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Panchenko, Alexander

Publications and source records attributed to Panchenko, Alexander.

4 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Efficient estimation of the modified Gromov–Hausdorff distance between unweighted graphs

Abstract Gromov–Hausdorff distances measure shape difference between the objects representable as compact metric spaces, e.g. point clouds, manifolds, or graphs. Computing any Gromov–Hausdorff distance is equivalent to solving an NP-hard optimization problem, deeming the notion impractical for applications. In this paper we propose a polynomial algorithm for estimating the so-called modified Gromov–Hausdorff (mGH) distance, a relaxation of the standard Gromov–Hausdorff (GH) distance with similar topological properties. We implement the algorithm for the case of compact metric spaces induced by unweighted graphs as part of Python library , and demonstrate its performance on real-world and synthetic networks. The algorithm finds the mGH distances exactly on most graphs with the scale-free property. We use the computed mGH distances to successfully detect outliers in real-world social and computer networks.

Oles, Vladyslav (ORCID:0000000188727463)↗
DOE OSTI2014

Discrete models of fluids: spatial averaging, closure and model reduction

We consider semidiscrete ODE models of single-phase fluids and two-fluid mixtures. In the presence of multiple fine-scale heterogeneities, the size of these ODE systems can be very large. Spatial averaging is then a useful tool for reducing computational complexity of the problem. The averages satisfy exact balance equations of mass, momentum, and energy. These equations do not form a satisfactory continuum model because evaluation of stress and heat flux requires solving the underlying ODEs. To produce continuum equations that can be simulated without resolving microscale dynamics, we recently proposed a closure method based on the use of regularized deconvolution. Here we continue the investigation of deconvolution closure with the long term objective of developing consistent computational upscaling for multiphase particle methods. The structure of the fine-scale particle solvers is reminiscent of molecular dynamics. For this reason we use nonlinear averaging introduced for atomistic systems by Noll, Hardy, and Murdoch-Bedeaux. We also consider a simpler linear averaging originally developed in large eddy simulation of turbulence. We present several simple but representative examples of spatially averaged ODEs, where the closure error can be analyzed. Based on this analysis we suggest a general strategy for reducing the relative error of approximate closure. For problems with periodic highly oscillatory material parameters we propose a spectral boosting technique that augments the standard deconvolution and helps to correctly account for dispersion effects. We also conduct several numerical experiments, one of which is a complete mesoscale simulation of a stratified two-fluid flow in a channel. In this simulation, the operation count per coarse time step scales sublinearly with the number of particles.

Multiscale modeling, discrete models, fluid flow↗
DOE OSTI2011

Dimension reduction method for ODE fluid models

We develop a dimension reduction method for large size ODE systems obtained from a dis- cretization of partial differential equations of viscous fluid flow of nearly constant density. The method is also applicable to other large size classical particle systems with negligibly small variations of concentration. We propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution. To illustrate the computa- tional advantages of the proposed reduction method we use it to solve a system of Smoothed Particle Hydrodynamic ODEs describing Poiseuille flows driven by uniform and periodic (in space) body forces. For the Poiseuille flow driven by the uniform force the coarse solution was obtained with the zero-order deconvolution. For the flow driven by the periodic body force, the first-order deconvolution was necessary to obtain a sufficiently accurate solution.

dimension reduction↗