Research
Postdoc (Aug 2016 - Feb 2018)
This research project is in the context of Electronic Components and Systems for European Leadership Joint Undertaking programme. The main objective of the research is to develop a standardized method to create multi-domain LED-based design and simulation tools for the European solid-state lighting industry.
LED-based lighting technology applications have been advancing from the basic needs to value creation and smart lighting. Thermal management is a key issue in designing and developing efficient LED-based luminaire products. DCTMs (Dynamic Compact Thermal Models) are required for predicting the thermal behaviours of LED chips fast and accurately in system level simulations. Mathematical MOR (Model Order Reduction) methods can be used for extracting DCTMs. My primary role in this research project is to create a MIMO (Multi-Input-Multi-Output) DCTM, which is capable of handling multiple heat sources and multiple temperature monitoring points.
Please visit the consortium website http://delphi4led.org for more information.
PhD (Aug 2012 - July 2016)
Thesis: Solution Methods for Indefinite Systems of Linear Equations in Saddle-point Form
The numerical approximation of many scientific and engineering problems leads to block-structured indefinite linear systems (having both positive and negative eigenvalues) in saddle-point (neither minimum nor maximum) form:
where A is an n-by-n symmetric matrix, B is an m-by-n constraint matrix, and C is an m-by-m symmetric (possibly a null) matrix, x and f are the vectors of length n, and y and g are the vectors of length m.
These systems originate for instance from discretization of partial differential equations using mixed finite element methods, constrained optimization problems, generalized least squares problems, and network analysis in electronic circuits and water distribution. In making the numerical models realistic and accurate enough, they can easily have millions of degrees of freedom. A significant portion of the computational time in numerical simulations is spent in solving these large linear systems. Numerical linear algebra algorithms for solving these systems more efficiently in terms of robustness, memory requirements and computational complexity are in high demand for software development. Designing such algorithms is intimately connected with understanding and exploiting the structure of the resulting block matrix system.
The research carried out in the thesis develops numerical solution techniques for saddle-point systems by exploiting the properties and structures of the associated block matrices. The principles of numerical linear algebra and combinatorial optimization techniques are used for developing these new techniques. The following are the main specific areas of studies carried out in this thesis:
- Investigate and validate the existing numerical solution methods for saddle-point systems.
- Develop new variants of factorization methods based on the block properties and block structures of saddle-point matrices.
- Develop combinatorial optimization techniques using graph theory for sparse matrix algorithms.
- Do analyses on numerical stability and computational complexity of the proposed methods.
- Develop new variants of preconditioning techniques for solving the saddle-point systems using Krylov subspace methods.
- Acquire strong foundations on numerical linear algebra and optimization.
- Explore and understand the application problems that give rise to saddle point systems.
In general, findings from this research contribute to the areas of scientific computing and numerical linear algebra, particularly for the development of robust and scalable solvers for large-scale linear systems.