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We embark in a program of studying the problem of better approximating surfaces by triangulations(triangular meshes) by considering the approximating triangulations as finite metric spaces and the target smooth surface as their…
A multi-resolution hexahedron element and method is presented with a new multi-resolution analysis (MRA) framework. The MRA framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are…
This paper is devoted to studying the global and finite convergence of the semi-smooth Newton method for solving a piecewise linear system that arises in cone-constrained quadratic programming problems and absolute value equations. We first…
We present a novel and comparative analysis of finite element discretizations for a nonlinear Rosenau-Burgers model including a biharmonic term. We analyze both continuous and mixed finite element approaches, providing stability, existence,…
The thin plate spline smoother is a classical model for fnding a smooth function from the knowledge of its observation at scattered locations which may have random noises. We consider a nonconforming Morley finite element method to…
We introduce with geometric means a density matrix decomposition of a multipartite quantum system of a finite dimension into two density matrices: a separable one, also known as the best separable approximation, and an essentially entangled…
A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of…
A multiscale QM/classical approach is presented, that is able to model the optical properties of complex nanostructures composed of a molecular system adsorbed on metal nanoparticles. The latter are described by a combined…
A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional…
Extracting scientific results from high-energy collider data involves the comparison of data collected from the experiments with synthetic data produced from computationally-intensive simulations. Comparisons of experimental data and…
Assessing the similarity of matrices is valuable for analyzing the extent to which data sets exhibit common features in tasks such as data clustering, dimensionality reduction, pattern recognition, group comparison, and graph analysis.…
We present a new accuracy condition for the construction of continuous mass-lumped elements. This condition is less restrictive than the one currently used and enabled us to construct new mass-lumped tetrahedral elements of degrees 2 to 4.…
Classical algorithms in numerical analysis for numerical integration (quadrature/cubature) follow the principle of approximate and integrate: the integrand is approximated by a simple function (e.g. a polynomial), which is then integrated…
This paper presents a quantum algorithm for efficiently computing partial sums and specific weighted partial sums of quantum state amplitudes. Computation of partial sums has important applications, including numerical integration,…
Successful scientific applications of large-scale molecular dynamics often rely on automated methods for identifying the local crystalline structure of condensed phases. Many existing methods for structural identification, such as Common…
We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely…
Millimeter (mm) wave massive MIMO has the potential for delivering orders of magnitude increases in mobile data rates, with compact antenna arrays providing narrow steerable beams for unprecedented levels of spatial reuse. A fundamental…
In this work, we present an efficient numerical implementation of the finite element method for modal analysis that leverages various symmetry operations, including spatial symmetry in point groups and space-time symmetry in…
The main purpose of this article is to facilitate the implementation of space-time finite element methods in four-dimensional space. In order to develop a finite element method in this setting, it is necessary to create a numerical…
We present a novel finite element analysis of inelastic structures containing Shape Memory Alloys (SMAs). Phenomenological constitutive models for SMAs lead to material nonlinearities, that require substantial computational effort to…