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The virtual element method (VEM) is a stabilized Galerkin method that is robust and accurate on general polygonal meshes. This feature makes it an appealing candidate for simulations involving meshes with embedded interfaces and evolving…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
Volumetric maps are widely used in robotics due to their desirable properties in applications such as path planning, exploration, and manipulation. Constant advances in mapping technologies are needed to keep up with the improvements in…
This article presents a priori error estimates of the miscible displacement of one compressible fluid by another in a porous medium. The study utilizes the $H(\rm div)$ conforming virtual element method (VEM) for the approximation of the…
The virtual element method (VEM) is a Galerkin approximation method that extends the finite element method to polytopal meshes. In this paper, we present two different conforming virtual element formulations for the numerical approximation…
In this article we propose a Weighted Stochastic Mesh (WSM) Algorithm for approximating the value of a discrete and continuous time optimal stopping problem. We prove that in the discrete case the WSM algorithm leads to semi-tractability of…
This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…
Maximum marginal likelihood estimation (MMLE) can be formulated as the optimization of a free energy functional. From this viewpoint, the Expectation-Maximisation (EM) algorithm admits a natural interpretation as a coordinate descent method…
Acknowledging the ever-increasing demand for composites in the engineering industry, this paper focuses on the failure of composites at the microscale and augmenting the use of multiscale modelling techniques to make them better for various…
A volume-preserving parameterization is a bijective mapping that maps a 3-manifold onto a specified canonical domain that preserves the local volume. This paper formulates the computation of ball-shaped volume-preserving parameterizations…
This paper presents a new algorithm, Weighted Squared Volume Minimization (WSVM), for generating high-quality tetrahedral meshes from closed triangle meshes. Drawing inspiration from the principle of minimal surfaces that minimize squared…
Meshing complex engineering domains is a challenging task. Arbitrary polyhedral meshes can provide the much needed flexibility in automated discretization of such domains. The geometric property of the polyhedral meshes such as the…
A refined a priori error analysis of the lowest order (linear) nonconforming Virtual Element Method (VEM) for approximating a model Poisson problem is developed in both 2D and 3D. A set of new geometric assumptions is proposed on shape…
This paper introduces a numerical algorithm to compute the $L_2$ optimal transport map between two measures $\mu$ and $\nu$, where $\mu$ derives from a density $\rho$ defined as a piecewise linear function (supported by a tetrahedral mesh),…
We design an adaptive virtual element method (AVEM) of lowest order over triangular meshes with hanging nodes in 2d, which are treated as polygons. AVEM hinges on the stabilization-free a posteriori error estimators recently derived in [8].…
This work presents a Virtual Element Method (VEM) formulation tailored for two-dimensional axisymmetric problems in linear elasticity. By exploiting the rotational symmetry of the geometry and loading conditions, the problem is reduced to a…
In this paper, we propose an efficient approach for the compression and representation of volumetric data utilizing coordinate-based networks and multi-resolution hash encoding. Efficient compression of volumetric data is crucial for…
We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approximation and a greedy approach for finding the maximal volume…
The trending integrations of Battery Energy Storage System (BESS, stationary battery) and Electric Vehicles (EV, mobile battery) to distribution grids call for advanced Demand Side Management (DSM) technique that addresses the scalability…
Deep learning-based lossless compression methods offer substantial advantages in compressing medical volumetric images. Nevertheless, many learning-based algorithms encounter a trade-off between practicality and compression performance.…