Most multiphysics problems are nonlinear. In this posting, we introduce the idea of ramping the nonlinearities in the problem to improve convergence. Dr.S.Ravindran Cite 1 Recommendation Popular answers (1). Stationary (time-invariant) models with nonlinearities may converge very slowly. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. P&S Comsol Team: Arif Gngr , Yannik Horst , Stefano Valente. 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. Set initial conditions in the physics to the appropriate dependent model variable names rather than the default 0. 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. The segregated approach, on the other hand, solves sets of unknowns separately. The other low-level default settings within the Stationary Solver are chosen for robustness. Stationary (time-invariant) models with nonlinearities may converge very slowly. Version 5.3 COMSOL does not assume any legal liability for the accuracy of the data disclosed. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. Not assigning proper boundary conditions: Especially if you have ports. Different physics have different default solvers. 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. In the COMSOL Multiphysics software, this step of the modeling workflow is made. Then use this file to provide the initial conditions in time dependent model. The default Initial Values for the unknowns in most physics interfaces are zero. One of the key concepts there was the idea of mesh convergence as you refine the mesh, the solution will become more accurate. The Fully Coupled solution approach, with the Plot While Solving enabled. This information is presented in the context of a very simple 1D finite element problem, and builds upon our previous entry on Solving Linear Static Finite Element Models. Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. This is relatively expensive to do, but will lead to the most robust convergence. Note: there is no way to couple this field with the time dependent nature of this physics. The coupling terms between the different groups are thus neglected. 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. 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. There will always already be either a Segregated or Fully Coupled feature beneath this. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. Learn how your comment data is processed. The nature of simulating nature: A Q&A with IBM Quantum researcher Dr. Jamie We've added a "Necessary cookies only" option to the cookie consent popup. 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. Does anyone know what should cause this problem? Wish you all the best. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. If the default iterative solver is not converging, try switching to a direct solver, as described here: Understanding the Fully Coupled vs. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. 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 fully coupled and segregated approaches are discussed below. 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. k(T) = 10[W/m/K]*exp(-(T-293[K])/100[K]) 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. The advantages of the continuation method are two-fold. Function: / Failed to evaluate expression. It may also reveal that the model itself is ill-posed in some way. Why? 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. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. If it does so, use a finer increment in that range. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version 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 is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. If some, or all, of the needed materials properties needed by the physics interfaces are not defined, the model will generate an error at runtime. Numerically ill-conditioned means that the system matrix is nearly singular and that it will be difficult to solve on a finite-precision computer. New Stationary Engineer jobs added daily. Nonlinearities arise as a consequence of the governing equation, as a material nonlinear expression, or as a coupling term between physics. listed if standards is not an option). Cooling and Solidification of Metal. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. Solving for laminar flow using Comsol - YouTube Comsol help video number 2: Solving a laminar flow problem in a slit. Here we introduce the two classes of algorithms used to solve multiphysics finite element problems in COMSOL Multiphysics. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. The unknowns are segregated into groups, usually according the physics that they represent, and these groups are solved one after another. k(T) = 10[W/m/K]+10[W/m/K]*(T>400[K]) 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. 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. Not assigning proper boundary conditions: Especially if you have ports. Popular answers (1) This problem generally occurs when there is some mistake in the physics or study section or wrong selection of the mesh size. "After the incident", I started to be more careful not to trip over things. Nonlinearity ramping is an especially useful technique if any of the nonlinear terms in the model are very abrupt. 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. The settings controlling the predictor type. Hence Comsol solved for the stationary solution at different points of time. That is, they are tuned to achieve convergence in as many cases as possible. The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). Alle Rechte vorbehalten. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. This is a review for cards & stationery in Brea, CA: "Love this store!!! For more details, see: Performing a Mesh Refinement Study, Mesh refinement may often need to be combined with load or nonlinearity ramping and may require a set of studies, first starting with a relatively coarse mesh for nonlinearity ramping, refining the mesh, and the ramping further on the refined mesh. Solver . There will always already be either a Segregated or Fully Coupled feature beneath this. - Variable: B1 - Defined as: 1/ ( ( (comp1.cH2 (unit_m_cf^3))/unit_mol_cf)^2.5) Failed to evaluate variable. There will always already be either a Segregated or Fully Coupled feature beneath this. This guide applies solely to nonlinear stationary models. 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, 2023 by COMSOL. Your internet explorer is in compatibility mode and may not be displaying the website correctly. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. Note: there is no way to couple this . Staging Ground Beta 1 Recap, and Reviewers needed for Beta 2, Simulation of effect of heated resistance on temperature distribution in laminar flow, COMSOL: Diffusion in Transport of Diluted Species Produces Unphysical Results. Posted 26 set 2019, 11:57 GMT-4 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. Most multiphysics problems are nonlinear. 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. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help. 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. This approach is known as a Continuation Method with a Constant predictor. - Feature: Stationary Solver 1 (sol1/s1) Each physics is thus solved as a standalone problem, using the solution from any previously computed steps as initial values and linearization points. In many physics areas there exist alternative physics formulations specifically meant for solving cases where the geometry has an extreme aspect ratio. To switch between these solver types, go to the Stationary Solver node within the Study sequence. We have also introduced meshing considerations for linear static problems, as well as how to identify singularities and what to do about them when meshing. We are planning to continuously update this page throughout the semester and hopefully, this will become a reference during your projects as well. A linear finite element model is one in which all of the material properties, loads, boundary conditions, etc are constant with respect to the solution, and the governing partial differential equations are themselves linear. COMSOL does not assume any legal liability for the accuracy of the data disclosed. Nonlinearities arise as a consequence of the governing equation, as a material nonlinear expression, or as a coupling term between physics. 