demo_fem2_discfunc.m

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function demo_fem2_discfunc
%function demo_fem2_discfunc
% This demo shows the basic functionality of the discrete function class
% Fem.DiscFunc.

% IM, 08.09.2016

% poisson_model
params = [];
pdeg = 4;
params.pdeg = pdeg;
params.dimrange = 3;
params.debug = 1;
params.numintervals = 5;

model = poisson_model(params);
% add fields for generic fem
model = generic_fem_model_adapter(model);

% construct grid
grid = construct_grid(model);
% generate discrete function info
df_info_scalar = Fem.Lagrange.DefaultInfo(model.pdeg, grid);
df_info = Fem.CompositeFunctionSpace(df_info_scalar, 'dim1', ...
    copy(df_info_scalar), 'dim2', ...
    copy(df_info_scalar), 'dim3');

disp('model initialized, display function space:');
display(df_info);

% initialize vectorial discrete function, extract scalar
% component and plot basis function
df = Fem.DiscFunc([], df_info); % initialize zero df

fprintf('\n');
disp('initialization of discrete function successful, display:');
display(df);

disp('press enter to continue');
pause;

% dof consistency / dofmap ?

% global dof access:
fprintf('\n');
disp('example of dof access, scalar component extraction and plot:');    
% set second vector component in 4th basis function nonzero
ncomp = 2;
locbasisfunc_index = 4;
df.dofs((ncomp-1)*df_info_scalar.ndofs + locbasisfunc_index) = 1;
% extract scalar component
dfscalar = get_component(df, 2); % should be nonzero function
disp(['entry should be 1 : ', ...
    num2str(dfscalar.dofs(locbasisfunc_index))]);

% automatic plot of all dimensions, id-strings are used as titles
params = [];
params.subsampling_level = 6;
figure, plot(df, params);

disp('press enter to continue');
pause;
close all

% interpolate global gaussian function, plot result
fprintf('\n');
disp('interpolation of global function and plot:');
func = @(glob, params) exp(-10*sum((glob-repmat([0.5, 0.5], size(glob, 1), 1)).^2, 2));
df_gauss = interpol_global(df_info_scalar, func);
figure, plot(df_gauss);
title('df: interpolated gaussian');

disp('press enter to continue');
pause;

% interpolate the derivatives (smaller pdeg), plot results
fprintf('\n');
disp('evaluation of derivatives (interpolation of local functions) and plot:');
df_info_scalar2 = Fem.Lagrange.DefaultInfo(model.pdeg-1, grid);

func = @(vgrid,el,lcoord,params) subsref(df_gauss.evaluate_derivative(el,lcoord), ...
    struct('type', '()', 'subs', {{':', 1}}));
df_dx = interpol_local(df_info_scalar2, func);

figure, plot(df_dx);
title('df/dx');

func = @(vgrid,el,lcoord,params) subsref(df_gauss.evaluate_derivative(el,lcoord), ...
    struct('type', '()', 'subs', {{':', 2}}));
df_dy = interpol_local(df_info_scalar2, func);

figure, plot(df_dy);
title('df/dy');

disp('press enter to continue');
pause;
close all

% norm computations
fprintf('\n');
disp('examples of norm computation:')
dfscalar.dofs(:) = 1;
disp(['L2-norm(f(x,y)=1) = ', num2str(l2_norm(dfscalar))]);
disp(['H10-norm(f(x,y)=1) = ', num2str(h10_norm(dfscalar))]);
disp('previous vector-valued function, only one DoF nonzero:');
disp(['L2-norm(f(0.6,0)=(0,1,0)) = ', num2str(l2_norm(df))]);
disp(['H10-norm(f(0.6,0)=(0,1,0)) = ', num2str(h10_norm(df))]);

end