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Foil 17 Iterative Methods and Analogy to Diffusion with an Artificial Time

From CPS615-Basic PDE Solver Discussion and Sparse Matrix Formulation Delivered Lectures of CPS615 Basic Simulation Track for Computational Science -- 8 November 96. by Geoffrey C. Fox *
Secs 457.9
We must use Iterative methods to solve the linear equations coming from solution of large elliptic equations (Laplace's equation in example we will study)
We can motivate iteration by studying an "artificial" diffusion equation
subject to y having same boundary conditions (in x for all "artificial time" t ) as original equation
that we needed to solve
Consider ANY trial function y = y(0) at t = 0
Then we solve (*) and look at converged solution as t
As
The iteration of (*) in t gives a solution of (**) in limit of infinite t

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