Low-Rank Alternating Direction Implicit Iteration in pyMOR

The low-rank alternating direction implicit (LR-ADI) iteration is an effective method for solving large-scale Lyapunov equations. In the software library pyMOR, solutions to Lyapunov equations play an important role when reducing a model using the balanced truncation method. In this article we introduce the LR-ADI iteration as well as pyMOR, while focusing on its features which are relevant for integrating the iteration into the library. We compare the run time of the iteration's pure pyMOR implementation with those achieved by external libraries available within the pyMOR framework.

Bounday-Layer Asymptotics on the Contact Interface in the Impact Problem

The information of boundary condition in the contact interface reflected complex properties of visco-elastic material with various contact conditions. Numerical results and the asymptotic estimates were calculated. It is presented by the software which are consistent with the boundary-layer analysis in our previous papers. In this paper, the application of computer simulating and related numerical result on the contact boundary-layer has been discussed. Numerical results were calculated (by using HPC platform, NAG toolbox for Matlab) and shown by use of the software i.e. LS-DYNA. The numerical scheme yields the convergent finite element analysis (FEA) solution and stable semi-discrete Galerkin-ADI (G-ADI) iteration.

Air Movement in Buildings Using Computational Fluid Dynamics

This paper presents the development of a three-dimensional numerical model to study the distributions of indoor air velocity, air temperature, contaminant concentration, and ventilation effectiveness in a two-zone enclosure. The numerical model is based on the k–ε two-equation model of turbulence and the SIMPLE algorithm. The false-time step and ADI iteration procedure are employed. The results of the computed velocity and temperature profiles and convective heat transfer by the model are in good agreement with the measurements as well as with the prediction of the PHOENICS code.