/// <summary>
/// Developed by: Mehrdad Negahban
/// Date: 12/26/2012
///
/// Purpose: CrankNicholson solver using sparse matrix for first order transient problem (C dU/dt + K U = F)
/// Comments:
///
/// Date modified:
/// Modified by:
/// Comments:
/// </summary>
public override void SolveFEMSystem()
{
//Set up the load vector and stiffness matrix
int NDF = Unknowns_NDoF; //Get the size of the unknowns temperature (one per node)
Vector F_old = new Vector(NDF); //Make global load vector (old)
Vector F_new = new Vector(NDF); //Make global load vector (new)
MatrixSparseLinkedList K = new MatrixSparseLinkedList(NDF); // Make global stiffness matrix
MatrixSparseLinkedList C = new MatrixSparseLinkedList(NDF); // Make global thermal mass matrix
//Assemble F, K, C
int NE = Elements.Length; //Get the number of elements
for (int i = 0; i < NE; i++)
{
Elements[i].CalculateAndAssemble_FeAndKeAndCe(ref F_old, ref K, ref C);
}
//Adjust for boundary conditions
int NBE = BoundaryElements.Length;
for (int i = 0; i < NBE; i++)
{
BoundaryElements[i].AdjustK(Times.Values[StartIndex], ref K);
}
K = 0.5 * K;
C = C / DTime;
MatrixSparseLinkedList C1 = C - K;
C = C + K; // Calculate Chat and store in C
//Adjust C for boundary condition
for (int i = 0; i < NBE; i++)
{
BoundaryElements[i].AdjustChat(Times.Values[StartIndex], ref C);
}
C.LUDecomposition_Parallel();//Run LU decomposition on C
//Adjust F for BC
for (int i = 0; i < NBE; i++)
{
BoundaryElements[i].AdjustF(Times.Values[StartIndex], ref F_old);
}
F_old = 0.5D * F_old;
//Store initial time and temperature
Vector U_old = new Vector(Ut[StartIndex]);
Node_ND.Set_UnknownForNode(Nodes, U_old);
StoreSensors(StartIndex);
Vector Fhat;
double RTime = Times.Values[StartIndex];
for (int i = StartIndex; i < NumberOfStepsToStore; i++)
{
for (int j = 0; j < NumberOfStepsToSkipOutput; j++)
{
RTime += DTime; //Increment to new time
Element_ND.Time = RTime; //Give new time to all elements
F_new = new Vector(NDF);
for (int k = 0; k < NE; k++)
{
Elements[k].CalculateAndAssemble_Fe(ref F_new); //Calculate new F
}
//Adjust new F for BC
for (int k = 0; k < NBE; k++)
{
BoundaryElements[k].AdjustF(RTime, ref F_new);
}
F_new = 0.5 * F_new;
Fhat = F_old + F_new + C1 * U_old; //Get Fhat
//Adust Fhat for BC
for (int k = 0; k < NBE; k++)
{
BoundaryElements[k].AdjustFhat(RTime, ref F_new);
}
U_old.Values = C.SolveLinearSystemForwardEliminationAndBackSubstitution(Fhat.Values); //Solve for new temperatures
F_old = F_new; //Move new F to old F for next step
}
Times.Values[i + 1] = RTime; //Store time
Ut[i + 1] = new Vector(U_old); //Store vector of node temperatures
Solver_Output_Info.StoreAStep(i + 1, Times.Values[i + 1], Ut[i + 1], DTime, NumberOfStepsToSkipOutput);
Solver_Output_Info.SaveToFile(Solver_Output_Info.Make_OuptutAddress());
Node_ND.Set_UnknownForNode(Nodes, U_old);
StoreSensors(i + 1);
}
}
/// <summary>
/// Developed by: Mehrdad Negahban
/// Date: 12/27/2012
///
/// Purpose: Newmark method to solve second order transient N-D problem using sparse matrix model (M d^2U/dt^2 + K U = F)
