How to set FEATool equation coefficient in MATLAB programmatically

I'm creating/modifying a FEATool model programmatically and would like to set equation coefficients directly in the model data structure.

For example, suppose I have a physics mode identified by a "mode_tag" and want to change its source term coefficient "f". I can access the equation coefficients with

    fea.phys.(mode_tag).eqn.coef

but I'm not quite sure how this array is organized, or how to reliably find and update a particular coefficient.

How can I set the source term f for a physics mode programmatically? Also, how are coefficient values stored when the physics mode is defined on several subdomains?

Note! The next release of FEATool Multiphysics will have a utility function seteqncoef that simplifies (and performs the below steps) in one function call/command.

Equation coefficients for a physics mode are stored in the fea.phys.(mode_tag).eqn.coef cell array.

The columns contain the coefficient tag/name, display label, description, and coefficient values, respectively. The coefficient values in the last column are themselves stored as a cell array, with one entry for each applicable subdomain.

For example, to set the source coefficient f:

% Get equation/subdomain coefficients.
eqn_coef = fea.phys.(mode_tag).eqn.coef;

% Find the source-term coefficient.
f_tag = ['f_', mode_tag];
f_row = find(strcmp(f_tag, eqn_coef(:,1)));

% Set the value.
eqn_coef{f_row,4} = {f};

% Store the modified coefficients back in the physics fea.phys.(mode_tag).
fea.phys.(mode_tag).eqn.coef = eqn_coef;

Here mode_tag is the tag of the physics fea.phys.(mode_tag). FEATool generates coefficient tags by combining the coefficient name with the physics-mode tag, so the source coefficient will typically have a tag such as

f_<mode_tag>

For example, if

mode_tag = 'ht';  % Default mode tag for Heat-transfer physics mode

the corresponding source coefficient tag is

f_ht

The important detail is that column 4 contains one coefficient value per subdomain. For a physics mode defined together with a geometry that has a single subdomain

eqn_coef{f_row, 4} = {f};

is sufficient. If the mode applies to several subdomains, the entries can be specified separately. For example:

eqn_coef{f_row, 4} = {1, 'x+y', 2.5};

would assign different source values/expressions to three subdomains. It can also be useful to inspect the coefficient table directly:

eqn_coef = fea.phys.(mode_tag).eqn.coef;
eqn_coef(:, 1:3)

This shows the available coefficient tags, labels, and descriptions and avoids relying on the row number of a particular coefficient. A more defensive version can check that the requested coefficient exists

eqn_coef = fea.phys.(mode_tag).eqn.coef;

f_tag = ['f_', mode_tag];
f_row = find(strcmp(f_tag, eqn_coef(:, 1)), 1);

if isempty(f_row)
    error('Coefficient "%s" was not found.', f_tag);
end

eqn_coef{f_row, 4} = {f};
fea.phys.(mode_tag).eqn.coef = eqn_coef;

The same approach can be used for other equation coefficients: inspect fea.phys.(mode_tag).eqn.coef(:,1) for the corresponding coefficient tag, locate that row, and update its fourth-column value.