Introduction

Abstract

The universe consists of matter and energy as depicted in Fig. 1.1; the aim of the engineering science is to understand both and try to model and develop any system. Many physical phenomena can be described mathematically by the same class of system. Any system can be represented by a set of continuous Partial Differential Equations (PDEs) or discrete Ordinary Differential Equations (ODEs). At the same time, any set of PDEs should be transformed into a system of ODEs which can be linear ODEs or nonlinear ODEs. So, discretization is needed which approximates the behavior of the continuous systems. For example, Maxwell’s equations in electromagnetic describe the behavior of the system continuously in time and space [1]. Most CAD tools use the numerical Finite Element Method (FEM) approximation to accurately discretize in space, model and simulate these continuous structure-level VLSI systems. Solving linear ODEs results in matrix form system that can be solved using direct method such as Gaussian elimination method or indirect method (iterative methods) such as Jacobi method, and solving nonlinear ODEs can be done by Newton’s method. These methods are useful for moderately sized problems.