/// Comments: May add artificial damping (+ C dU/dt)
///
/// Date modified:
/// Modified by:
/// Comments:
/// </summary>
public override void SolveFEMSystem()
{
double beta = Newmark_beta;
double gamma = Newmark_gamma;
//Set up the load vector and stiffness matrix
int NDF = Unknowns_NDoF; //Get the size of the unknowns temperature (one per node)
Vector F = new Vector(NDF); //Make global load vector (old)
Vector F_new = new Vector(NDF); //Make global load vector (new)
MatrixSparseLinkedList K = new MatrixSparseLinkedList(NDF); // Make global stiffness matrix
MatrixSparseLinkedList M = new MatrixSparseLinkedList(NDF); // Make global thermal mass matrix
//Assemble F, K, C
int NE = Elements.Length; //Get the number of elements
for (int i = 0; i < NE; i++)
{
Elements[i].CalculateAndAssemble_FeAndKeAndMe(ref F, ref K, ref M);
}
MatrixSparseLinkedList CDamping = ArtificialDamping_Factor_M * M + ArtificialDamping_Factor_K * K;
MatrixSparseLinkedList Mhat = M + (gamma * DTime) * CDamping + (beta * DTime * DTime) * K;
Mhat.LUDecomposition_Parallel();
//Adjust for boundary conditions
int NBE = BoundaryElements.Length;
for (int i = 0; i < NBE; i++)
{
BoundaryElements[i].AdjustF(Times.Values[StartIndex], ref F);
BoundaryElements[i].AdjustK(Times.Values[StartIndex], ref K);
}
//Initial conditions
Vector u_old = new Vector(Ut[StartIndex]);
Vector v_old = new Vector(Vt[StartIndex]);
//Initial acceleration
Vector a_old = M.SolveLinearSystem(F - K * u_old);
Node_ND.Set_UnknownForNode(Nodes, u_old);
StoreSensors(StartIndex);
double RTime = 0.0D;
for (int i = StartIndex; i < NumberOfStepsToStore; i++)
{
for (int j = 0; j < NumberOfStepsToSkipOutput; j++)
{
RTime += DTime; //Increment to new time
Element_ND.Time = RTime; //Give new time to all elements
F_new = new Vector(NDF);
for (int k = 0; k < NE; k++)
{
Elements[k].CalculateAndAssemble_Fe(ref F_new); //Calculate new F
}
//Adjust new F for BC
for (int k = 0; k < NBE; k++)
{
BoundaryElements[k].AdjustF(RTime, ref F_new);
}
//solve for new values
u_old += DTime * v_old + (0.5D * DTime * DTime * (1.0D - 2.0D * beta)) * a_old;
for (int k = 0; k < NBE; k++)
{
BoundaryElements[k].AdjustU(RTime, ref u_old);
}
v_old += ((1.0D - gamma) * DTime) * a_old;
for (int k = 0; k < NBE; k++)
{
BoundaryElements[k].AdjustV(RTime, ref v_old);
}
a_old.Values = Mhat.SolveLinearSystemForwardEliminationAndBackSubstitution((F_new - CDamping * v_old - K * u_old).Values);
u_old += (beta * DTime * DTime) * a_old;
for (int k = 0; k < NBE; k++)
{
BoundaryElements[k].AdjustU(RTime, ref u_old);
}
v_old += (gamma * DTime) * a_old;
for (int k = 0; k < NBE; k++)
{
BoundaryElements[k].AdjustV(RTime, ref v_old);
}
}
Times.Values[i + 1] = RTime; //Store time
Ut[i + 1] = new Vector(u_old); //Store vector of node displacements
Vt[i + 1] = new Vector(v_old); //Store vector of node velocity
Solver_Output_Info.StoreAStep(i + 1, Times.Values[i + 1], Ut[i + 1], Vt[i + 1], DTime, NumberOfStepsToSkipOutput);
Solver_Output_Info.SaveToFile(Solver_Output_Info.Make_OuptutAddress());
Node_ND.Set_UnknownForNode(Nodes, u_old);
StoreSensors(i + 1);
}
}