Related papers: Effective numerical integration on complex shaped …
We discuss a cheap tetrahedra-free approach to the numerical integration of polynomials on polyhedral elements, based on hyperinterpolation in a bounding box and Chebyshev moment computation via the divergence theorem. No conditioning…
This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…
We develop a theoretical framework for the analysis of stabilized cut finite element methods for the Laplace-Beltrami operator on a manifold embedded in $\mathbb{R}^d$ of arbitrary codimension. The method is based on using continuous…
In this paper, we introduce new generalized barycentric coordinates (coined as {\em moment coordinates}) on nonconvex quadrilaterals and convex hexahedra with planar faces. This work draws on recent advances in constructing interpolants to…
Fragment-based shape signature techniques have proven to be powerful tools for computer-aided drug design. They allow scientists to search for target molecules with some similarity to a known active compound. They do not require reference…
We present a systematic computational framework for generating positive quadrature rules in multiple dimensions on general geometries. A direct moment-matching formulation that enforces exact integration on polynomial subspaces yields…
The paper studies several approaches to numerical integration over a domain defined implicitly by an indicator function such as the level set function. The integration methods are based on subdivision, moment--fitting, local…
Currently, components of consistent mass matrix are computed using various numerical integration schemes, each one alters in number of integration (Gauss) points, requires different amount of computations and possess different level of…
An important question in the theory of approximate integration is to study the conditions on the nodes $x_{k,n}$ and weights $w_{k,n}$ that allow an estimate of the form $$ \sup_{f\in \mathcal{B}_\gamma}|\sum_k…
This paper proposes a novel approach that combines variational integration with the bonded discrete element method (BDEM) to achieve faster and more accurate fracture simulations. The approach leverages the efficiency of implicit…
A mixed finite element method (MFEM), using dual-parametric piecewise bi-quadratic and affine (DP-Q2-P1) finite element approximations for the deformation and the pressure like Lagrange multiplier respectively, is developed and analyzed for…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
We significantly extend recently developed methods to faithfully reconstruct unknown quantum states that are approximately low-rank, using only a few measurement settings. Our new method is general enough to allow for measurements from a…
Complex signed measures of finite total variation are a powerful signal model in many applications. Restricting to the $d$-dimensional torus, finitely supported measures allow for exact recovery if the trigonometric moments up to some order…
We develop a finite element discretization for the weakly symmetric equations of linear elasticity on tetrahedral meshes. The finite element combines, for $r \geq 0$, discontinuous polynomials of $r$ for the displacement,…
This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their positivity and optimization over probability measures supported…
We endeavour to estimate numerous multi-dimensional means of various probability distributions on a common space based on independent samples. Our approach involves forming estimators through convex combinations of empirical means derived…
We introduce an image based algorithmic tool for analyzing multi-component shapes here. Due to the generic concept of multi-component shapes, our method can be applied to the analysis of a wide spectrum of applications where real objects…
In this work, we investigate the possibility of compressing a quantum system to one of smaller dimension in a way that preserves the measurement statistics of a given set of observables. In this process, we allow for an arbitrary amount of…
This paper presents a novel method for polynomial approximation (Hermite approximation) using the fusion of value and derivative information. Therefore, the least-squares error in both domains is simultaneously minimized. A covariance…