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This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. 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, they are tuned to achieve convergence in as many cases as possible. It is sometimes necessary to manually scale the dependent variables. That is, the material property changes instantaneously from 10W/m/K to 20W/m/K at 400K. Communication over the phone, in person, and through email was very easy. -Detail: NaN or Inf found when solving linear system using SOR. Not assigning proper boundary conditions: Especially if you have ports. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. 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. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. 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. What are some highly rated cards & stationery in Brea, CA? First, it is physically intuitive, often matching how one would perform an experiment. Any trademarks referenced in this document are the property of their respective owners. Full text of the 'Sri Mahalakshmi Dhyanam & Stotram'. 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. Common Mistakes: Not assigning materials to all the domains. 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. Multiphysics problems are often 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. As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. COMSOL does not assume any legal liability for the accuracy of the data disclosed. Near the top of the Stationary Solver log, the software will report if a linear or nonlinear solver is being used. These are some cards & stationery with a large number of reviews in Brea, CA. listed if standards is not an option). The algorithm is, generally speaking, a Newton's method approach. Using this technique systematically, along with the techniques described previously, will usually identify the nonlinearities in the model that are leading to issues. Changes to these low-level settings from the defaults will usually be quite model- and case-specific. 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. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. In the COMSOL Multiphysics software, this step of the modeling workflow is made. Consult your product manuals for complete trademark details. The technique of load ramping is not always reasonable for all problems. It is also possible to manually refine the mesh. Nonlinearities arise as a consequence of the governing equation, as a material nonlinear expression, or as a coupling term between physics. 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. Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. 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. Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. Here we introduce the two classes of algorithms used to solve multiphysics finite element problems in COMSOL Multiphysics. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. As we saw in Load Ramping of Nonlinear Problems, we can use the continuation method to ramp the loads on a problem up from an unloaded case where we know the solution. Is there a way to use the stationary solution obtained in Comsol 4.2 as the initial conditions in a time dependent model? "After the incident", I started to be more careful not to trip over things. $130,000.00. Numerically ill-conditioned means that the system matrix is nearly singular and that it will be difficult to solve on a finite-precision computer. Cooling and Solidification of Metal. 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. The exceptions are the Heat Transfer interfaces, which have a default Initial Value of 293.15K, or 20C, for the temperature fields. The advantages of the continuation method are two-fold. Version 5.3 For example, in a Solid Mechanics (wherein the software is solving for the displacement field within the solid) applying two opposite and equal Boundary Load conditions on a part is not sufficient to define the displacement. 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. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. Your Discussion has gone 30 days without a reply. With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. k(T) = 10[W/m/K]+10[W/m/K]*(T>400[K]) 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 relatively expensive to do, but will lead to the most robust convergence. In this posting, we introduce the idea of ramping the nonlinearities in the problem to improve convergence. Feature: Stationary Solver 1 (sol1/s1) Adaptation gives the same mesh: adaptmesh1. Different physics have different default solvers. The settings controlling the predictor type. Again, introduce a Global Parameter that gets ramped from exactly zero to one. This information is relevant both for understanding the inner workings of the solver and for understanding how memory requirements grow with problem size. How do/should administrators estimate the cost of producing an online introductory mathematics class? Hi ! There will always already be either a Segregated or Fully Coupled feature beneath this. This segregated approach is used by default for most 3D multiphysics models, and the software will automatically segregate the problem into appropriate groups. To start a new discussion with a link back to this one, click here. Is it possible to rotate a window 90 degrees if it has the same length and width? Browse other questions tagged, Where developers & technologists share private knowledge with coworkers, Reach developers & technologists worldwide. Again, introduce a Global Parameter that gets ramped from exactly zero to one. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. The former approach solves for all unknowns in the problem at once, and considers all coupling terms between all unknowns within a single iteration. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. COMSOL does not assume any legal liability for the accuracy of the data disclosed. SGP handled 7 different prints for me at once and they all came out perfectly, in a timely manner. 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: Alternatively, delete and re-create the study. Building on these topics, we will now address how to prepare your mesh for efficiently solving nonlinear finite element problems. What did people search for similar to stationary stores in Brea, CA? COMSOL does not assume any legal liability for the accuracy of the data disclosed. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. k(T) = 10[W/m/K]+10[W/m/K]*(T>400[K]) Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. Understanding the Fully Coupled vs. I use comsol multiphysics 5.2a and . If your matrix is singular than no solver in the world can solve Ax=B. This segregated approach is used by default for most 3D multiphysics models, and the software will automatically segregate the problem into appropriate groups. $131,100.00, Simplified Vehicle Operations Project Engineer, $115,000.00 Then I stored the resulting solution, and used it to to solve the stationary solver again by using the solver manager. COMSOL makes every reasonable effort to verify the information you view on this page. 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. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. The Fully Coupled solution approach, with the Plot While Solving enabled. Hi Jason, If you are unsure if your problem is linear and stationary, look at the Log. 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. What are people saying about cards & stationery in Brea, CA? 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. There are two approaches that can be used when iteratively solving the nonlinear system of equations: a Fully Coupled or a Segregated approach. The algorithm is, generally speaking, a Newton's method approach. Multiphysics problems are often nonlinear. The other low-level default settings within the Stationary Solver are chosen for robustness. Your internet explorer is in compatibility mode and may not be displaying the website correctly. With respect to any nonlinearities, replace them by a reasonable linearized term. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. The default solver for most 3D models is an iterative solver, which is more sensitive to ill-conditioned 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. 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. It may also reveal that the model itself is ill-posed in some way. The objective here is to simplify the model to a state where the model will solve, with linear approximations. I highly recommend this flower shop. 