Patent ID: 6457033
Filing Date: 2002-09-24
Classification: G06F

Abstract:
An apparatus for analyzing a diffusion state by analyzing diffusion quantity f in a space having a diffusion source therein by using a diffusion equationf(r, t)/âˆ‚t=s(r, t)+Dâˆ‡2f(r, t) in which a partial differential of said f with respect to time âˆ‚f(r, t)/âˆ‚t, where r denotes spacial vector and t denotes, time is equal to a sum of the diffusion source s and a product of a diffusion coefficient D and a second order differential âˆ‡2f of a gradient âˆ‡ of said f, to determine the diffusion quantity f in said space, wherein said apparatus comprises:(a) means for Fourier-transforming spacial components with respect to f(r, t) and s(r, t) in both sides of said diffusion equation; (b) means for modifying each of the Fourier components obtained by the Fourier-transformation into a differential equation having a form df(t)/dt=s(t)âˆ’cf(t) representing each spacial frequency component where f(t) and s(t) are Fourier components of f(r, t) and s(r, t), respectively, c includes a component of square of wave number k, and boundary conditions of f(t) may be appropriately determined; (c) means for solving said differential equation relating to the Fourier components by repeating a finite difference method using a given finite difference equation relating to f(t+&Dgr;t), f(t) and s(t) in which f(t) and s(t) are multiplied by a value of an exponential function having a product of said c and a time interval &Dgr;t with a minus sign on its shoulder, respectively; and (d) means for summing up the solutions of the differential equations relating to said Fourier components which are obtained by the finite difference equation to output the sum as a solution of the original diffusion equation.