Related papers: A Framework for FFT-based Homogenization on Anisot…
In this paper a sublinear time algorithm is presented for the reconstruction of functions that can be represented by just few out of a potentially large candidate set of Fourier basis functions in high spatial dimensions, a so-called…
This paper presents a general, nonlinear isogeometric finite element formulation for rotation-free shells with embedded fibers that captures anisotropy in stretching, shearing, twisting and bending -- both in-plane and out-of-plane. These…
To obtain the initial pressure from the collected data on a planar sensor arrangement in photoacoustic tomography, there exists an exact analytic frequency domain reconstruction formula. An efficient realization of this formula needs to…
The phase-field crystal (PFC) model describes crystal lattices at diffusive timescales. Its amplitude expansion (APFC) can be applied to the investigation of relatively large systems under some approximations. However, crystal symmetries…
The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially…
A panoptic view of architectured planar lattices based on star-polygon tilings was developed. Four star-polygon-based lattice sub-families, formed of systematically arranged triangles, squares, or hexagons, were investigated numerically and…
We propose a unified mathematical framework for classifying phases of matter. The framework is based on different types of combinatorial structures with a notion of locality called lattices. A tensor lattice is a local prescription that…
This work develops a unified framework for inferring, representing, and statistically characterizing an anisotropic strength surface directly from molecular dynamics data. Large-scale tensile loading simulations are used to generate failure…
This note constructs a local generalized finite element basis for elliptic problems with heterogeneous and highly varying coefficients. The basis functions are solutions of local problems on vertex patches. The error of the corresponding…
The fast marching algorithm, and its variants, solves numerically the generalized eikonal equation associated to an underlying riemannian metric. A major challenge for these algorithms is the non-isotropy of the riemannian metric.…
A new construction of decomposition smoothness spaces of homogeneous type is considered. The smoothness spaces are based on structured and flexible decompositions of the frequency space $\mathbb{R}^d\backslash\{0\}$. We construct simple…
A key problem in approximation theory is the recovery of high-dimensional functions from samples. In many cases, the functions of interest exhibit anisotropic smoothness, and, in many practical settings, the nature of this anisotropy may be…
Textures in images can often be well modeled using self-similar processes while they may at the same time display anisotropy. The present contribution thus aims at studying jointly selfsimilarity and anisotropy by focusing on a specific…
The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency support of the trigonometric polynomial is known. We suggest a construction based on…
We propose a novel framework for fast integral operations by uncovering hidden geometries in the row and column structures of the underlying operators. This is accomplished through the \texttt{Questionnaire} algorithm, an iterative…
It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling…
We demonstrate a method to experimentally calibrate the refractive index modulation in photorefractive lattices, a task rarely addressed that is crucial for quantitative comparisons of theories with experiments. We consider the linear…
We introduce a framework generalizing lattice reduction algorithms to module lattices in order to practically and efficiently solve the $\gamma$-Hermite Module-SVP problem over arbitrary cyclotomic fields. The core idea is to exploit the…
Several variants of the recently proposed Density Matrix Embedding Theory (DMET) [G. Knizia and G. K-L. Chan, Phys. Rev. Lett. 109, 186404 (2012)] are formulated and tested. We show that spin symmetry breaking of the lattice mean-field…
Phase-field models of microstructural pattern formation during alloy solidification are commonly solved numerically using the finite-difference method, which is ideally suited to carry out computationally efficient simulations on massively…