Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. If instead the model is linear, see: Knowledgebase 1260: What to do when a linear stationary model is not solving. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. 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. Comsol help video number 2: Solving a laminar flow problem in a slit.. k(T) = 10[W/m/K]*exp(-(T-293[K])/100[K]) The memory requirements will always be lower than with the fully coupled approach, and the overall solution time can often be lower as well. Under Initial values of variables solved for, the default value of the Settingslist is Physics controlled. The former approach solves for all unknowns in the problem at once, and considers all coupling terms between all unknowns within a single iteration. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. Solving for laminar flow using Comsol - YouTube Comsol help video number 2: Solving a laminar flow problem in a slit. Not entering required material parameters. 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. 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. Discussion Closed This discussion was created more than 6 months ago and has been closed. The unknowns are segregated into groups, usually according the physics that they represent, and these groups are solved one after another. They are usually called comp1.u, comp1.v, and comp1.w though. With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. The default solver for most 3D models is an iterative solver, which is more sensitive to ill-conditioned problems. Then I stored the resulting solution, and used it to to solve the stationary solver again by using the solver manager. Any trademarks referenced in this document are the property of their respective owners. This is relatively expensive to do, but will lead to the most robust convergence. 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. comp1.u2, comp1.v2, and comp1.w2 are usually variables associated with the x,y, and z component of deformation in COMSOL. The algorithm is, generally speaking, a Newton's method approach. Building on these topics, we will now address how to prepare your mesh for efficiently solving nonlinear finite element problems. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. This case is generally difficult, or impossible, to solve since this material property is non-smooth. Linear solvers. Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. An example model that combines the techniques of nonlinearity ramping and adaptive mesh refinement with multiple study steps is: 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. 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. I am following the same model as Comsol provide us on the web. Set initial conditions in the physics to the appropriate dependent model variable names rather than the default 0. 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. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version 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. 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. Thanks, Andres. This information is relevant both for understanding the inner workings of the solver and for understanding how memory requirements grow with problem size. 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. A Global Parameter has to be introduced (in the above screenshot, P) and is ramped from a value nearly zero up to one. replace it with the expression: 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. The idea behind the GCRO-DR method is to retain the subspace determined while solving previous systems and use it to reduce the cost of solving the next system. Not entering required material parameters. Reply . Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. They deal with COMSOL package and train users. Cooling and Solidification of Metal. That is, they are tuned to achieve convergence in as many cases as possible. Your email address will not be published. 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. Perhaps this approach could be adapted to represent your model. Why is there a voltage on my HDMI and coaxial cables? The exceptions are the Heat Transfer interfaces, which have a default Initial Value of 293.15K, or 20C, for the temperature fields. Then use this file to provide the initial conditions in time dependent model. - The issue here has do with the iterative algorithm used to solve nonlinear stationary models. 140K views 8 years ago COMSOL Multiphysics Tutorial for Beginners Please note that an updated version of the content in this video can be found in the Modeling Workflow video in the COMSOL. In such cases it will be particularly helpful to ramp the load gradually in time, from consistent initial values. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). Starting from zero initial conditions, the nonlinear solver will most likely converge if a sufficiently small load is applied. Communication over the phone, in person, and through email was very easy. Why? P&S Comsol Team: Arif Gngr , Yannik Horst , Stefano Valente. Understanding the Fully Coupled vs. That is, start by first solving a model with a small, but non-zero, load. 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. 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: The memory requirements will always be lower than with the fully coupled approach, and the overall solution time can often be lower as well. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. Screenshot showing a Solver Configuration that has been altered. To switch between these solver types, go to the Stationary Solver node within the Study sequence. Please dont hesitate to post comments below or send emails to us if you experience any other problems. Hi Alexis, Here, we will examine techniques for accelerating the convergence of these two methods. What is \newluafunction? To switch between these solver types, go to the Stationary Solver node within the Study sequence. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Create the time-dependent step or study. The issue here has do with the iterative algorithm used to solve 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. The algorithm is, generally speaking, a Newton's method approach. 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. Such problems must solved in the time domain. Set "Values for dependent variables" in study step settings to User ControlledSolutionYour Stationary Study. Each physics is thus solved as a standalone problem, using the solution from any previously computed steps as initial values and linearization points. Consult your product manuals for complete trademark details. Use this parameter to modify the nonlinearity expressions in the model. (Frequency Domain should be the last step) Iterative , Direct . Function: / Failed to evaluate expression. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. 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. 