Void Mat::MakeDiag(Real k)
{
Int i, j;
for (i = 0; i < Rows(); i++)
for (j = 0; j < Cols(); j++)
if (i == j)
Elt(i,j) = k;
else
Elt(i,j) = vl_zero;
}
//
// Finds the element with the largest coefficient contained in the minimal coefficients
// BUBBLE functins are considered only.
//
void OdeProb::MaxMinCoef(EltInfo& eltInfo) const
{
double coef, minCoef;
eltInfo.m_maxMinCoef = 0; // Initialization
for(size_t n = 0; n < EltNo(); n++) // For each element
{
const Element& e = Elt(n);
minCoef = DBL_MAX;
for(size_t j = 1; j < e.DofNo() - 1; j++) // For each BUBBLE DOF in element
{
const int dof = e.m_dof[j];
if(dof < 0) // Skip Dirichlet boundary conditions
continue;
// Find the smallest coefficient for element "e"
coef = fabs(m_y->Get(dof));
if(coef < minCoef)
minCoef = coef;
}
// Set the largest coefficient with minimal coefficients
if(minCoef > eltInfo.m_maxMinCoef)
{
eltInfo.m_eltId = n;
eltInfo.m_maxMinCoef = minCoef;
eltInfo.m_eigVal = 0;
}
}
}
Void Mat::MakeBlock()
{
Int i, j;
for (i = 0; i < Rows(); i++)
for (j = 0; j < Cols(); j++)
Elt(i,j) = vl_one;
}
Void Mat::MakeDiag()
{
Int i, j;
for (i = 0; i < Rows(); i++)
for (j = 0; j < Cols(); j++)
Elt(i,j) = (i == j) ? vl_one : vl_zero;
}
//
// Assembling algorithm for equation solving
//
void OdeProb::Assemble()
{
size_t i, j, psiI, psiJ;
int ni; // row position in matrix S
int nj; // column position in matrix S
// const size_t M = Dim();
const size_t N = EltNo(); // Number of elements
// const double bndr[3] = {0, m_left.m_val, m_right.m_val};
// Element loop
for(size_t n = 0; n < N; n++)
{
const Element& e = Elt(n);
const size_t DofNo = e.DofNo();
// Loop over basis functions
for(i = 0; i < DofNo; i++)
{
ni = e.m_dof[i];
if(ni < 0)
continue;
psiI = e.PsiId(i);
// Loop over basis functions
for(j = i; j < DofNo; j++)
{
psiJ = e.PsiId(j);
nj = e.m_dof[j];
if(nj > -1)
m_s->Set(ni, nj) += CalcS(e, psiI, psiJ);
//else // Dirichlet boundary conditions are ZERO, hence it can be skiped
// m_b->Set(ni) -= bndr[-nj] * CalcS(e, psiI, psiJ);
}
// Contribution of the vertex basis function $v_{m_1}$ to the right hand side $b$
m_b->Set(ni) += CalcB(e, psiI);
}
}
}
//
// Returns the value of the solution at $x$
//
double OdeProb::GetSol(double x) const
{
int m1;
// The equation must be solved!
assert(m_y);
assert(IsInRange(x));
const size_t n = FindElt(x);
const Element& e = Elt(n);
// s - Locat coordiante for element "e"
const double s = std::min(std::max(e.Xinv(x), -1.0), 1.0); // MIN, MAX - To avoid the rounding errors
// Sum over all basis function with support on the element $e$
double val = 0;
/*
// Left vertex basis function
m1 = e.m_dof.front();
if(m1 > -1)
val += m_y->Get(m1) * Basis(0, s);
else
{
// Apply the Dirichlet boundary conditions
if(m_left.m_type == BndrType_Dir)
val += m_left.m_val * Basis(0, s);
}
// Right vertex basis function
m1 = e.m_dof.back();
if(m1 > -1)
val += m_y->Get(m1) * Basis(1, s);
else
{
// Apply the Dirichlet boundary conditions
if(m_right.m_type == BndrType_Dir)
val += m_right.m_val * Basis(1, s);
}
// Bubble basis functions
for(size_t j = 1; j < e.m_dof.size() - 1; j++)
{
m1 = e.m_dof[j];
val += m_y->Get(m1) * Basis(j, s);
}
*/
// It works only with zero Dirichlet bpundary conditions
for(size_t i = 0; i < e.m_dof.size(); i++)
{
const int m = e.m_dof[i];
if(m < 0)
continue;
const size_t psiI = e.PsiId(i);
val += m_y->Get(m) * Basis(psiI, s);
}
// Non-zero Dirichlet bpundary conditions are applied
{
// Left vertex basis function
assert(m_left.m_type == BndrType_Dir);
m1 = e.m_dof.front();
if(m1 < 0)
{
const size_t psiI = e.PsiId(0);
val += m_left.m_val * Basis(psiI, s);
}
// Right vertex basis function
assert(m_right.m_type == BndrType_Dir);
m1 = e.m_dof.back();
if(m1 < 0)
{
const size_t psiI = e.PsiId(1);
val += m_right.m_val * Basis(psiI, s);
}
}
return val;
}