private int get_matrix_index(matrix_class i_the_matrix, int i_id, int row_count)
{
for (int i = 0; i < row_count; i++)
{
if (i_the_matrix.GetRow(i)[1] == i_id)
{
return(i);
}
}
return(-1);
}
private void first_order_solver(ref RichTextBox richTextBox_analysis_status)
{
richTextBox_analysis_status.Clear(); // clear the richTextBox_AnalysisUpdate
// loop variable
int i, j, k;
int dof = inpt_fe_object.main_mesh.all_points.Count;
int edge_count = inpt_fe_object.main_mesh.all_edges.Count;
int elmt_count = inpt_fe_object.main_mesh.all_triangles.Count;
matrix_class global_k_matrix = new matrix_class(dof, dof);
matrix_class global_f_matrix = new matrix_class(dof, 1);
matrix_class global_dof_matrix = new matrix_class(dof, 1);
// create nodes, edges and elements just for analysis
matrix_class all_nodes_matrix = new matrix_class(dof, 6);
matrix_class all_edges_matrix = new matrix_class(edge_count, 8);
matrix_class all_elements_matrix = new matrix_class(elmt_count, 8);
// create node matrix
for (i = 0; i < dof; i++)
{
// node index, node id, node x coord, node y coord, node heat source, node specififed temperature
all_nodes_matrix.SetRow(i, new double[] { i,
inpt_fe_object.main_mesh.all_points[i].id,
inpt_fe_object.main_mesh.all_points[i].x,
inpt_fe_object.main_mesh.all_points[i].y,
inpt_fe_object.main_mesh.all_points[i].heat_source,
inpt_fe_object.main_mesh.all_points[i].spec_temp });
}
// create edges matrix
for (i = 0; i < edge_count; i++)
{
// edge index, edge id, start node index, end node index, edge heat source, edge specified temperature, edge heat transfer coeff, edge ambient temp
all_edges_matrix.SetRow(i, new double[] { i,
inpt_fe_object.main_mesh.all_edges[i].edge_id,
get_matrix_index(all_nodes_matrix, inpt_fe_object.main_mesh.all_edges[i].start_pt.id, dof),
get_matrix_index(all_nodes_matrix, inpt_fe_object.main_mesh.all_edges[i].end_pt.id, dof),
inpt_fe_object.main_mesh.all_edges[i].heat_source,
inpt_fe_object.main_mesh.all_edges[i].specified_temp,
inpt_fe_object.main_mesh.all_edges[i].heat_transfer_coeff,
inpt_fe_object.main_mesh.all_edges[i].ambient_temp });;
}
richTextBox_analysis_status.AppendText("Number of Nodes " + inpt_fe_object.main_mesh.all_points.Count.ToString() + "\n\n");
richTextBox_analysis_status.AppendText("Number of Edges " + inpt_fe_object.main_mesh.all_edges.Count.ToString() + "\n\n");
richTextBox_analysis_status.AppendText("Number of Elements " + inpt_fe_object.main_mesh.all_triangles.Count.ToString() + "\n\n");
// create element matrix
for (i = 0; i < elmt_count; i++)
{
// extract current element
pslg_datastructure.triangle2d current_element = inpt_fe_object.main_mesh.all_triangles[i];
// element index, element id, vertex 1 index, vertex 2 index, vertex 3 index, edge 1 index, edge 2 index, edge 3 index
all_elements_matrix.SetRow(i, new double[] { i,
inpt_fe_object.main_mesh.all_triangles[i].face_id,
get_matrix_index(all_nodes_matrix, inpt_fe_object.main_mesh.all_triangles[i].vertices[0].id, dof),
get_matrix_index(all_nodes_matrix, inpt_fe_object.main_mesh.all_triangles[i].vertices[1].id, dof),
get_matrix_index(all_nodes_matrix, inpt_fe_object.main_mesh.all_triangles[i].vertices[2].id, dof),
get_matrix_index(all_edges_matrix, inpt_fe_object.main_mesh.all_triangles[i].edge_id[0], edge_count),
get_matrix_index(all_edges_matrix, inpt_fe_object.main_mesh.all_triangles[i].edge_id[1], edge_count),
get_matrix_index(all_edges_matrix, inpt_fe_object.main_mesh.all_triangles[i].edge_id[2], edge_count) });
// extract the edges of the element
