Related papers: Effective numerical integration on complex shaped …
This paper presents a new progressive compression method for triangular meshes. This method, in fact, is based on a schema of irregular multi-resolution analysis and is centered on the optimization of the rate-distortion trade-off. The…
We suggest a method for simultaneously generating high order quadrature weights for integrals over Lipschitz domains and their boundaries that requires neither meshing nor moment computation. The weights are determined on pre-defined…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum…
The aim of this paper is to develop and analyze numerical schemes for approximately solving the backward problem of subdiffusion equation involving a fractional derivative in time with order $\alpha\in(0,1)$. After using quasi-boundary…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
Compressed sensing is a technique for finding sparse solutions to underdetermined linear systems. This technique relies on properties of the sensing matrix such as the restricted isometry property. Sensing matrices that satisfy the…
We study the efficient construction of good polynomial lattice rules, which are special instances of quasi-Monte Carlo (QMC) methods. The integration rules obtained are of particular interest for the approximation of multivariate integrals…
Due to the influence of imaging equipment and complex imaging environments, most images in daily life have features of intensity inhomogeneity and noise. Therefore, many scholars have designed many image segmentation algorithms to address…
Effective demagnetizing factors that connect the sample magnetic moment with the applied magnetic field are calculated numerically for perfectly diamagnetic samples of various non-ellipsoidal shapes. The procedure is based on calculating…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
Time-domain Boundary Element Methods (BEM) have been successfully used in acoustics, optics and elastodynamics to solve transient problems numerically. However, the storage requirements are immense, since the fully populated system matrices…
Magnetic Soft Catheters (MSCs) are capable of miniaturization due to the use of an external magnetic field for actuation. Through careful design of the magnetic elements within the MSC and the external magnetic field, the shape along the…
We present a new method for computing the impedance matrix elements in the method of moments for geometries described by bilinear quadrilaterals (BQ) and for higher-order basis functions (HOBF). Our method is restricted to the Magnetic…
We study quadratic optimization with indicator variables and an M-matrix, i.e., a PSD matrix with non-positive off-diagonal entries, which arises directly in image segmentation and portfolio optimization with transaction costs, as well as a…
The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to…
We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at…
The ability to completely characterize the state of a quantum system is an essential element for the emerging quantum technologies. Here, we present a compressed-sensing inspired method to ascertain any rank-deficient qudit state, which we…
A general method is described for finding algebraic expressions for matrix elements of any one- and two-particle operator for an arbitrary number of subshells in an atomic configuration, requiring neither coefficients of fractional…
Quantum computing has shown great potential in various quantum chemical applications such as drug discovery, material design, and catalyst optimization. Although significant progress has been made in quantum simulation of simple molecules,…