It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. There will also be a red cross over the Materials branch icon. (Frequency Domain should be the last step) The technique of load ramping is not always reasonable for all problems. My comment is perhaps a bit nave but it seems to me that you could simply deactivate the \frac{\partial \cdot}{\partial t} term of the background field equation but keep its connexion to the solid to get what you want. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. If instead the model is linear, see: Knowledgebase 1260: What to do when a linear stationary model is not solving. The default Initial Values for the unknowns in most physics interfaces are zero. Your internet explorer is in compatibility mode and may not be displaying the website correctly. If the model is nonlinear, see: Improving Convergence of Nonlinear Stationary Models. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. This is for COMSOL 5.2, but should be similar for 4.2: Create the stationary study. It is also possible to manually refine the mesh. Alternatively, delete and re-create the study. By default, the COMSOL Multiphysics software determines these values heuristically depending on the physics as, for example, the specified initial values or a solution from an earlier study step. Note that while COMSOL employees may participate in the discussion forum, COMSOL software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team. The technique of load ramping is not always reasonable for all problems. COMSOL makes every reasonable effort to verify the information you view on this page. In such cases it will be particularly helpful to ramp the load gradually in time, from consistent initial values. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. Nonlinearity ramping is an especially useful technique if any of the nonlinear terms in the model are very abrupt. Improving Convergence of Nonlinear Stationary Models, Knowledgebase 1030: Error: "Out of memory", Knowledgebase 1030: Performing a Mesh Refinement Study, Understanding the Fully Coupled vs. It is also possible to manually refine the mesh. Your internet explorer is in compatibility mode and may not be displaying the website correctly. If instead the model is linear, see: Knowledgebase 1260: What to do when a linear stationary model is not solving. The memory requirements will always be lower than with the fully coupled approach, and the overall solution time can often be lower as well. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. This case is generally difficult, or impossible, to solve since this material property is non-smooth. Within either of these features, it can also be helpful to enable the Results While Solving option, as shown in the screenshot below, to visualize the iterations being taken during the solution. Your internet explorer is in compatibility mode and may not be displaying the website correctly. $130,000.00. A Global Parameter has to be introduced (in the above screenshot, P) and is ramped from a value nearly zero up to one. listed if standards is not an option). For example, in an Electric Currents problem, you may want to consider a system of materials including a good conductor such as copper (with an electric conductivity of ~6e7 S/m) and an insulative material such as glass (which can have electric conductivity of ~1e-14 S/m.) 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. Here we introduce the two classes of algorithms used to solve multiphysics finite element problems in COMSOL Multiphysics. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help. so many cute little stationary items , hair". Load ramping and nonlinearity ramping can be used in combination, but start with only one or a few of the loads or nonlinearities being ramped. Stationary (time-invariant) models with nonlinearities may converge very slowly. Consult your product manuals for complete trademark details. Cooling and Solidification of Metal. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Sometimes, reducing the model complexity can be quite challenging and it can be better to start from as simple a case as possible and gradually increase the complexity. These can be used alone, or in combination with other interfaces. The problem is that when I run my model this message appear: Undefined value found. It may also reveal that the model itself is ill-posed in some way. As a rough rule of thumb, once the aspect ratio between the largest characteristic dimension to the smallest approaches 100:1, you might start to run into issues and should look to alternative ways of posing the problem, especially in a 3D model. If it does so, use a finer increment in that range. At a value of P=0 the above expression is linear, and at a value of P=1 the expression is equal to the original nonlinear expression. Common Mistakes: Not assigning materials to all the domains. The Fully Coupled solution approach, with the Plot While Solving enabled. It may also reveal that the model itself is ill-posed in some way. Nonlinearities arise as a consequence of the governing equation, as a material nonlinear expression, or as a coupling term between physics. If you do not hold an on-subscription license, you may find an answer in another Discussion or in the Knowledge Base. