arXiv subjects

Qiaoling Zhang

Publications and source records attributed to Qiaoling Zhang.

7 recordsLinked to original sources

arXiv2026

Proactive Coded Caching Scheme for D2D Networks

Coded caching and device-to-device (D2D) communication are two effective techniques for alleviating network traffic. Secure transmission and file privacy have also become critical concerns in these domains. However, prevailing coded caching schemes typically assume that a user's cached content is inaccessible to others, overlooking the risk of file privacy leakage due to attacks targeting the cache itself. In this paper, we propose a secure coded caching scheme for D2D networks that guarantees both file privacy and secure delivery. We demonstrate that the proposed scheme achieves order-optimal performance when the file size is sufficiently large and the cache memory is ample.

cs.IT↗

arXiv2019

An Immersed Discontinuous Galerkin Method for Compressible Navier-Stokes Equations on Unstructured Meshes

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are advanced in time with an explicit time marching scheme. The discretisation meshes may contain simplicial (triangular or tetrahedral) elements of different sizes and need not be structured. On the discretisation mesh the fluid domain boundary is represented with an implicit signed distance function. The cut-elements partially covered by the solid domain are integrated after tessellation with the marching triangle or tetrahedra algorithms. Two alternative techniques are introduced to overcome the excessive stable time step restrictions imposed by cut-elements. In the first approach the cut-basis functions are replaced with the extrapolated basis functions from the nearest largest element. In the second approach the cut-basis functions are simply scaled proportionally to the fraction of the cut-element covered by the solid. To achieve high-order accuracy additional nodes are introduced on the element faces abutting the solid boundary. Subsequently, the faces are curved by projecting the introduced nodes to the boundary. The proposed approach is verified and validated with several two- and three-dimensional subsonic and hypersonic low Reynolds number flow applications, including the flow over a cylinder, a space capsule and an aerospace vehicle.

math.NA↗

arXiv2019

Manifold-based isogeometric analysis basis functions with prescribed sharp features

We introduce manifold-based basis functions for isogeometric analysis of surfaces with arbitrary smoothness, prescribed $C^0$ continuous creases and boundaries. The utility of the manifold-based surface construction techniques in isogeometric analysis was demonstrated in Majeed and Cirak (CMAME, 2017). The respective basis functions are derived by combining differential-geometric manifold techniques with conformal parametrisations and the partition of unity method. The connectivity of a given unstructured quadrilateral control mesh in $\mathbb R^3$ is used to define a set of overlapping charts. Each vertex with its attached elements is assigned a corresponding conformally parametrised planar chart domain in $\mathbb R^2$, so that a quadrilateral element is present on four different charts. On the collection of unconnected chart domains, the partition of unity method is used for approximation. The transition functions required for navigating between the chart domains are composed out of conformal maps. The necessary smooth partition of unity, or blending, functions for the charts are assembled from tensor-product B-spline pieces and require in contrast to earlier constructions no normalisation. Creases are introduced across user tagged edges of the control mesh. Planar chart domains that include creased edges or are adjacent to the domain boundary require special local polynomial approximants. Three different types of chart domain geometries are necessary to consider boundaries and arbitrary number and arrangement of creases. The new chart domain geometries are chosen so that it becomes trivial to establish local polynomial approximants that are always $C^0$ continuous across tagged edges. The derived non-rational manifold-based basis functions are particularly well suited for isogeometric analysis of Kirchhoff-Love thin shells with kinks.