3 Replies, Please login with a confirmed email address before reporting spam. If your matrix is singular than no solver in the world can solve Ax=B. Required fields are marked *. Today's top 351 Stationary Engineer jobs in Brea, California, United States. Comsol help video number 2: Solving a laminar flow problem in a slit.. Stationary Solver Use the Stationary Solver () to find the solution to linear and nonlinear stationary problems (also called static or steady-state problems). Full text of the 'Sri Mahalakshmi Dhyanam & Stotram'. 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. Tutti i diritti sono riservati. I'm trying to model a solid that's moving through a steady background field in a background flow, I want to take into account the effect of movement of the solid after each time step so I have to use stationary solver after each time step in order to see how field has changed after solid moved. 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. 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. The former approach solves for all unknowns in the problem at once, and considers all coupling terms between all unknowns within a single iteration. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Hi Alexis, If it does so, use a finer increment in that range. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. -Detail: NaN or Inf found when solving linear system using SOR. Use this parameter to modify the nonlinearity expressions in the model. Under Initial values of variables solved for, the default value of the Settingslist is Physics controlled. At low flow speeds the flow solution will be time invariant, but at higher flow rates there will be vortex shedding, a time-varying change in the flow field behind the cylinder. A classic example of this is fluid flow around a cylinder with high, but constant, flow rates. Alternatively, delete and re-create the study. 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. The former approach solves for all unknowns in the problem at once, and considers all coupling terms between all unknowns within a single iteration. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. It is also possible to manually refine the mesh. They worked with me. The exceptions are the Heat Transfer interfaces, which have a default Initial Value of 293.15K, or 20C, for the temperature fields. I'm trying to model a solid that's moving through a steady background field in a background flow, I want to take into account the effect of movement of the solid after each time step so I have to use stationary solver after each time step in order to see how field has changed after solid moved. This case is generally difficult, or impossible, to solve since this material property is non-smooth. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. First, it is physically intuitive, often matching how one would perform an experiment. If you see this, right-click on the Solution feature and select Reset Solver to Default. Any trademarks referenced in this document are the property of their respective owners. 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. 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. Segregated approach and Direct vs. Iterative linear solvers, About the time step setting of the solver, Introducing Goal Seeking into the Segregated Solver. For the Nozomi from Shinagawa to Osaka, say on a Saturday afternoon, would tickets/seats typically be available - or would you need to book? Changes to these low-level settings from the defaults will usually be quite model- and case-specific. P&S Comsol Team: Yannik Horst, Manuel Kohli, Xinzhi Zhang. This guide applies solely to nonlinear stationary models. 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. Thanks, Andres. Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. Segregated approach and Direct vs. Iterative linear solvers, Time dependent function and stationary study, Combining Adaptive Mesh Refinement with Data Filtering, What to do when a linear stationary model is not solving, Galleria dei Modelli e delle App di Simulazione, 2023 da COMSOL. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. There are two approaches that can be used when iteratively solving the nonlinear system of equations: a Fully Coupled or a Segregated approach. Once a simplified solvable version of the model has been found, gradually increase the model complexity again, re-introducing nonlinearities and multiphysics couplings. If you are unsure if your problem is linear and stationary, look at the Log. there is no defined multiphysics for it as I know, I have a standing accoustic wave and a flow in the background but I don't see their connection. This can arise as a consequence of extreme variations in the material properties, or high aspect ratio geometry. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. The stationary solver is used both for Stationary (time-invariant) and Frequency Domain (time-harmonic) study types. Once a simplified solvable version of the model has been found, gradually increase the model complexity again, re-introducing nonlinearities and multiphysics couplings. Multiphysics problems are often nonlinear. However, it is usually not possible to know this ahead of time. Click the link in the email we sent to to verify your email address and activate your job alert. The fully coupled and segregated approaches are discussed below. 3. listed if standards is not an option). Sign in to create your job alert for Stationary Engineer jobs in Brea, California, United States. This algorithm was also useful for understanding what happens near a failure load. Studysteps might be listed in wrong order: Not assigning materials to all the domains. Changes to these low-level settings from the defaults will usually be quite model- and case-specific. Wrong ordering of study steps. Tutti i diritti sono riservati. If instead the model is linear, see: Knowledgebase 1260: What to do when a linear stationary model is not solving. This will use the initial conditions you specified in your physics setting (usually 0 is used in the physics settings). As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. 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. So far, weve learned how to mesh and solve linear and nonlinear single-physics finite element problems, but have not yet considered what happens when there are multiple different interdependent physics being solved within the same domain. Unknown function or operator. Your email address will not be published. If it does so, use a finer increment in that range. Feature: Stationary Solver 1 (sol1/s1) Attempt to evaluate nonintegral power of negative number. Your internet explorer is in compatibility mode and may not be displaying the website correctly. Hello, 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. Building on these topics, we will now address how to prepare your mesh for efficiently solving nonlinear finite element problems. We use COMSOL Multiphysics for solving distributed optimal control of un-steady Burgers equation without constraints and with pointwise control constraints. The solver settings are stored at Study > Solver Configurations > Solution. Note the star symbol on the Solution feature. A classic example of this is fluid flow around a cylinder with high, but constant, flow rates. Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. The advantages of the continuation method are two-fold. How do/should administrators estimate the cost of producing an online introductory mathematics class? Your internet explorer is in compatibility mode and may not be displaying the website correctly. I am following the same model as Comsol provide us on the web. Common Mistakes: Not assigning materials to all the domains. Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. Not entering required material parameters. Discussion Closed This discussion was created more than 6 months ago and has been closed. 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.
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