two dimensions, of a level set method for multiphase curvature motion known as the Voronoi implicit interface method. Our tests…
This work has explored interface evolution and pinch-off mechanism of the droplet formation in two-phase flow through cross-flow microfluidic device. The two-dimensional mathematical model equations have been solved using the finite element…
In this paper, we develop and analyze a trilinear immersed finite element method for solving three-dimensional elliptic interface problems. The proposed method can be utilized on interface-unfitted meshes such as Cartesian grids consisting…
We introduce a new numerical technique, namely triangular tessellation, to calculate the free energy associated with the adsorption of a colloidal particle at a flat interface. The theory and numerical scheme presented here are sufficiently…
We developed a computational framework for simulating thin fluid flow in narrow interfaces between contacting solids, which is relevant for a range of engineering, biological and geophysical applications. The treatment of this problem…
In this paper, we propose a novel mesh-free numerical method for solving the elliptic interface problems based on deep learning. We approximate the solution by the neural networks and, since the solution may change dramatically across the…
Reverse Engineering a CAD shape from other representations is an important geometric processing step for many downstream applications. In this work, we introduce a novel neural network architecture to solve this challenging task and…
In this work, a 2D contour generation algorithm is proposed for irregular regions. The contour of the physical domain is approximated by mesh segments using the known coordinates of the contour. For this purpose, the algorithm uses a…
A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged…
Reconstructing meshes from point clouds is a fundamental task in computer vision with applications spanning robotics, autonomous systems, and medical imaging. Selecting an appropriate learning-based method requires understanding trade-offs…
Recently, machine learning has been used to substitute parts of conventional computational fluid dynamics, e.g. the cell-face reconstruction in finite-volume solvers or the curvature computation in the Volume-of-Fluid (VOF) method. The…
This research proposes a novel adjustable algorithm for reconstructing 3D body shapes from front and side silhouettes. Most recent silhouette-based approaches use a deep neural network trained by silhouettes and key points to estimate the…
Many algorithms for the computation of correspondences between deformable shapes rely on some variant of nearest neighbor matching in a descriptor space. Such are, for example, various point-wise correspondence recovery algorithms used as a…
A flat sheet programmed with a planar pattern of spontaneous shape change will morph into a curved surface. Such metric mechanics is seen in growing biological sheets, and may be engineered in actuating soft matter sheets such as…
In this work, we develop a cutting method for solving problems with moving and growing interfaces in 3D. This new method is able to resolve large displacement or deformation of immersed objects by combining the Arbitrary Lagrangian-Eulerian…