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. There are two approaches that can be used when iteratively solving the nonlinear system of equations: a Fully Coupled or a Segregated approach. Not entering required material parameters. replace it with the expression: From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. The memory requirements will always be lower than with the fully coupled approach, and the overall solution time can often be lower as well. Consult your product manuals for complete trademark details. - - Feature: Stationary Solver 1 (sol1/s1) Stationary Engineer Jobs in Brea, California, United States, $87,400.00 COMSOL does not assume any legal liability for the accuracy of the data disclosed. Within either of these features, it can also be helpful to enable the Results While Solving option, as shown in the screenshot below, to visualize the iterations being taken during the solution. COMSOL 22.9K subscribers Adding a study to your simulation is necessary in order to solve your problem. "After the incident", I started to be more careful not to trip over things. Changes to these low-level settings from the defaults will usually be quite model- and case-specific. A classic example of this is fluid flow around a cylinder with high, but constant, flow rates. This guide applies solely to nonlinear stationary models. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. replace it with the expression: numeric (each ports needs their ownboundary mode analysis in the study if they are numerically defined)Wave excitation: on/off(input/output), - Feature: Stationary Solver 1 (sol1/s1) Division by zero. Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. If it is not clear that any of the above strategies are working, it is useful to take a more general approach to verifying the general validity of the model. Building on these topics, we will now address how to prepare your mesh for efficiently solving nonlinear finite element problems. Instead, use a nonlinear material property expression that ramps from a very smooth function to a very nearly discontinuous one. In the COMSOL Multiphysics software, this step of the modeling workflow is made. In particular, choosing an improper initial condition or setting up a problem without a solution will simply cause the nonlinear solver to continue iterating without converging. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. First, it is physically intuitive, often matching how one would perform an experiment. The Fully Coupled solution approach, with the Plot While Solving enabled. - Variable: B1 - Defined as: 1/ ( ( (comp1.cH2 (unit_m_cf^3))/unit_mol_cf)^2.5) Failed to evaluate variable. Stationary (time-invariant) models with nonlinearities may converge very slowly. This is relatively expensive to do, but will lead to the most robust convergence. The objective here is to simplify the model to a state where the model will solve, with linear approximations. Any trademarks referenced in this document are the property of their respective owners. Here we introduce a more robust approach to solving nonlinear problems. If the model is very large, and if you do not have very much memory in your computer, you may get an error message regarding memory. Cooling and Solidification of Metal. Trying to understand how to get this basic Fourier Series. For the Nozomi from Shinagawa to Osaka, say on a Saturday afternoon, would tickets/seats typically be available - or would you need to book? The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). (I am begginer in comsol) Thank you. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. If this was solved using the Solid Mechanics physics interface the thin walls of the container would need to be explicitly modeled, but the wall thickness is much smaller than the overall can dimensions. The technique of load ramping is not always reasonable for all problems. This involves a systematic reduction in the model complexity. However, it is usually not possible to know this ahead of time. The exceptions are the Heat Transfer interfaces, which have a default Initial Value of 293.15K, or 20C, for the temperature fields. This information is relevant both for understanding the inner workings of the solver and for understanding how memory requirements grow with problem size. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. P&S Comsol Team: Manuel Kohli, Raphael Schwanninger, Feature: Stationary Solver 1 (sol1/s1) This solver is automatically used when a Stationary or Frequency Domain study is added to the model. Starting from zero initial conditions, the nonlinear solver will most likely converge if a sufficiently small load is applied. I use comsol multiphysics 5.2a and . That is: It is also possible to compute the derivative of the solution with respect to the continuation parameter and use that derivative (evaluated at the iteration) to compute a new initial value: where is the stepsize of the continuation parameter. Making statements based on opinion; back them up with references or personal experience. The fully coupled and segregated approaches are discussed below. Unknown function or operator. The unknowns are segregated into groups, usually according the physics that they represent, and these groups are solved one after another. Therefore, it is recommended to use Adaptive Mesh Refinement which will automatically refine the mesh only in regions where it is needed, and coarsen the mesh elsewhere. