Engineering topics
Publications and source records attributed to Vassilevski, PanayotS..
This project is intended to take a graph and build a smaller (upscaled) graph that is representative of the original in some way. We represent the graph Laplacian in a mixed form, solve some local eigenvalue problems to uncover near-nullspace modes, and use those modes as coarse degrees of freedom.
ParELAGMC is a parallel distributed memory C++ library for multilevel Monte Carlo (MLMC) simulations with algebraically constructed coarse spaces for estimating statistical moments of a quantity of interest involving solutions of partial differential equations with uncertain coefficients. A primary focus of the library is the scalable generation of Gaussian random fields using a novel stochastic PDE (SPDE) sampling technique for large-scale simulations. A key feature in the SPDE sampling technique is a novel non-matching mesh embedding technique to mitigate artificial boundary artifacts that are inherent in the method. Example applications to uncertainty quantification of subsurface flow simulations in the mixed finite element setting are provided as well.
smoothG is a collection of parallel C++ classes/functions that algebraically constructs reduced models of different resolutions from a given high-fidelity graph model. In addition, smoothG also provides efficient linear solvers for the reduced models. Other than pure graph problem, the software finds its application in subsurface flow and power grid simulations in which graph Laplacians are found