So here starts my research ...

This is my research proposal:

SURGE Research Proposal

Name: Abhishek Verma
College: National Institute of Technology, Trichy
Department: Computer Science and Engineering
Email id: cs10464@nitt.edu, vermaa@iitk.ac.in
Mentor: Dr. Phalguni Gupta

Topic: Solver for sparse Symmetric Positive Definite(SPD) system of linear equations.

I intend to implement a Solver in C for sparse symmetric positive definite system of linear equations. Large sparse linear systems occur frequently in engineering and scientific applications, and the solution of these systems is an important and costly step. Common sources of SPD matrices are finite element analysis of structures, the pressure correction phase of a segregated fluid dynamics simulation, and the analysis of electrical networks. The Cholesky decomposition of SPD matrices is faster than other methods for solving these linear equations. It requires about n^3/ 3 Floating Point Operations (FLOPs), where n is the size of the matrix. Hence they are twice as cheap as the LU Decomposition, which requires 2 n^3/ 3 FLOPs.

Solution of Linear equations of higher orders (N>1000) can be found by implementing Distributed Computing. I intend to implement this in Cilk. It is a language for multithreaded parallel programming based on ANSI C. Cilk is designed for general purpose parallel programming, but it is especially effective for exploiting dynamic, highly asynchronous parallelism. It can run on a wider variety of platforms, including massively parallel computers, symmetric multiprocessors, and networks of workstations.

A number of serial and parallel software packages for solving more general systems are available. Some of them are Watson Sparse Matrix Package (WSMP), Multifrontal Massively Parallel sparse direct Solver (MUMPS), Unsymmetric MultiFrontal (UMF) Package, etc. The algorithms involved in these shall be studied in detail and their performance will be tested and compared on several standard matrices from various scietific areas.