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See also: Knowledge Base 1254: Controlling the Time Dependent solver timesteps. If the material properties entered are incorrect for the governing equation, the model will generate an error at runtime, usually a Singular Matrix error. Have you taken a look at this [blog post](https://www.comsol.com/blogs/modeling-fluid-structure-interaction-in-multibody-mechanisms/)? Consult your product manuals for complete trademark details. 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. In the extreme case, suppose one wants to model an instantaneous change in properties, such as: Review the model setup to resolve these. comp1.u2, comp1.v2, and comp1.w2 are usually variables associated with the x,y, and z component of deformation in COMSOL. Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. If it does so, use a finer increment in that range. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. Learn how your comment data is processed. In this post, we will delve deeper into how to choose an appropriate mesh to start your mesh convergence studies for linear static finite element problems. Solving for laminar flow using Comsol - YouTube Second, the continuation method will automatically take smaller load increments if a solution cannot be found. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. The continuation method will again backtrack and try intermediate values of the ramping parameter, thus giving you the nearest approximation to the abrupt transition that is solvable. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. The other low-level default settings within the Stationary Solver are chosen for robustness. This guide applies solely to nonlinear stationary models. 3 Replies, Please login with a confirmed email address before reporting spam. 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. Hi Jason, To learn more, see our tips on writing great answers. In this case, it would likely be reasonable to treat the insulative material as a perfect insulator, omit it from the analysis, and use the Electric Insulation boundary condition instead of modeling those domains. As a second example, when solving for Electric Currents, do not model perfect electrical insulators as materials with zero conductivity, instead, omit the domain from the model and use the Electric Insulation boundary condition. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. The coupling terms between the different groups are thus neglected. Your internet explorer is in compatibility mode and may not be displaying the website correctly. In many physics areas there exist alternative physics formulations specifically meant for solving cases where the geometry has an extreme aspect ratio. Does anyone know how to solve error in stationary solver in COMSOL Common Mistakes: Not assigning materials to all the domains. In this posting, we introduce the idea of ramping the nonlinearities in the problem to improve convergence. 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. This is a review for cards & stationery in Brea, CA: "Love this store!!! GCRO-DR is a method for Krylov subspace recycling. This approach is known as a Continuation Method with a Constant predictor. This is relatively expensive to do, but will lead to the most robust convergence. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. Repeat this for every nonlinearity of the model. This case is generally difficult, or impossible, to solve since this material property is non-smooth. That is, start by first solving a model with a small, but non-zero, load. Not assigning proper boundary conditions: Especially if you have ports. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. $140,000.00, $120,000.00 Connect and share knowledge within a single location that is structured and easy to search. 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. How do/should administrators estimate the cost of producing an online introductory mathematics class? The following are possible reasons why a linear stationary model will fail to solve, along with resolutions: The combination of the constraints and boundary conditions must be sufficient to define a unique solution to the problem, in terms of the field variables being solved. 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. Not meshing all the domains. Solver . listed if standards is not an option). Perhaps this approach could be adapted to represent your model. 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. Segregated approach and Direct vs. It may also reveal that the model itself is ill-posed in some way. An example model that combines the techniques of nonlinearity ramping and adaptive mesh refinement with multiple study steps is: There will always already be either a Segregated or Fully Coupled feature beneath this. This case is generally difficult, or impossible, to solve since this material property is non-smooth. 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. Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems. Examine the model and identify all terms that introduce nonlinearities, such as multiphysics couplings, nonlinear materials relationships, and nonlinear boundary conditions. How to Add a Study to Your Simulation in COMSOL Multiphysics Such problems must solved in the time domain. Direct Iterative , Direct . 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. See also: Knowledge Base 1254: Controlling the Time Dependent solver timesteps. It is also possible to manually refine the mesh. Stationary in the COMSOL Multiphysics Programming Reference Manual Damped Newton Methods The nonlinear solver uses an affine invariant form of the damped Newton method as described in Ref. An example model that combines the techniques of nonlinearity ramping and adaptive mesh refinement with multiple study steps is: You can unsubscribe from these emails at any time. If instead the model is linear, see: Knowledgebase 1260: What to do when a linear stationary model is not solving. Each physics is thus solved as a standalone problem, using the solution from any previously computed steps as initial values and linearization points. With sufficient simplification, a model can be reduced to a linear problem, and if this simplified model does not converge, see: What to do when a linear stationary model is not solving. 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. Dun & Bradstreet gathers Office Supplies, Stationery, and Gift Retailers business information from trusted . Wish you all the best. The coupling terms between the different groups are thus neglected. This information is relevant both for understanding the inner workings of the solver and for understanding how memory requirements grow with problem size. COMSOL Blog Series on COMSOL Multiphysics Solvers The default Initial Values for the unknowns in most physics interfaces are zero. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. This can arise as a consequence of extreme variations in the material properties, or high aspect ratio geometry. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. Create the time-dependent step or study. Nonlinearities arise as a consequence of the governing equation, as a material nonlinear expression, or as a coupling term between physics. Again, introduce a Global Parameter that gets ramped from exactly zero to one. 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. The technique of load ramping is not always reasonable for all problems. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. Your internet explorer is in compatibility mode and may not be displaying the website correctly. I want to conduct a simulation to find a solution (u) and its first derivative (ux) using a 3D stationary model. Once a simplified solvable version of the model has been found, gradually increase the model complexity again, re-introducing nonlinearities and multiphysics couplings. Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. Instead, use a nonlinear material property expression that ramps from a very smooth function to a very nearly discontinuous one. - Variable: B1 - Defined as: 1/ ( ( (comp1.cH2 (unit_m_cf^3))/unit_mol_cf)^2.5) Failed to evaluate variable. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. Here we introduce a more robust approach to solving nonlinear problems. 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. Understanding the Fully Coupled vs. Iterative - COMSOL Multiphysics The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. First, it is physically intuitive, often matching how one would perform an experiment. 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. Consult your product manuals for complete trademark details. I am following the same model as Comsol provide us on the web. Therefore, an initial value of zero is almost always reasonable if a very small load is applied. The default Initial Values for the unknowns in most physics interfaces are zero. 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. Reply . Segregated approach and Direct vs. However, load ramping will not work in all cases, or may be inefficient. (Frequency Domain should be the last step) The unknowns are segregated into groups, usually according the physics that they represent, and these groups are solved one after another. Solving such models in a stationary sense should simply require solving a single (large) system of linear equations and should always be solvable, but there are cases when the software will fail to find a solution. In the extreme case, suppose one wants to model an instantaneous change in properties, such as: The technique of load ramping is not always reasonable for all problems. k(T) = 10[W/m/K]*exp(-(T-293[K])/100[K]) Solving for laminar flow using Comsol - YouTube Comsol help video number 2: Solving a laminar flow problem in a slit. In that case, the continuation method will automatically backtrack and try to solve for intermediate values in the range of 0.6 through 0.8. It is also possible to manually refine the mesh. The memory requirements will always be lower than with the fully coupled approach, and the overall solution time can often be lower as well. Instead, use a nonlinear material property expression that ramps from a very smooth function to a very nearly discontinuous one. We are planning to continuously update this page throughout the semester and hopefully, this will become a reference during your projects as well. About the Stationary Solver The following background information about the Stationary Solver discusses these topics: Damped Newton Methods, Termination Criterion for the Fully Coupled and Segregated Attribute Nodes, Linear Solvers versus Nonlinear Solvers, and Pseudo Time Stepping. Screenshot showing a Solver Configuration that has been altered. k(T) = 10[W/m/K]+10[W/m/K]*(T>400[K]) - Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Find detailed information on Office Supplies, Stationery, and Gift Retailers companies in Brea, California, United States of America, including financial statements, sales and marketing contacts, top competitors, and firmographic insights. replace it with the expression: Using the first order optimality. Save my name, email, and website in this browser for the next time I comment. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Posted 26 set 2019, 11:57 GMT-4 so many cute little stationary items , hair". A Global Parameter has to be introduced (in the above screenshot, P) and is ramped from a value nearly zero up to one. The issue here has do with the iterative algorithm used to solve nonlinear stationary models. Studysteps might be listed in wrong order: Not assigning materials to all the domains. Office Supplies, Stationery, and Gift Retailers Companies in Brea 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. The fully coupled and segregated approaches are discussed below. 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. - In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. Knowledgebase 1260: What to do when a linear stationary model is not solving, Knowledge Base 1240: Manually Setting the Scaling of Variables, What to do when a linear stationary model is not solving, Knowledge Base 1254: Controlling the Time Dependent solver timesteps. Any trademarks referenced in this document are the property of their respective owners. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. The Automatic predictor setting will use the constant predictor when a segregated solution approach is being used, and use the linear predictor when the fully coupled approach is used. P&S: COMSOL Design Tool for Photonic Devices. Cooling and Solidification of Metal. The continuation method will again backtrack and try intermediate values of the ramping parameter, thus giving you the nearest approximation to the abrupt transition that is solvable. Not entering required material parameters. It can be useful while solving sequences of linear systems arising from, for example, nonlinear problems. A classic example of this is fluid flow around a cylinder with high, but constant, flow rates. It may also reveal that the model itself is ill-posed in some way. k(T,P) = 10[W/m/K]*((1-P)+P*exp(-(T-293[K])/100[K])) 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. That is, start by first solving a model with a small, but non-zero, load. In this blog post we introduce the two classes of algorithms that are used in COMSOL to solve systems of linear equations that arise when solving any finite element problem. 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. Examine the model and identify all terms that introduce nonlinearities, such as multiphysics couplings, nonlinear materials relationships, and nonlinear boundary conditions.