Computational Methods and Applications
The talk aims to present few of my past steps on scientific computations.
My very first work was on the formulation, analysis and implementation of iterative ADI methods for the solution of linear equations systems arising from the discretization of k-D elliptic PDEs using cubic splines.
A next step was on Interface Relaxation (IR) Methods for Elliptic Problems. This was about the formulation, theoretical study, analysis and error estimation for a variety of such methods with numerical results and applications.
IR methods are closely connected with Problem Solving Environments for complex multi-physics and multi-domain problems. The design, implementation and study of their efficiency on distributed computer systems followed.
Finally, new approaches that enable fast and accurate simulation of large-scale power delivery networks found in contemporary ICs were investigated. These methodologies combine an iterative linear system solution algorithm along with two problem-specific preconditioners. Experimental evaluation demonstrated that the proposed approaches can achieve up to two or three orders of magnitude speedup for power grid electrical analysis compared to state-of-the-art direct and iterative solvers.