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Numerous approximation algorithms for problems on unit disk graphs have been proposed in the literature, exhibiting a sharp trade-off between running times and approximation ratios. We introduce a variation of the known shifting strategy…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. They…
We describe a short, reproducible workflow for applying finite differences on nonuniform grids determined by a positive weight function g. The grid is obtained by equidistribution, mapping uniform computational coordinates $\xi\in[0,1]$ to…
Object rearrangement is a widely-applicable and challenging task for robots. Geometric constraints must be carefully examined to avoid collisions and combinatorial issues arise as the number of objects increases. This work studies the…
With the current burst of network theory (especially in connection with social and biological networks) there is a renewed interest on realizations of given degree sequences. In this paper we propose an essentially new degree sequence…
One-weight codes, in which all nonzero codewords share the same weight, form a highly structured class of linear codes with deep connections to finite geometry. While their classification is well understood in the Hamming and rank metrics -…
The concept of detecting arrays was developed to locate and detect interaction faults arising between the factors in a component-based system during software testing. In this paper, we propose a family of consecutive detecting arrays (CDAs)…
The paper studies a general scheme for constructing metrics on a product of metric spaces by means of a family of continuous convex functions. This construction includes the conventional $p$-metrics and generates metrics that are…
Let $A$ be a finite-dimensional algebra over a field $F$ with char$(F)\ne 2$. We show that a linear map $D:A\to A$ satisfying $xD(x)x\in [A,A]$ for every $x\in A$ is the sum of an inner derivation and a linear map whose image lies in the…
Efficient operation of distribution grids in the smart-grid era is hindered by the limited presence of real-time nodal and line meters. In particular, this prevents the easy estimation of grid topology and associated line parameters that…
The definition of $1$-planar graphs naturally extends graph planarity, namely a graph is $1$-planar if it can be drawn in the plane with at most one crossing per edge. Unfortunately, while testing graph planarity is solvable in linear time,…
This note describes the full approximation storage (FAS) multigrid scheme for an easy one-dimensional nonlinear boundary value problem. The problem is discretized by a simple finite element (FE) scheme. We apply both FAS V-cycles and…
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This…
In this paper, we introduce and study the multilevel-planarity testing problem, which is a generalization of upward planarity and level planarity. Let $G = (V, E)$ be a directed graph and let $\ell: V \to \mathcal P(\mathbb Z)$ be a…
On the basis of the generalized argument principle, here we develop a numerical scheme for locating zeros and poles of a meromorphic function. A subdivision-transformation-calculation scheme is proposed to ensure the algorithm stability. A…
Positive semidefinite (PSD) matrices are indispensable in many fields of science. A similarity measurement for such matrices is usually an essential ingredient in the mathematical modelling of a scientific problem. This paper proposes a…
Aiming to generate easy-to-handle assembly sequences for robotic assembly, this study tackles assembly sequence generation by considering two tradeoff objectives: (1) insertion conditions and (2) degrees of constraints among assembled…
A periodically loaded waveguide composed of periodic discrete nonlinear gain and radiating elements supports a stable oscillation regime related to the presence of an exceptional point of degeneracy (EPD). After reaching saturation, the EPD…
Multidimensional arrays (NDArrays) are a central abstraction in modern scientific computing environments. Unfortunately, they can make reasoning about programs harder as the number of different array shapes used in an execution of a program…