math.NA↗

arXiv2019

On the Dynamic Centralized Coded Caching Design

Coded caching scheme provides us an effective framework to realize additional coded multicasting gain by exploiting coding into multiple transmitted signals. The goal of coded caching design is to jointly optimize the placement and delivery scheme so as to minimize the amount of transmitted coded signals. However, few research efforts consider multiple-round coded caching design problem, in which fixed and mobile users may coexist in one network different number of active users present in successive rounds. Obviously, such dynamic network configurations may lead to undesired frequent placement caching content updating at user sides, if we assume coded caching scheme for each round separately. Thus how to tailor the coded caching design, such that the frequent caching content updating in the placement phase can be avoided, and simultaneously retaining full caching gain in delivery phase in multiple rounds will become highly desirable. In this paper, by carefully examining the bipartite graph representation of the coded caching scheme, a dynamic centralized coded caching design is proposed on the basis of the concatenating-based placement and the saturating matching based delivery scheme. Our analysis unveils that, the proposed dynamic coded caching scheme can realize the flexible coded multicast, and is order optimal.

cs.IT↗

arXiv2019

Manifold-based B-splines on unstructured meshes

We introduce new manifold-based splines that are able to exactly reproduce B-splines on unstructured surface meshes. Such splines can be used in isogeometric analysis (IGA) to represent smooth surfaces of arbitrary topology. Since prevalent computer-aided design (CAD) models are composed of tensor-product B-spline patches, any IGA suitable construction should be able to reproduce B-splines. To achieve this goal, we focus on univariate manifold-based constructions that can reproduce B-splines. The manifold-based splines are constructed by smoothly blending together polynomial interpolants defined on overlapping charts. The proposed constructions automatically reproduce B-splines in regular parts of the mesh, with no extraordinary vertices, and polynomial basis functions in the remaining parts of the mesh. We study and compare analytically and numerically the finite element convergence of several univariate constructions. The obtained results directly carry over to the tensor-product case.

math.NA↗

arXiv2018

Reduced Transmission in Multi-Server Coded Caching

Coded caching has been widely used in the wireless network for shifting the some transmissions during the peak traffic times to the off-peak traffic times. Multi-server coded caching, which can share responsibility for the total amount of transmission in the wireless network during the peak traffic times by means of the collaboration among these servers, can be seen everywhere in our life. The three servers setting (two data servers and one parity check server) is used in practice, e.g. redundant array of independent disks-4. In this scenario, there are total $N$ files which are equally stored in two data servers respectively and $K$ users each of which has the memory size of $M$ files. Each server connects to users by an independently channel. During the off-peak traffic times, two data servers place some parts of each files in each user's cache. In that time, servers do not know users' requests in future. During the peak traffic times each user just requests one file from $N$ files. Luo et al. in 2016 proposed the first coded caching scheme for this setting. In this paper, we proposed some method that further reduces the amount of transmission in each channel when $\frac{KM}{N}$ is odd. This method also improves the transmission rate for systems with general multiply servers.

cs.IT↗

arXiv2018

Subdivision surfaces with isogeometric analysis adapted refinement weights

Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are becoming available in a number of geometric modelling systems for engineering design. The subdivision refinement rules are usually adapted from knot insertion rules for splines. The quadrilateral Catmull-Clark scheme considered in this work is equivalent to cubic B-splines away from extraordinary, or irregular, vertices with other than four adjacent elements. Around extraordinary vertices the surface consists of a nested sequence of smooth spline patches which join $C^1$ continuously at the point itself. As known from geometric design literature, the subdivision weights can be optimised so that the surface quality is improved by minimising short-wavelength surface oscillations around extraordinary vertices. We use the related techniques to determine weights that minimise finite element discretisation errors as measured in the thin-shell energy norm. The optimisation problem is formulated over a characteristic domain and the errors in approximating cup- and saddle-like quadratic shapes obtained from eigenanalysis of the subdivision matrix are minimised. In finite element analysis the optimised subdivision weights for either cup- or saddle-like shapes are chosen depending on the shape of the solution field around an extraordinary vertex. As our computations confirm, the optimised subdivision weights yield a reduction of $50\%$ and more in discretisation errors in the energy and $L_2$ norms. Although, as to be expected, the convergence rates are the same as for the classical Catmull-Clark weights, the convergence constants are improved.

math.NA↗