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. Changes to these low-level settings from the defaults will usually be quite model- and case-specific. Hi Jason, listed if standards is not an option). Click the link in the email we sent to to verify your email address and activate your job alert. That is, within each outer Newton-type iteration, the segregated approach solves for each segregated group sequentially. Use a manually defined mesh to avoid elements with extreme aspect ratios and perform a mesh refinement study, as described here: Performing a Mesh Refinement Study, For problems that are ill-conditioned, using a direct solver is often called for. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. 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. Stationary Solver Use the Stationary Solver () to find the solution to linear and nonlinear stationary problems (also called static or steady-state problems). 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. Trying to understand how to get this basic Fourier Series. I want to conduct a simulation to find a solution (u) and its first derivative (ux) using a 3D stationary model. Changes to these low-level settings from the defaults will usually be quite model- and case-specific. For example, if there is a temperature-dependent material property such as: Why do many companies reject expired SSL certificates as bugs in bug bounties? The other low-level default settings within the Stationary Solver are chosen for robustness. listed if standards is not an option). 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. With respect to any nonlinearities, replace them by a reasonable linearized term. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Your Discussion has gone 30 days without a reply. Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. - If instead the model is linear, see: Knowledgebase 1260: What to do when a linear stationary model is not solving. 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. In such cases it will be particularly helpful to ramp the load gradually in time, from consistent initial values. Wrong ordering of study steps. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. What sort of strategies would a medieval military use against a fantasy giant? There are two approaches that can be used when iteratively solving the nonlinear system of equations: a Fully Coupled or a Segregated approach. Therefore, an initial value of zero is almost always reasonable if a very small load is applied. $131,100.00, Simplified Vehicle Operations Project Engineer, $115,000.00 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. 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. This involves a systematic reduction in the model complexity. If you see this, right-click on the Solution feature and select Reset Solver to Default. Discussion Closed This discussion was created more than 6 months ago and has been closed. In the COMSOL Multiphysics software, this step of the modeling workflow is made. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. The advantages of the continuation method are two-fold. The stationary solver is used both for Stationary (time-invariant) and Frequency Domain (time-harmonic) study types. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. 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. This is for COMSOL 5.2, but should be similar for 4.2: Create the stationary study. Get notified about new Stationary Engineer jobs in Brea, California, United States. 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. GCRO-DR is a method for Krylov subspace recycling. Not assigning proper boundary conditions: Especially if you have ports. One of the key concepts there was the idea of mesh convergence as you refine the mesh, the solution will become more accurate. Repeat this for every nonlinearity of the model. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. My comment is perhaps a bit nave but it seems to me that you could simply deactivate the term of the background field equation but keep its connexion to the solid to get what you want. Examine the model and identify all terms that introduce nonlinearities, such as multiphysics couplings, nonlinear materials relationships, and nonlinear boundary conditions. If you try to enter a variable that is undefined, the automatic syntax highlighting will identify this as you enter it, and it is best practice to resolve this immediately. listed if standards is not an option). COMSOL 22.9K subscribers Adding a study to your simulation is necessary in order to solve your problem. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. Making statements based on opinion; back them up with references or personal experience. If it does so, use a finer increment in that range. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. 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. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. 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. The objective here is to simplify the model to a state where the model will solve, with linear approximations. . 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. 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. The settings controlling the predictor type. Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems. The advantages of the continuation method are two-fold. 3 Replies, Please login with a confirmed email address before reporting spam. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. Posted 26 set 2019, 11:57 GMT-4 That is, the material property changes instantaneously from 10W/m/K to 20W/m/K at 400K. This approach is known as a Continuation Method with a Constant predictor. Therefore, an initial value of zero is almost always reasonable if a very small load is applied. Near the top of the Stationary Solver log, the software will report if a linear or nonlinear solver is being used. Not meshing all the domains. 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. Cooling and Solidification of Metal. There will also be a red cross over the Materials branch icon. A classic example of this is fluid flow around a cylinder with high, but constant, flow rates. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. Most multiphysics problems are nonlinear. This algorithm was also useful for understanding what happens near a failure load. 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. Understanding the Fully Coupled vs. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. Such problems must solved in the time domain. To learn more, see our tips on writing great answers. Cooling and Solidification of Metal. 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. Most multiphysics problems are nonlinear. This is for COMSOL 5.2, but should be similar for 4.2: Create the stationary study. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity.

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