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 default Initial Values for the unknowns in most physics interfaces are zero. Here, we will examine techniques for accelerating the convergence of these two methods. The issue here has do with the iterative algorithm used to solve nonlinear stationary models. It may also reveal that the model itself is ill-posed in some way. The difference between the phonemes /p/ and /b/ in Japanese. The settings controlling the predictor type. It is sometimes necessary to manually scale the dependent variables. Have you taken a look at this blog post? Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. 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. . 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. 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. Can I tell police to wait and call a lawyer when served with a search warrant? Why is there a voltage on my HDMI and coaxial cables? thanks for reply 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. I personally liked emailing them the file, ", "This flower shop is the best! 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. Connect and share knowledge within a single location that is structured and easy to search. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. k(T) = 10[W/m/K]*exp(-(T-293[K])/100[K]) If so, see: Knowledgebase 1030: Error: "Out of memory". 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. 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. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version 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. - Tutti i diritti sono riservati. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Wrong ordering of study steps. Starting from zero initial conditions, the nonlinear solver will most likely converge if a sufficiently small load is applied. The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). - Feature: Stationary Solver 1 (sol1/s1) 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 Fully Coupled solution approach, with the Plot While Solving enabled. View the Settings window for the Materials branch to get a list of all domains with undefined materials and add a material to those domains. However, if a lower-level change has been manually made to the solver settings, the software will not automatically use the correct default solver. The segregated approach, on the other hand, solves sets of unknowns separately. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. Any trademarks referenced in this document are the property of their respective owners. Discussion Closed This discussion was created more than 6 months ago and has been closed. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. 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. As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. Examine the model and identify all terms that introduce nonlinearities, such as multiphysics couplings, nonlinear materials relationships, and nonlinear boundary conditions. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. Therefore, an initial value of zero is almost always reasonable if a very small load is applied. 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. 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. Once a simplified solvable version of the model has been found, gradually increase the model complexity again, re-introducing nonlinearities and multiphysics couplings. The stationary solver is used both for Stationary (time-invariant) and Frequency Domain (time-harmonic) study types. One of the key concepts there was the idea of mesh convergence as you refine the mesh, the solution will become more accurate. 3 Replies, Please login with a confirmed email address before reporting spam. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. 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. They worked with me. 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. COMSOL makes every reasonable effort to verify the information you view on this page. An example model that combines the techniques of nonlinearity ramping and adaptive mesh refinement with multiple study steps is: Not assigning proper boundary conditions: Especially if you have ports. This algorithm was also useful for understanding what happens near a failure load. Computational Fluid Dynamics (CFD), API In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. The conditions on the geometric aspect ratio are relatively more strict. This is for COMSOL 5.2, but should be similar for 4.2: Create the stationary study. Reply . The issue here has do with the iterative algorithm used to solve nonlinear stationary models. An example would be a linear static structural model of an aluminum beverage can. Today's top 351 Stationary Engineer jobs in Brea, California, United States. Required fields are marked *. Some models are numerically ill-conditioned due to the setup. 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. Hence Comsol solved for the stationary solution at different points of time. This doesn't seem to me the most elegant of methods, since I am essentially solving a stationary solution using a time dependent Not assigning proper boundary conditions: Especially if you have ports. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. listed if standards is not an option). Changes to these low-level settings from the defaults will usually be quite model- and case-specific. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version The fully coupled and segregated approaches are discussed below. Wrong ordering of study steps. Cooling and Solidification of Metal. Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. This involves a systematic reduction in the model complexity. The unknowns are segregated into groups, usually according the physics that they represent, and these groups are solved one after another. Reviews on Stationary Stores in Brea, CA - Typo, Mievic, Posh Paper, Morning Glory, Select Graphics & Printing, Daiso Japan, Urban Outfitters, Office Depot, Barnes & Noble If you try to solve such a model, there will be an error at runtime that will provide information about the variable name and where it is being called. See also: Knowledge Base 1254: Controlling the Time Dependent solver timesteps. This involves a systematic reduction in the model complexity. 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. In such cases it will be particularly helpful to ramp the load gradually in time, from consistent initial values. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. Such a case would be better to address instead with the Shell physics interface, which is specially formulated for handling thin-walled structural parts. See Knowledge Base 1240: Manually Setting the Scaling of Variables. k(T) = 10[W/m/K]*exp(-(T-293[K])/100[K]) P&S Comsol Team: Yannik Horst, Manuel Kohli, Xinzhi Zhang. Leverage your professional network, and get hired. Near the top of the Stationary Solver log, the software will report if a linear or nonlinear solver is being used. Hello, Learn how your comment data is processed. This involves a systematic reduction in the model complexity. 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. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Review the model setup to resolve these. Dun & Bradstreet gathers Office Supplies, Stationery, and Gift Retailers business information from trusted . November 11, 2013. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Each physics is thus solved as a standalone problem, using the solution from any previously computed steps as initial values and linearization points. How can I check before my flight that the cloud separation requirements in VFR flight rules are met? 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. 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. Do you also know how to solve this problem: using stationary solution as the initial conditions in time dependent model, How Intuit democratizes AI development across teams through reusability. Note the star symbol on the Solution feature. Not entering required material parameters. Your internet explorer is in compatibility mode and may not be displaying the website correctly. The settings controlling the predictor type. If it does so, use a finer increment in that range. The segregated approach, on the other hand, solves sets of unknowns separately. Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems. Not entering required material parameters. Perhaps this approach could be adapted to represent your model. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. Nonlinearities arise as a consequence of the governing equation, as a material nonlinear expression, or as a coupling term between physics.