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. Note that while COMSOL employees may participate in the discussion forum, COMSOL software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team. With respect to multiphysics couplings, rather than solving the problem using a fully coupled approach (the default) solve the problem sequentially, with one physics being solved after another. As we saw previously in the blog entry on Solving Nonlinear Static Finite Element Problems, not all nonlinear problems will be solvable via the damped Newton-Raphson method. Note: there is no way to couple this field with the time dependent nature of this physics. In our previous blog entry, we introduced the Fully Coupled and the Segregated algorithms used for solving steady-state multiphysics problems in COMSOL. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. For example, if ramping P over values of: 0.2,0.4,0.6,0.8,1.0 the nonlinear solver may fail to converge for a value of 0.8. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. Does anyone know what should cause this problem? The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. Perhaps this approach could be adapted to represent your model. Acidity of alcohols and basicity of amines. In this posting, we introduce the idea of ramping the nonlinearities in the problem to improve convergence. This involves a systematic reduction in the model complexity. By providing your email address, you consent to receive emails from COMSOL AB and its affiliates about the COMSOL Blog, and agree that COMSOL may process your information according to its Privacy Policy. That is, the material property changes instantaneously from 10W/m/K to 20W/m/K at 400K. The other low-level default settings within the Stationary Solver are chosen for robustness. The latter method is known as the Continuation Method with a Linear predictor, and is controlled within the Study Configurations as shown in the screenshot below. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. This will use the initial conditions you specified in your physics setting (usually 0 is used in the physics settings). Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Review the model setup to resolve these. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. If all of the above approaches have been tried and you are certain that the problem itself is well-posed, consider that the nonlinear problem may not, in fact, have a stationary (time-invariant) solution. See also: Knowledge Base 1254: Controlling the Time Dependent solver timesteps. Check the solver log to see if the continuation method is backtracking. 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. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. An example model that combines the techniques of nonlinearity ramping and adaptive mesh refinement with multiple study steps is: 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. Hello guys. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. If you define this nonlinearity ramping such that the first case (P=0) is a purely linear problem, then you are guaranteed to get a solution for this first step in the ramping. For example, in Solid Mechanics, if the Poisson Ratio set to 0.5, then the model will not solve, as this value in incompatible with the theory of linear elasticity. Discussion Closed This discussion was created more than 6 months ago and has been closed. See Knowledge Base 1240: Manually Setting the Scaling of Variables. Not entering required material parameters. Also, keep in mind that a linear stationary model should solve regardless of how coarse the mesh is (albeit to a low accuracy) so you can always start with as coarse a mesh as possible, and refine the mesh (See also: Knowledgebase 1030: Performing a Mesh Refinement Study. Sometimes, reducing the model complexity can be quite challenging and it can be better to start from as simple a case as possible and gradually increase the complexity. The former approach solves for all unknowns in the problem at once, and considers all coupling terms between all unknowns within a single iteration. replace it with the expression: Click the link in the email we sent to to verify your email address and activate your job alert. Changes to these low-level settings from the defaults will usually be quite model- and case-specific. The latter method is known as the Continuation Method with a Linear predictor, and is controlled within the Study Configurations as shown in the screenshot below. You can write the discrete form of the equations as f(U) = 0, where f(U) is the residual vector and U is the solution vector. Version 5.3 For example, if ramping P over values of: 0.2,0.4,0.6,0.8,1.0 the nonlinear solver may fail to converge for a value of 0.8. That is, start by first solving a model with a small, but non-zero, load. It is quite rare that changing these settings is superior to using a combination of the other techniques in this Knowledgebase, although it is possible to tune these settings to reduce solution time and memory requirements, once a model is already converging. The settings controlling the predictor type. Some models are numerically ill-conditioned due to the setup. The conditions on the geometric aspect ratio are relatively more strict.