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## Improving Convergence of Multiphysics Problems

Stationary time-invariant models with nonlinearities may converge very slowly. A nonlinearity can be introduced into the model either in the governing equation, or by making any of the material properties, loads, or boundary conditions dependent upon the solution. Multiphysics problems are often nonlinear.

If instead the model is linear, see: Knowledgebase What to do when a linear stationary model is not solving. This guide applies solely to nonlinear stationary models. The issue here has do with the iterative algorithm used to solve nonlinear stationary models.

The algorithm is, generally speaking, a Newton's method approach. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. The software then computes an initial solution and from there it iteratively re-computes the solution, taking into account how these intermediate solutions affect the nonlinearities. When the difference in the computed solutions between successive iterations is sufficiently small, or when the residual is sufficiently small, the problem is considered converged to within the specified tolerance.

Assuming a well-posed problem, the solver may converge slowly or not at all if the initial values are poor, if the nonlinear solver is not able to approach the solution via repeated iterations, or if the mesh is not fine enough to resolve the spatial variations in the solution. The default Initial Values for the unknowns in most physics interfaces are zero. The exceptions are the Heat Transfer interfaces, which have a default Initial Value of Convergence can be poor when the initial values do not provide a good starting point for this iterative approach.

If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. One can say that, in general, if the loads on a nonlinear system are zero, the system will be at rest; that is, the solution will be zero.

Therefore, an initial value of zero is almost always reasonable if a very small load is applied. Starting from zero initial conditions, the nonlinear solver will most likely converge if a sufficiently small load is applied.

That is, start by first solving a model with a small, but non-zero, load. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition.

Extending this logic, if one wants to solve for any arbitrary load on a nonlinear system, it makes sense to solve a sequence of intermediate problems with gradually increasing load values and using the solutions from each previous step as the initial condition for the next step. This approach is known as a Continuation Method with a Constant predictor. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. A Global Parameter has to be introduced in the above screenshot, P and is ramped from a value nearly zero up to one.

This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads.This website uses cookies to function and to improve your experience. By continuing to use our site, you agree to our use of cookies.

### Plotting the Algebraic Residual to Study Model Convergence

Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here. Hello Sean Vogel Your Discussion has gone 30 days without a reply.

If you do not hold an on-subscription license, you may find an answer in another Discussion or in the Knowledge Base. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' or the latest version listed if standards is not an option.

North America. Log Out Log In Contact. OK Learn More. Discussion Forum. Forum Home. New Discussion. Send Private Message Flag post as spam. Please login with a confirmed email address before reporting spam. Send a report to the moderators. Hi there I'm using Comsol to simulate a oscillating Flow in a tube.

At the beginning everything worked quite well. Most of the time steps are just skipped and marked with an 'out'. At some point Comsol stops solving and responds that there is no convergence. I then tried, to at least be able to calculate a solution, to increase the tolerance.

But it didn't help. Does anybody has an idea why the solution is not converging?We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services. We use cookies to make interactions with our website easy and meaningful, to better understand the use of our services, and to tailor advertising.

For further information, including about cookie settings, please read our Cookie Policy. By continuing to use this site, you consent to the use of cookies. We value your privacy. Asked 2nd Feb, When I use the direct solver, it solves fine. When I switch to iterative, I cannot get it to solve.

I have to use iterative due to the large number of elements in real caseso direct solver is out of the question. Heat Transfer. Comsol Multiphysics. Most recent answer. Shiuh-Hwa Shyu. WuFeng University. I should say segregate, not stagger. Popular Answers 1. Abhilash Kumar Tilak. Few days back i was also facing this problem in direct solver and found that there was a little mistake in the boundary conditions.

All Answers 7. I believe it has something to do with their scheme. My experience of coding is that it will encounter stability problem. In my Ph. D dissertation, we took that approach in using Legendre collocation method to our problem. Very hard to converge. So, later we split the velocity and pressure into two stages.

### Improving Convergence of Nonlinear Stationary Models

This stablize our scheme. If you took staggered approach, it becomes easier to converge. Another issue is that SOR is less stable than direct method. If you have to adopt SOR because of matrix size problem, the use it wisely. For example, make itseveral blocks.

In each block, direct solve. In connection or while need to update the flow filed, use SOR. This's all my experience.

But, looking back to the basic linear algebra, make sense. Without using too much mathematics, nowaday in my advising graduate students, I'll tell them that: imaging there are errors in your flow field and the problem is non-linear, or the coefficient of your PDE is associate with your flow-field solution.

Just imaging how the error can be propagate, then it will be very easy to choose the right matrix solver or the numerical scheme. But the problem is, hard to use for solving CFD problem using iterative solver. This is how I am doing now.Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here. Posted 28 avr. I used the eigenfrequency study to find the first three modes, and it converged to the right soluction with no issues.

When I use the frequency domain study with conditions I stated above, I set the freuquency to the first mode freuncy that was found by the eigenfrequency study, and it coverges with no problems. I am not sure to what I should attribute the problem to in my settings.

I have tried running an Adaptive Mesh in the frequency domain study, a parameter sweep for the gravity to improve convergence with no luck. I think what happens, is that the deflection is really high at the resonant frequency and that, somehow, messes the mesh up. I have tried to solve the problem by adding damping to reduce deflection at the resonant frequency, that didn't work either.

The most probable cause is that you have zero or very low damping. At resonance, this gives a singular matrix analytically: infinte displacements. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' or the latest version listed if standards is not an option.

