Dr Mohamad Abid Bazaz

2010-2013
Current Position: Asst. Prof, NIT Srinagar, J&K.

The importance of numerical simulations has steadily increased across virtually all scientific and engineering disciplines. In many application areas, experiments have been largely replaced by numerical simulations in order to save costs in design and development. High accuracy simulation requires high fidelity mathematical models which, in turn, induce dynamical systems of very large dimensions. The ensuing demands on computational resources can be overwhelming and efficient model utilization becomes a necessity. It often is both possible and prudent to produce a lower dimensional model that approximates the response of original one to high accuracy. There are many model reduction strategies in use that are remarkably effective in the creation of compact, efficient and high fidelity dynamical system models. Krylov-subspace based reduction is one of the most popular methods for reduced order modeling of very large systems with sizes ranging from tens of thousands to millions. However, one of the main drawbacks of this method is the lack of a proper stopping criterion. In Chapter 3 of this dissertation, we propose a simple and efficient stopping criterion for automated and efficient order selection for Krylov-based reduction techniques. Numerical experiments conducted on some benchmark problems validate the proposed criterion. Typically, a reduced order model represents a specific instance of the physical system under study, and as a consequence will have high fidelity only for small variations around that base system instance. Significant modifications to the physical model such as geometric variations, changes in material properties, or alterations in boundary conditions generally necessitate generation of new reduced models. Since the generation of a high fidelity reduced model may be comparable in expense to a brief simulation of an instance of the original full order model, the benefits of model reduction will be fully realized only if the parameter dependency found in the original dynamical system can be preserved in some fashion within thereduced model. This precisely is the goal of Parametrized Model Order Reduction which is one of the thrust areas in research related to model order reduction at present. In Chapter 4 of this dissertation, we present a two-step reduction strategy for differential-algebraic system obtained after finite element discretization of the parametric transient electromagnetic computational problem. For this problem, we assume a parametric dependence which allows a symbolic parametric presence in the Finite Element model. The strategy proposed for this system results in a drastically reduced model with the parametric dependence symbolically preserved, thereby allowing repetitive simulations in the reduced space without the need to refer back to the original system. The problem of parametric reduction of large systems becomes complicated if the parametric dependence cannot be expressed analytically. This is the case with parameters like geometrical variations which have a direct influence on discretiza- tions and as such do not have have an explicit presence in the Finite Element Models. For parametric reduction of such systems, a framework based on matrix.

Publications

Journals

• Mohammad Abid Bazaz, Mashuq-un-Nabi and S Janardhanan, "Automated and Efficient Order Selection in Krylov based Model Order Reduction", International Journal of Modeling, Identification and Control, Vol. 18, No. 4, pp. 332-340, 2013, doi : 10.1504/IJMIC.2013.053538


• Mohammad Abid Bazaz, Mashuq un Nabi and S Janardhanan, "Modelling and Simulation Strategy for Parametric Transient Electromagnetic Simulations", International Journal of Modeling, Identification and Control, Vol. 18, No. 3, pp. 251-260, 2013, doi : 10.1504/IJMIC.2013.052819.

Conferences

• M.A. Bazaz, M. Nabi, "Krylov subspace based reduced order modelling of induction heating systems", IEEE Sponsored International Conference on Process Automation, Control and Computing, PACC_2011, Coimbatore, pp. 1-5, 20-22 July, 2011. doi: 10.1109/PACC.2011.5978998.


• M.A. Bazaz, M. Nabi, S. Janardhanan, "Parameterized Model Order Reduction for fast transient electromagnetic simulations", IEEE Sponsored International Conference on Power, Signals, Controls and Computation, EPSCICON-2012, Thrissur, Kerela, pp. 1-4, 3-6 Jan. 2012. doi: 101109/EPSCICON.2012.6175271.


• M.A. Bazaz, M. Nabi, S. Janardhanan, "A review of Parametric Model Order Reduction Techniques", IEEE Sponcered International Conference on Signal Processing, Computing and Control, ISPCC-2012, Simla, pp. 1-6, 15-17 March 2012. doi:10.1109/ISPCC.2012.6224356.


• M.A. Bazaz, M. Nabi, S. Janardhanan, "Two-step reduction procedure for parametric transient electromagnetic computations", IEEE Sponsored International Conference on Modelling, Identification and Control, ICMIC-2012, Wuhan, China, pp. 1204-1209, 24-26 June 2012.


• M.A. Bazaz, M. Nabi, S. Janardhanan, "A stopping criterion for Krylov based Model Order Reduction Techniques", IEEE Sponsored International Conference on Modelling, Identification and Control, ICMIC-2012, Wuhan, China, pp. 921-925, 24-26 June 2012.


• Mohammad Abid Bazaz, Shahkar Ahmad Nahvi, Mashuq-un- Nabi, S Janardhanan, "Adaptive Parameter Space Sampling in Matrix Interpolatory pMOR", IEEE-RDCAPE, Noida, U.P. , India, March 2015.


• Shahkar Ahmad Nahvi, Mohammad Abid Bazaz, Mashuq-un- Nabi, S Janardhanan, "Fast Simulation of Nonlinear Dynamical Systems for Application in Reduced Order Modelling", Proc. of the European control conference (ECC-2014), Strasbourgh, France, July 2014.


• M. Nabi, M. Bazaz, P. Guha, "Krylov-Subspace Based Model Order Reduction for Field-Circuit Coupled Systems", 19th European Conference on Circuit theory and design 2009 (ECCTD'09), Antalya, Turkey, 23rd -27th August, 2009, pp. 480-484.


• P. Guha, M. Bazaz & M. Nabi, "Model Based Reduction for field circuit Coupled Systems", International Conference on Computer Applications In Electrical Engg. Recent Advances, Roorkee, India, Oct 2013.