pslg_datastructure.edge2d current_elm_edge1 = inpt_fe_object.main_mesh.all_edges[(int)all_elements_matrix[i, 5]];
pslg_datastructure.edge2d current_elm_edge2 = inpt_fe_object.main_mesh.all_edges[(int)all_elements_matrix[i, 6]];
pslg_datastructure.edge2d current_elm_edge3 = inpt_fe_object.main_mesh.all_edges[(int)all_elements_matrix[i, 7]];
// conduction matrix
matrix_class conduction_matrix = new matrix_class(2, 2);
conduction_matrix.SetRow(0, new double[] { current_element.thermal_conductivity_x, 0.0 });
conduction_matrix.SetRow(1, new double[] { 0.0, current_element.thermal_conductivity_y });
// linear shape function parameters
double a_i, b_i, c_i, a_j, b_j, c_j, a_k, b_k, c_k;
a_i = (all_nodes_matrix[(int)all_elements_matrix[i, 3], 2] * all_nodes_matrix[(int)all_elements_matrix[i, 4], 3]) -
(all_nodes_matrix[(int)all_elements_matrix[i, 4], 2] * all_nodes_matrix[(int)all_elements_matrix[i, 3], 3]);
b_i = all_nodes_matrix[(int)all_elements_matrix[i, 3], 3] - all_nodes_matrix[(int)all_elements_matrix[i, 4], 3];
c_i = all_nodes_matrix[(int)all_elements_matrix[i, 4], 2] - all_nodes_matrix[(int)all_elements_matrix[i, 3], 2];
a_j = (all_nodes_matrix[(int)all_elements_matrix[i, 4], 2] * all_nodes_matrix[(int)all_elements_matrix[i, 2], 3]) -
(all_nodes_matrix[(int)all_elements_matrix[i, 2], 2] * all_nodes_matrix[(int)all_elements_matrix[i, 4], 3]);
b_j = all_nodes_matrix[(int)all_elements_matrix[i, 4], 3] - all_nodes_matrix[(int)all_elements_matrix[i, 2], 3];
c_j = all_nodes_matrix[(int)all_elements_matrix[i, 2], 2] - all_nodes_matrix[(int)all_elements_matrix[i, 4], 2];
a_k = (all_nodes_matrix[(int)all_elements_matrix[i, 2], 2] * all_nodes_matrix[(int)all_elements_matrix[i, 3], 3]) -
(all_nodes_matrix[(int)all_elements_matrix[i, 3], 2] * all_nodes_matrix[(int)all_elements_matrix[i, 2], 3]);
b_k = all_nodes_matrix[(int)all_elements_matrix[i, 2], 3] - all_nodes_matrix[(int)all_elements_matrix[i, 3], 3];
c_k = all_nodes_matrix[(int)all_elements_matrix[i, 3], 2] - all_nodes_matrix[(int)all_elements_matrix[i, 2], 2];
// B_matrix of linear triangle
matrix_class b_matrix = new matrix_class(2, 3);
b_matrix.SetRow(0, new double[] { b_i, b_j, b_k });
b_matrix.SetRow(1, new double[] { c_i, c_j, c_k });
b_matrix = (1.0 / (2.0 * current_element.element_area)) * b_matrix;
// element conduction matrix
matrix_class element_conduction_matrix = new matrix_class(3, 3);
element_conduction_matrix = (current_element.element_thickness * current_element.element_area) * (b_matrix.Transpose() * (conduction_matrix * b_matrix));
// element convection matrix
double c_param = (-2.0 * current_element.heat_transfer_coeff) / (current_element.element_thickness);
matrix_class element_convection_matrix = new matrix_class(3, 3);
element_convection_matrix.SetRow(0, new double[] { 2, 1, 1 });
element_convection_matrix.SetRow(1, new double[] { 1, 2, 1 });
element_convection_matrix.SetRow(2, new double[] { 1, 1, 2 });
element_convection_matrix = ((c_param * current_element.element_area) / 12.0) * element_convection_matrix;
// element heat convection due to edge exposed to ambient temperature (internal edges shouldn't have convection (user caution is required))
// element convection due to edge i-j convection
matrix_class element_edge_ij_convection_matrix = new matrix_class(3, 3);
element_edge_ij_convection_matrix.SetRow(0, new double[] { 2, 1, 0 });
element_edge_ij_convection_matrix.SetRow(1, new double[] { 1, 2, 0 });
element_edge_ij_convection_matrix.SetRow(2, new double[] { 0, 0, 0 });
