# convergence

## An efficient convergence test for the fixed point method

The fixed point method consists to find the solution of F(X)=X.

One can not get fixed with the convergence condition |F'(X)|<1 because if the function has an optimum then |F'(X)|=0 even if the solution is not yet reached.

We introduce an efficient convergence test with the condition:

|Xn+1 - Xn| ≤ epsilon1 And |F(Xn+1)-Xn+1| ≤ epsilon2

## Converged, but to the right solution??

Hello eveybody,

I am confused in using numerical schemes: What can convergence of a numerical scheme tell us and what not??? lets assume that a numerical scheme does converge to "A result" or "A number", but how could we be sure that the scheme has actually converged to the "RIGHT solution" and not a WRONG one??

Any input is appreciated!

Setareh

## ABAQUS Reinforced Concrete Beam Model

Choose a channel featured in the header of iMechanica:

Hi All,

I am trying to model a simply supported reinforced concrete beam with longitudinal reinforcement. I am using 8-node solid elements for the concrete, and 2-node truss elements for the longitudinal reinforcement bars. I have embedded the reinforcement bars in the concrete using an Embedded Region constraint. I am then applying a displacement at the midspan (deflection control). I am using the Concrete Damaged Plasticity model for the concrete. My model begins to run but will not converge. Some of the error messages that I get are:

## Reg. Convergence and Mesh Density

Choose a channel featured in the header of iMechanica:

Hi

I am using a FORTRAN FE code for 4 quad elements with a viscoelastic material and with contact analysis. The routine follows a Newton Raphson iteration scheme and which makes the residual zero for convergence. I am using direct sparse matrix solver from the FORTRAN math library. 