void
Element::invertMatrix( const ColumnMajorMatrix & A,
ColumnMajorMatrix & Ainv )
{
Real Axx = A(0,0);
Real Axy = A(0,1);
Real Axz = A(0,2);
Real Ayx = A(1,0);
Real Ayy = A(1,1);
Real Ayz = A(1,2);
Real Azx = A(2,0);
Real Azy = A(2,1);
Real Azz = A(2,2);
mooseAssert( detMatrix( A ) > 0, "Matrix is not positive definite!" );
Real detInv = 1 / detMatrix( A );
Ainv(0,0) = +(Ayy*Azz-Azy*Ayz) * detInv;
Ainv(0,1) = -(Axy*Azz-Azy*Axz) * detInv;
Ainv(0,2) = +(Axy*Ayz-Ayy*Axz) * detInv;
Ainv(1,0) = -(Ayx*Azz-Azx*Ayz) * detInv;
Ainv(1,1) = +(Axx*Azz-Azx*Axz) * detInv;
Ainv(1,2) = -(Axx*Ayz-Ayx*Axz) * detInv;
Ainv(2,0) = +(Ayx*Azy-Azx*Ayy) * detInv;
Ainv(2,1) = -(Axx*Azy-Azx*Axy) * detInv;
Ainv(2,2) = +(Axx*Ayy-Ayx*Axy) * detInv;
}
Real
NonlinearRZ::volumeRatioOld(unsigned int qp) const
{
ColumnMajorMatrix Fnm1T;
fillMatrix( qp, _grad_disp_r_old, _grad_disp_z_old, _disp_r_old, Fnm1T);
Fnm1T.addDiag( 1 );
return detMatrix(Fnm1T);
}
Real
Nonlinear3D::volumeRatioOld(unsigned int qp) const
{
ColumnMajorMatrix Fnm1T(_grad_disp_x_old[qp], _grad_disp_y_old[qp], _grad_disp_z_old[qp]);
Fnm1T(0, 0) += 1;
Fnm1T(1, 1) += 1;
Fnm1T(2, 2) += 1;
return detMatrix(Fnm1T);
}
Real
NonlinearPlaneStrain::volumeRatioOld(unsigned int qp) const
{
Real strain_zz_old;
if (_have_strain_zz)
strain_zz_old = _strain_zz_old[qp];
else if (_have_scalar_strain_zz && _scalar_strain_zz.size()>0)
strain_zz_old = _scalar_strain_zz_old[qp];
else
strain_zz_old = 0.0;
ColumnMajorMatrix Fnm1T;
fillMatrix( qp, _grad_disp_x_old, _grad_disp_y_old, strain_zz_old, Fnm1T);
Fnm1T.addDiag( 1 );
return detMatrix(Fnm1T);
}