element_edge_ij_convection_matrix = ((current_elm_edge1.heat_transfer_coeff * current_elm_edge1.edge_length * current_element.element_thickness) / 6.0) * element_edge_ij_convection_matrix;
// element convection due to edge j-k convection
matrix_class element_edge_jk_convection_matrix = new matrix_class(3, 3);
element_edge_jk_convection_matrix.SetRow(0, new double[] { 0, 0, 0 });
element_edge_jk_convection_matrix.SetRow(1, new double[] { 0, 2, 1 });
element_edge_jk_convection_matrix.SetRow(2, new double[] { 0, 1, 2 });
element_edge_jk_convection_matrix = ((current_elm_edge2.heat_transfer_coeff * current_elm_edge2.edge_length * current_element.element_thickness) / 6.0) * element_edge_jk_convection_matrix;
// element convection due to edge k-i convection
matrix_class element_edge_ki_convection_matrix = new matrix_class(3, 3);
element_edge_ki_convection_matrix.SetRow(0, new double[] { 2, 0, 1 });
element_edge_ki_convection_matrix.SetRow(1, new double[] { 0, 0, 0 });
element_edge_ki_convection_matrix.SetRow(2, new double[] { 1, 0, 2 });
element_edge_ki_convection_matrix = ((current_elm_edge3.heat_transfer_coeff * current_elm_edge3.edge_length * current_element.element_thickness) / 6.0) * element_edge_ki_convection_matrix;
// element heat source matrix
matrix_class element_heat_source_matrix = new matrix_class(3, 1);
element_heat_source_matrix.SetColumn(0, new double[] { 1, 1, 1 });
element_heat_source_matrix = ((current_element.heat_source * current_element.element_area * current_element.element_thickness) / 3.0) * element_heat_source_matrix;
// element heat convection 1 matrix
matrix_class element_heat_convection_matrix = new matrix_class(3, 1);
element_heat_convection_matrix.SetColumn(0, new double[] { 1, 1, 1 });
element_heat_convection_matrix = ((c_param * current_element.ambient_temp * current_element.element_area) / 3.0) * element_heat_convection_matrix;
// edge heat source matrix
matrix_class edge_heatsource_matrix = new matrix_class(3, 1);
// edge heat soure due to edge i-j source
matrix_class edge_ij_heatsource_matrix = new matrix_class(3, 1);
edge_ij_heatsource_matrix.SetColumn(0, new double[] { 1, 1, 0 });
edge_ij_heatsource_matrix = ((current_elm_edge1.heat_source * current_elm_edge1.edge_length * current_element.element_thickness) / 2.0) * edge_ij_heatsource_matrix;
// edge heat soure due to edge j-k source
matrix_class edge_jk_heatsource_matrix = new matrix_class(3, 1);
edge_jk_heatsource_matrix.SetColumn(0, new double[] { 0, 1, 1 });
edge_jk_heatsource_matrix = ((current_elm_edge2.heat_source * current_elm_edge2.edge_length * current_element.element_thickness) / 2.0) * edge_jk_heatsource_matrix;
// edge heat soure due to edge k-i source
matrix_class edge_ki_heatsource_matrix = new matrix_class(3, 1);
edge_ki_heatsource_matrix.SetColumn(0, new double[] { 1, 0, 1 });
edge_ki_heatsource_matrix = ((current_elm_edge3.heat_source * current_elm_edge3.edge_length * current_element.element_thickness) / 2.0) * edge_ki_heatsource_matrix;
edge_heatsource_matrix = edge_ij_heatsource_matrix + edge_jk_heatsource_matrix + edge_ki_heatsource_matrix;
// edge heat convection matrix
matrix_class edge_heatconvection_matrix = new matrix_class(3, 1);
// edge heat convection due to edge i-j ambient temperature
matrix_class edge_ij_heatconvection_matrix = new matrix_class(3, 1);
edge_ij_heatconvection_matrix.SetColumn(0, new double[] { 1, 1, 0 });
edge_ij_heatconvection_matrix = ((current_elm_edge1.heat_transfer_coeff * current_elm_edge1.ambient_temp * current_elm_edge1.edge_length * current_element.element_thickness) / 2.0) * edge_ij_heatconvection_matrix;
