Multilevel optimization aims at reducing the cost of executing a target network-based algorithm by exploiting coarsened, i.e., reduced or simplified, versions of the network. There is a growing interest in multilevel algorithms in networked systems, ...

Modelling spatio-temporal systems exhibiting multi-scale behaviour is a powerful tool in many branches of science, yet it still presents significant challenges. Here, we consider a general two-layer (agent-environment) modelling framework, where ...

“Statistical abstraction for multi-scale spatio-temporal systems” proposes a methodology that supports analysis of large-scaled spatio-temporal systems. These are represented via a set of agents whose behaviour depends on a perceived field. The proposed ...

Multilevel partitioning methods that are inspired by principles of multiscaling are the most powerful practical hypergraph partitioning solvers. Hypergraph partitioning has many applications in disciplines ranging from scientific computing to data science. ...

Various algebraic multigrid algorithms have been developed for solving problems in scientific and engineering computation over the past decades. They have been shown to be well-suited for solving discretized partial differential equations on unstructured ...

This paper presents a numerical coarsening method for corotational elasticity, which enables interactive large deformation of high-resolution heterogeneous objects. Our method derives a coarse elastic model from a high-resolution discretization of ...

Given a social network, can we quickly 'zoom-out' of the graph? Is there a smaller equivalent representation of the graph that preserves its propagation characteristics? Can we group nodes together based on their influence properties? These are ...

We study the coarsening rates for attachment-limited kinetics which is modeled by volume-preserving mean-curvature flow. Attachment-limited kinetics is observed during solidification processes, in which the system is divided into two domains of the two ...

Requirements for efficient parallelization of many complex and irregular applications can be cast as a hyper graph partitioning problem. The current-state-of-the art software libraries that provide tool support for the hyper graph partitioning problem ...

We consider a two-phase system governed by a Cahn--Hilliard type equation with a highly disparate diffusion mobility. It has been observed from recent numerical simulations that the microstructure evolution described by such a system displays a coarsening ...

We propose efficient and accurate algorithms for computing certain area preserving geometric motions of curves in the plane, such as area preserving motion by curvature. These schemes are based on a new class of diffusion generated motion algorithms ...

A new paradigm of adaptivity is to execute refinement, coarsening, and smoothing of meshes on manifolds with incomplete information about their geometry and yet preserve position and curvature accuracy. We refer to this collectively as geometrically ...

Smoluchowski’s coagulation equation is a fundamental mean-field model of clustering dynamics. We consider the approach to self-similarity (or dynamical scaling) of the cluster size distribution for the “solvable” rate kernels $K(x,y)=2,x+y$, and $xy$. ...

The minimum linear arrangement problem is widely used and studied in many practical and theoretical applications. In this paper we present a linear-time algorithm for the problem inspired by the algebraic multigrid approach which is based on weighted ...

Certain liquids on solid substrates form a configuration of droplets connected by a precursor layer. This configuration coarsens: The average droplet size grows while the number of droplets decreases and the characteristic distance between them increases. ...

The purpose of this paper is twofold. First we introduce improved versions of our algorithms for refining and coarsening 2D and 3D nested triangular and tetrahedral grids, and secondly the application of these algorithms in the simulation of 2D and 3D ...

A new method is developed for finite element (FE) domain decomposition. This method employs a hybrid graph-genetic algorithm for graph partitioning and correspondingly bisects finite element (FE) meshes.A weighted incidence graph is first constructed ...