Page 273 - Process Modelling and Simulation With Finite Element Methods

260 Process Modelling and Simulation with Finite Element Methods

Optimization Method for ECT Inversion
A common way of treating inversion problems is to minimize an error norm
defined on the discrepancy between the predicted solutions of the forward
problem and the measured boundary data. How does it work? First we need to
package our forward ECT model as an m-file function. The first step is to reset
the model m-file on the ECT forward problem, insert a stationary nonlinear
(actually linear will suffice) solver step, and a boundary integration to round off
the computation. Then save the model m-file to ect.m. Copy a version to
ect2.m, and we will begin surgery to package it as an m-file function. Begin
with the function call line
function [ql,q2,q31 =ect2 (el,e2,e3)
% FEMLAB Model M-file for ECT forward problem
% Generated 07-Nov-2002 09:53:56 by FEMLAB 2.3.0.145.
flclear fern
% FEMLAB Version
clear vrsn;
vrsn.name='FEMLAB 2.3';
vrsn .ma j or=O ;
vrsn.build=145;
fem.version=vrsn;

% Recorded command sequence
...
%WZ: Edit the constants to pass the arguments el,e2, and e3
% Define constants
fem.const={ ...
'eO', 1, ...
.
'el', el,. .
'e2', e2,. . .
'e3', e3,. . .
'e4', 0.05};
...
%WZ: Manufacture the output data
% Integrate on subdomains
...
ql=postint(fem,'0.707107*phix+0.707107*phiy',
'cont', 'internal', ...
'contorder',2, ...
'edim', 1, . . .
'solnum', 1, . .
.
'phase', 0, ...
'geomnum',l, ...
'dl', 24,. . .
'intorder',4, ...
I context , I local ) ;
% Integrate on subdomains
q2=postint(fem, '0.707107*phix-0.707107*phiy', ...
'cont', 'internal', ...
'contorder',2, ...
'edim', 1,. . .
.
'solnum', 1,. .
'phase', 0, . .
.
'geomnum' ,1, . . .