OK En savoir plus. Discussion Forum. Forum Home. New Discussion. Frequency Domain not Converging Posted 28 avr. Send Private Message Flag post as spam. Please login with a confirmed email address before reporting spam.

Send a report to the moderators. I would really apreciate your input or pointer to my problem. Attachments: 1st 5. Posted: 11 months ago 30 avr. Hi, The most probable cause is that you have zero or very low damping. Regards, Henrik.This website uses cookies to function and to improve your experience.

By continuing to use our site, you agree to our use of cookies. Here, we will examine techniques for accelerating the convergence of these two methods. As we just learned, the fully coupled approach to solving a steady-state nonlinear problem actually uses the exact same damped Newton-Raphson algorithm used to solve a single physics nonlinear problem.

Although this algorithm does converge well for many cases, it can fail or converge very slowly if the choice of initial conditions are poor. It should come as no surprise then that the techniques we have already looked at, such as Load Ramping and Nonlinearity Rampingare just as valid when applied to a multiphysics problem. In fact, there is really nothing to add to these techniques — they can be used equivalently. There is one new variation of the nonlinearity ramping technique, and that is to ramp the coupling between the physics.

Numericallyit is in fact identical to the nonlinearity ramping technique already discussed, but conceptually it is the magnitude of the couplings between the physics that is ramped up, rather than the magnitude of the nonlinearity in a single physics. The only difficulty is choosing, and implementing, the term that should be ramped. Luckily, most multiphysics problems have quite obvious couplings between the physics, which can be found simply by writing out the governing equations and boundary conditions and examining how the material properties and loads are dependent upon the variables being solved for.

The most important thing to remember is that the underlying algorithm used to solve a fully coupled multiphysics problem is exactly the same as the algorithm used to solve a nonlinear single physics problem. Keeping this in mind, you will find that fully coupled mutliphysics problems really do not pose any additional conceptual hurdles beyond understanding how the physics in the model interact with each other.

On the other hand, the segregated approach can lead to a variety of different solution strategies that can greatly accelerate solution convergence, and significantly affect the amount of memory needed to solve the problem. Consider the same problem from our previous blog post about a busbar that heats up due to current flow and experiences thermal stresses. First, the fully coupled solver starts from an initial guess and applies Newton-Raphson iterations until the solution has converged:.

When solving such a problem, you will get a Convergence Plot, which shows the error estimate decreasing between Newton-Raphson iterations. Ideally, the error should go down monotonically if it does converge, then start investigating ramping the loads, the nonlinearities, or the multiphysics couplings.

This approach will almost always require a more memory-intensive direct solver to solve the linear system of equations in each Newton-Raphson step.

Now, compare the fully coupled approach to the segregated approach, which solves each physics sequentially until convergence:.This website uses cookies to function and to improve your experience. By continuing to use our site, you agree to our use of cookies. Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' or the latest version listed if standards is not an option.

North America. Log Out Log In Contact. OK Learn More. Discussion Forum. Forum Home. New Discussion. Send Private Message Flag post as spam. Please login with a confirmed email address before reporting spam. Send a report to the moderators. I started simple to get the simulation running first by adding only Joule Heating Physics. As I have some air domains I also added the surface-to-surface radiation to those parts. Anyway, as soon as I start applying a voltage to the cables via the Electric current physics of joule heating the solver gets the following error even before and after adding the radiation physics no matter how coarse or fine I set the mesh settings: "Failed to find a solution.

Maximum number of Newton iterations reached. There was an error message from the linear solver. The relative residual 0. Returned solution is not converged.

Thanks Best regards Jan. Hi Jan, There are many possible reasons for non-convergence. One common rookie mistake that could lead to this is if you set up your model in such a way that it does not have any solution, or that it has multiple solutions. For instance, you'll want to check that there is somewhere for the heat generated in the system to flow to There is no stationary solution if you have a net positive heat source and only insulation boundary conditions.

Similarly, check that there is somewhere for currents injected into the system to leave. At the opposite end of the spectrum, a DC current problem without voltage specified anywhere has an infinite number of mathematical solutions, which differ from each other by a constant voltage and which the software can't choose from, so make sure you specify a gauge voltage somewhere to make the solution unique.

Like I said, there could be other reasons, so if the tips above don't help, you may want to post your file so other users can chime in with more educated answers. Best, Jeff. Hi Jeff, thanks for your reply. I checked all your tips and my simulation is working now. Another question I figured out is if there is a possibility of defining a normal current in a 2D model? So if I have the XY-plane I'm working at and want to define a current flowing in z-direction in one domain how can I do that?

Thanks for helping Jan.Questo sito web utilizza i cookie per rendere efficienti i nostri servizi e per migliorare la tua esperienza di navigazione. Continuando a usare il sito, accetti il loro utilizzo. Discussion Closed This discussion was created more than 6 months ago and has been closed. To start a new discussion with a link back to this one, click here. Posted 25 marUTC 2 Replies. Hello Sean Vogel Your Discussion has gone 30 days without a reply.

If you do not hold an on-subscription license, you may find an answer in another Discussion or in the Knowledge Base. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' or the latest version listed if standards is not an option. Esci Accedi Contatti. OK Ulteriori informazioni. Discussion Forum. Forum Home. New Discussion. Send Private Message Flag post as spam.

Please login with a confirmed email address before reporting spam. Send a report to the moderators. Hi there I'm using Comsol to simulate a oscillating Flow in a tube. At the beginning everything worked quite well. Most of the time steps are just skipped and marked with an 'out'.

At some point Comsol stops solving and responds that there is no convergence. I then tried, to at least be able to calculate a solution, to increase the tolerance.

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