// edge heat convection due to edge j-k ambient temperature
matrix_class edge_jk_heatconvection_matrix = new matrix_class(3, 1);
edge_jk_heatconvection_matrix.SetColumn(0, new double[] { 0, 1, 1 });
edge_jk_heatconvection_matrix = ((current_elm_edge2.heat_transfer_coeff * current_elm_edge2.ambient_temp * current_elm_edge2.edge_length * current_element.element_thickness) / 2.0) * edge_jk_heatconvection_matrix;
// edge heat convection due to edge k-i ambient temperature
matrix_class edge_ki_heatconvection_matrix = new matrix_class(3, 1);
edge_ki_heatconvection_matrix.SetColumn(0, new double[] { 1, 0, 1 });
edge_ki_heatconvection_matrix = ((current_elm_edge3.heat_transfer_coeff * current_elm_edge3.ambient_temp * current_elm_edge3.edge_length * current_element.element_thickness) / 2.0) * edge_ki_heatconvection_matrix;
edge_heatconvection_matrix = edge_ij_heatconvection_matrix + edge_jk_heatconvection_matrix + edge_ki_heatconvection_matrix;
// edge specified temperature matrix
matrix_class edge_spectemp_matrix = new matrix_class(3, 1);
// edge i-j specified temperature
matrix_class edge_ij_spectemp_matrix = new matrix_class(3, 1);
edge_ij_spectemp_matrix.SetColumn(0, new double[] { 1, 1, 0 });
edge_ij_spectemp_matrix = (current_elm_edge1.specified_temp / 2.0) * edge_ij_spectemp_matrix;
// edge j-k specified temperature
matrix_class edge_jk_spectemp_matrix = new matrix_class(3, 1);
edge_jk_spectemp_matrix.SetColumn(0, new double[] { 0, 1, 1 });
edge_jk_spectemp_matrix = (current_elm_edge2.specified_temp / 2.0) * edge_jk_spectemp_matrix;
// edge k-i specified temperature
matrix_class edge_ki_spectemp_matrix = new matrix_class(3, 1);
edge_ki_spectemp_matrix.SetColumn(0, new double[] { 1, 0, 1 });
edge_ki_spectemp_matrix = (current_elm_edge3.specified_temp / 2.0) * edge_ki_spectemp_matrix;
edge_spectemp_matrix = edge_ij_spectemp_matrix + edge_jk_spectemp_matrix + edge_ki_spectemp_matrix;
// element k matrix
matrix_class element_k_matrix = new matrix_class(3, 3);
element_k_matrix = element_conduction_matrix + (-element_convection_matrix) + element_edge_ij_convection_matrix + element_edge_jk_convection_matrix + element_edge_ki_convection_matrix;
// element f matrix
matrix_class element_f_matrix = new matrix_class(3, 1);
element_f_matrix = element_heat_source_matrix + element_heat_convection_matrix + edge_heatsource_matrix + edge_heatconvection_matrix;
// dof matrix carries the specified temperature
// element dof matrix
matrix_class element_dof_matrix = new matrix_class(3, 1);
element_dof_matrix = edge_spectemp_matrix;
// global k matrix
for (k = 0; k < 3; k++)
{
int v_index1 = (int)all_elements_matrix[i, 2 + k];
for (j = 0; j < 3; j++)
{
int v_index2 = (int)all_elements_matrix[i, 2 + j];
// global k matrix
global_k_matrix[v_index1, v_index2] = global_k_matrix[v_index1, v_index2] + element_k_matrix[k, j];
}
// global f matrix
global_f_matrix[v_index1, 0] = global_f_matrix[v_index1, 0] + element_f_matrix[k, 0];
// global dof matrix
global_dof_matrix[v_index1, 0] = global_dof_matrix[v_index1, 0] + element_dof_matrix[k, 0];
}
}
// Apply nodal heat source & specified temperature
for (i = 0; i < dof; i++)
{
// heat source at node
global_f_matrix[i, 0] = global_f_matrix[i, 0] + inpt_fe_object.main_mesh.all_points[i].heat_source;
// specified temperature
global_dof_matrix[i, 0] = global_dof_matrix[i, 0] + inpt_fe_object.main_mesh.all_points[i].spec_temp;
}
// Applying specified temperature as source
matrix_class global_spec_temp_matrix = new matrix_class(dof, 1);
