Error: Failed to find a solution. Returned solution is not converged

Solution Number: 964
Title: Error: Failed to find a solution. Returned solution is not converged
Platform: All Platforms
Applies to: All Products
Versions: All versions
Categories: Solver, Error Messages

Problem Description

I get this message: Failed to find a solution. The relative residual (0.28) is greater than the relative tolerance.
Returned solution is not converged.


Messages similar to this are returned for nonlinear problems that fail to converge, but also sometimes for linear problems.

When solving either a linear or a nonlinear problem, a set of linear equations are solved. In the nonlinear analysis, this is done in every iteration, and in a linear analysis once. The direct equation solvers will make an estimate of the error in the solution, and if that error is too large this error message is shown. This actually indicates that the numerical conditioning of the system of equations is bad. Most often this is caused by an unsuitable or erroneous physical formulation of the problem.

Here are some possible causes and cures:

  • Your model is highly nonlinear. This is often the case in for instance mass transport models with fast reactions. Try to cancel some known nonlinearity in the problem and gently ramp it up with the parametric solver. See further instructions in solution 103.
  • Your boundary conditions are inconsistent, either with each other or with your initial guess. Check your equation system and boundary conditions.
  • There is no stationary solution to your problem. For example, a constantly positive heat source surrounded by insulating walls results in a temperature field that increases forever, and never reaches a stationary state.¬† Running a time-dependent study can help you understand what is going on.
  • Non-unique solutions. For example, a cavity flow problem needs to have the pressure locked in some point or the problem will have an infinite number of solutions. Right-click the physics interface head node and select Pressure Point Constraint under Points. Constrain one point to an arbitrary pressure, for example 0.
  • The mesh is too coarse to resolve steep gradients. This is a common scenario, for example, near walls in natural convection problems. Try refining the mesh locally, where you expect spatial variations in the solution.
  • For time-dependent nonlinear models, see also¬†Solution 1127.
  • For time-dependent waves models, see also Solution 1118.
  • There are possible rigid body displacements in a structural mechanics problem.
  • There are cases when the there is no problem in the physics as such, but the stiffness matrix is still ill-conditioned. This could for example happen if the geometry has a very high aspect ratio, like if modeling a thin shell with solid elements in structural mechanics. You can then attempt to turn off the error control in the linear solver. To do this, go to the Direct node in the solver sequence. In the Error section, set Check error estimate to No. This will force the solver to return a solution unless the stiffness matrix is singular. When you do this, you should check the consistency of your solution thoroughly by for example comparing applied load to reactions.
  • In a frequency domain analysis, the problem will be ill conditioned close to the eigenfrequencies if the damping is very low or zero.


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