Dear all I am working on a arc-length-Newton-Raphson solution algorithm. To derive the arc-length method, I allow incremental load factor ∆λ to become a variable and redefine the residual equation. I used cylindrical arc-length method. In this method the iterative load factor is normally chosen as the solution to the quadratic equation. The success of the path-following technique depends crucially on the choice of the appropriate sign for the iterative load factor. Some criteria are listed below: 1) Stiffness determinant. Follow the sign of the stiffness determinant 2) Incremental work. Follow the sign of the predictor work increment 3) Secant path. Procedure 1 is widely used in commercial finite element codes and works well in the absence of bifurcations. Therefor, I need the sign of the determinant of the global tangent stiffness matrix which is a dealii::LinearAlgebraTrilinos::MPI::BlockSparseMatrix. How I can compute this sign?
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