global_spec_temp_matrix = -1 * (global_k_matrix * global_dof_matrix);
// Find the size of matrix after boundary condition is applied
int soln_matrix_count = 0;
for (i = 0; i < dof; i++)
{
if (global_dof_matrix[i, 0] == 0)
{
soln_matrix_count++;
}
}
richTextBox_analysis_status.AppendText("Total number of DOF without prescribed Temperature " + soln_matrix_count.ToString() + "\n\n");
// curtailed matrix after applying boundary condition
matrix_class curtailed_global_k_matrix = new matrix_class(soln_matrix_count, soln_matrix_count);
matrix_class curtailed_global_f_matrix = new matrix_class(soln_matrix_count, 1);
int r = 0, s = 0;
for (i = 0; i < dof; i++)
{
if (global_dof_matrix[i, 0] != 0)
{
continue;
}
else
{
// apply boundary condition to global f matrix
curtailed_global_f_matrix[r, 0] = global_f_matrix[i, 0] + global_spec_temp_matrix[i, 0];
s = 0;
for (j = 0; j < dof; j++)
{
if (global_dof_matrix[j, 0] != 0)
{
continue;
}
else
{
// apply boundary condition to global k matrix
curtailed_global_k_matrix[r, s] = global_k_matrix[i, j];
s++;
}
}
r++;
}
}
// Build matrix to use in mathnet.numerics
Matrix <double> A_var = Matrix <double> .Build.DenseOfArray(curtailed_global_k_matrix.return_matrix_as_double);
Vector <double> B_var = Vector <double> .Build.Dense(curtailed_global_f_matrix.GetColumn(0));
// solve the matrix using mathnet.numerics
Vector <double> x_var = A_var.Solve(B_var);
// global t matrix
double[] gloabl_t_val = new double[dof];
r = 0;
for (i = 0; i < dof; i++)
{
if (global_dof_matrix[i, 0] != 0)
{
gloabl_t_val[i] = global_dof_matrix[i, 0];
}
else
{
gloabl_t_val[i] = x_var[r];
r++;
}
}
// create element store list
List <pslg_datastructure.result_store.first_order_element_store> f_o_elements = new List <pslg_datastructure.result_store.first_order_element_store>();
// maximum and minimum z val
double max_zval = gloabl_t_val.Max();
double min_zval = gloabl_t_val.Min();
// set the contour intervals
double z_val_range = max_zval - min_zval;
double[] contour_interval = new double[static_parameters.n_contour_intervals];
for (i = 1; i < static_parameters.n_contour_intervals; i++)
{
contour_interval[i] = min_zval + ((z_val_range / static_parameters.n_contour_intervals) * i);
}
if (z_val_range <= 1E-10 || double.IsNaN(z_val_range) == true)
{
richTextBox_analysis_status.AppendText("!!!!!!!! Analysis Failed !!!!!!!! " + "\n\n");
return; // Exit sub
}
else
{
richTextBox_analysis_status.AppendText("Maximum Temperature " + max_zval.ToString() + "\n");
richTextBox_analysis_status.AppendText("Minimum Temperature " + min_zval.ToString() + "\n\n");
richTextBox_analysis_status.AppendText("!!!!!!!! Analysis Complete !!!!!!!! " + "\n\n");
}
// Set the results to output
for (i = 0; i < elmt_count; i++)
{
double[] elm_z_val = new double[3];
elm_z_val[0] = gloabl_t_val[(int)all_elements_matrix[i, 2]];
elm_z_val[1] = gloabl_t_val[(int)all_elements_matrix[i, 3]];
elm_z_val[2] = gloabl_t_val[(int)all_elements_matrix[i, 4]];
pslg_datastructure.result_store.first_order_element_store f_o_elm = new pslg_datastructure.result_store.first_order_element_store(inpt_fe_object.main_mesh.all_triangles[i],
elm_z_val, contour_interval, max_zval, min_zval);
f_o_elements.Add(f_o_elm);
}
// create result store and add it to the model
pslg_datastructure.result_store rslt_output = new pslg_datastructure.result_store();
rslt_output = new pslg_datastructure.result_store(1, f_o_elements, null, null, max_zval, min_zval, contour_interval);
inpt_fe_object.main_mesh.set_analysis_results(rslt_output);
}
