Improved version for paper

Author: aamorm

+bases/getPolynomials.m

@@ -1,4 +1,4 @@
-function symPolynomials = getPolynomials(order)
+function [symPolynomials, xyz] = getPolynomials(order)
     % GETPOLYNOMIALS Gives the symbolic representation of the polynomials that
     % compose the mixed-order curl-conforming hexahedral space.
     %

getKcFromHalfFilledCavity.m +math/getKcFromHalfFilledCavity.m

@@ -0,0 +1,31 @@
+%% Driver to show the operating principle of the basis functions.
+
+% Point defined in the reference element.
+pointToEvaluateInReferenceElement = [1/2, 1/2, 1/2];
+
+%% Using the coefficients given in the paper.
+% Table extracted from Table II in the manuscript.
+disp('Evaluating the bases from a stored table of coefficients')
+load('tableReferenceCoefficients');
+% Polynomial order of the basis functions
+orderBasisFunctions = 2;
+% Polynomials that compose the space of function in the reference hexahedron.
+[polynomialsInSpace, symXYZ] = bases.getPolynomials(orderBasisFunctions);
+% The proposed functions are a linear combination of these polynomials with the
+% coefficients obtained from the procedure shown in figure 3
+symbolicReferenceFunctions = tableReferenceCoefficients.'*polynomialsInSpace;
+symbolicReferenceFunctionEvaluated = zeros(size(symbolicReferenceFunctions));
+for indexFunctions = 1:size(symbolicReferenceFunctions,1)
+    for indexComponent = 1:size(symbolicReferenceFunctions,2)
+        symbolicReferenceFunctionEvaluated(indexFunctions,indexComponent) = vpa(subs(symbolicReferenceFunctions(indexFunctions,indexComponent), symXYZ, pointToEvaluateInReferenceElement));
+    end
+end
+
+%% This is the equivalent procedure following the workflow of this demonstrator.
+disp('Evaluating the bases following the workflow of the code')
+sysBasesObj = bases.SystematicBases();
+polyReferenceFunctionEvaluated = sysBasesObj.getBasesEvaluated(pointToEvaluateInReferenceElement);
+
+% We can compare both outputs to obtain that numerically both procedures yield
+% the same results.
+fprintf('The total error obtained is %e\n',sum(abs(symbolicReferenceFunctionEvaluated(:)-polyReferenceFunctionEvaluated(:))))

plotHalfFilledCavity.m +math/plotHalfFilledCavity.m

@@ -0,0 +1,18 @@
+%% Driver for the generation of basis functions following the pseudcode shown in the document.
+
+%% Obtention of the basis functions following the figure 2.
+% For demonstration purposes.
+disp("Removing the bases stored...")
+bases.SystematicBases.removeBases();
+% The bases are defined as an object, and here we define the polynomial q in the
+% dofs (6), (7), and (8).
+sysBasesObj = bases.SystematicBases();
+disp("Generating the new coefficients...")
+% We obtain the coefficients as the dual basis to the Nédélec dofs.
+sysBasesObj.getCoefficients();
+% We store the coefficients for using them later.
+disp("Storing the coefficients generated...")
+sysBasesObj.saveCoefficients();
+disp("Showing the coefficients of the polynomials...")
+bases.showPolynomials();
+sysBasesObj.showBases();

meshesHalfFilledTAP2021.mat +settings/meshesHalfFilledTAP2021.mat

@@ -14,18 +14,18 @@
 
 %% Obtention of analytic eigenvalues.
 % Eigenvalues for the first six modes.
-k101 = getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 1, 0, 300, 16);
-k102 = getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 1, 0, 600, 16);
-k103 = getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 1, 0, 800, 16);
-k201 = getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 2, 0, 540, 16);
-k202 = getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 2, 0, 760, 16);
-k301 = getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 3, 0, 750, 16);
+k101 = math.getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 1, 0, 300, 16);
+k102 = math.getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 1, 0, 600, 16);
+k103 = math.getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 1, 0, 800, 16);
+k201 = math.getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 2, 0, 540, 16);
+k202 = math.getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 2, 0, 760, 16);
+k301 = math.getKcFromHalfFilledCavity(a, b, c, h, epr, sigmaCond, 3, 0, 750, 16);
 numberKc = 6;
 kc = [k101 k201 k102 k301 k202 k103];
 
 %% Loading of the hexahedral meshes.
 % In this container are included the meshes used for the results.
-load('meshesHalfFilledTAP2021.mat','projectMeshes');
+load('+settings/meshesHalfFilledTAP2021.mat','projectMeshes');
 lengthMeshes = length(projectMeshes);
 % Container to store the error for the different eigenvalues.
 errorHalfConvergence = zeros(numberKc,lengthMeshes);
@@ -45,9 +45,6 @@
 % We store the coefficients for using them later.
 disp("Storing the coefficients generated...")
 sysBasesObj.saveCoefficients();
-disp("Showing the coefficients of the polynomials...")
-bases.showPolynomials();
-sysBasesObj.showBases();
 
 %% Running through all the meshes.
 for indexMesh = 1:length(projectMeshes)
@@ -75,4 +72,4 @@
 end
 
 %% Plotting the results.
-plotHalfFilledCavity(errorHalfConvergence,lengthHalfConvergence);
+math.plotHalfFilledCavity(errorHalfConvergence,lengthHalfConvergence);