The objective here is to simplify the model to a state where the model will solve, with linear approximations. listed if standards is not an option). Today's top 351 Stationary Engineer jobs in Brea, California, United States. With respect to any nonlinearities, replace them by a reasonable linearized term. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. Repeat this for every nonlinearity of the model. Nonlinearity ramping is an especially useful technique if any of the nonlinear terms in the model are very abrupt. Then I stored the resulting solution, and used it to to solve the stationary solver again by using the solver manager. November 11, 2013. $125,000.00, Project Engineer (In-person/Hybrid/Remote), $100,000.00 Here, we will examine techniques for accelerating the convergence of these two methods. (Frequency Domain should be the last step). This will use the initial conditions you specified in your physics setting (usually 0 is used in the physics settings). Communication over the phone, in person, and through email was very easy. Direct PARDISO Solver , PARDISO . 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. 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. k(T,P) = 10[W/m/K]*((1-P)+P*exp(-(T-293[K])/100[K])) A Global Parameter has to be introduced (in the above screenshot, P) and is ramped from a value nearly zero up to one. 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. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. If it does so, use a finer increment in that range. The segregated approach, on the other hand, solves sets of unknowns separately. Your internet explorer is in compatibility mode and may not be displaying the website correctly. 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. Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. 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. It may also reveal that the model itself is ill-posed in some way. Examine the model and identify all terms that introduce nonlinearities, such as multiphysics couplings, nonlinear materials relationships, and nonlinear boundary conditions. Using a predictor of type Constant will take the solution from the iteration and use it as the initial value for the iteration. Under Initial values of variables solved for, the default value of the Settingslist is Physics controlled. The coupling terms between the different groups are thus neglected. GCRO-DR is a method for Krylov subspace recycling. Here we introduce the two classes of algorithms used to solve multiphysics finite element problems in COMSOL Multiphysics. To learn more, see our tips on writing great answers. See also: Knowledge Base 1254: Controlling the Time Dependent solver timesteps. You can unsubscribe from these emails at any time. Cecilia M. came from the backroom to help me and went out of her way to help me even though I had not called before going into the store. Instead, use a nonlinear material property expression that ramps from a very smooth function to a very nearly discontinuous one. Using a predictor of type Constant will take the solution from the iteration and use it as the initial value for the iteration. 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. 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. The settings controlling the predictor type. Making statements based on opinion; back them up with references or personal experience. $131,100.00, Simplified Vehicle Operations Project Engineer, $115,000.00 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. This is relatively expensive to do, but will lead to the most robust convergence. There will also be a red cross over the Materials branch icon. Any trademarks referenced in this document are the property of their respective owners. That is, within each outer Newton-type iteration, the segregated approach solves for each segregated group sequentially. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. There will always already be either a Segregated or Fully Coupled feature beneath this. Mesh In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. Note: there is no way to couple this . Asking for help, clarification, or responding to other answers. 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. In such cases, see if one material (or the other) can be omitted from the analysis completely. 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. 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. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. . 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. Cooling and Solidification of Metal. - As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. The default solver for most 3D models is an iterative solver, which is more sensitive to ill-conditioned problems. 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. The other low-level default settings within the Stationary Solver are chosen for robustness. To start a new discussion with a link back to this one, click here. 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. 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. In the extreme case, suppose one wants to model an instantaneous change in properties, such as: Not assigning proper boundary conditions: Especially if you have ports. The fully coupled and segregated approaches are discussed below. Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. 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. Could you expand a little bit more why the coupling is impossible? listed if standards is not an option). The default Initial Values for the unknowns in most physics interfaces are zero. Your email address will not be published. This case is generally difficult, or impossible, to solve since this material property is non-smooth. Use this parameter to modify the nonlinearity expressions in the model. 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. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. We are planning to continuously update this page throughout the semester and hopefully, this will become a reference during your projects as well. That is, start by first solving a model with a small, but non-zero, load. 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. 0 Replies, Please login with a confirmed email address before reporting spam. 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. The advantages of the continuation method are two-fold. Posted 26 set 2019, 17:57 CEST Mesh Version 5.3 0 Replies. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. In the extreme case, suppose one wants to model an instantaneous change in properties, such as: COMSOL does not assume any legal liability for the accuracy of the data disclosed. Posted 26 set 2019, 11:57 GMT-4 If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. Review the model setup to resolve these. The default Initial Values for the unknowns in most physics interfaces are zero. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. COMSOL makes every reasonable effort to verify the information you view on this page. 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. What are some highly rated cards & stationery in Brea, CA? It is sometimes necessary to manually scale the dependent variables. That is, within each outer Newton-type iteration, the segregated approach solves for each segregated group sequentially. 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. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. When you use an iterative solver, COMSOL Multiphysics estimates the error of the solution while solving. Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems. Therefore, an initial value of zero is almost always reasonable if a very small load is applied. Repeat this for every nonlinearity of the model. The segregated approach, on the other hand, solves sets of unknowns separately. If it does so, use a finer increment in that range. Consult your product manuals for complete trademark details. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); This site uses Akismet to reduce spam. The advantages of the continuation method are two-fold. In the COMSOL Multiphysics software, this step of the modeling workflow is made. Name: actdep_int1, Your email address will not be published. Using this technique systematically, along with the techniques described previously, will usually identify the nonlinearities in the model that are leading to issues. Using the first order optimality. k(T) = 10[W/m/K]*exp(-(T-293[K])/100[K]) Instead, use a nonlinear material property expression that ramps from a very smooth function to a very nearly discontinuous one. In such cases it will be particularly helpful to ramp the load gradually in time, from consistent initial values. 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. A Global Parameter has to be introduced (in the above screenshot, P) and is ramped from a value nearly zero up to one. 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. COMSOL does not assume any legal liability for the accuracy of the data disclosed. 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. 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. The other low-level default settings within the Stationary Solver are chosen for robustness. What did people search for similar to stationary stores in Brea, CA? The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). This case is generally difficult, or impossible, to solve since this material property is non-smooth. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. 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. Building on these topics, we will now address how to prepare your mesh for efficiently solving nonlinear finite element problems. 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. Hi Jason, listed if standards is not an option). If the material properties entered are incorrect for the governing equation, the model will generate an error at runtime, usually a Singular Matrix error. The technique of load ramping is not always reasonable for all problems. 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. The issue here has do with the iterative algorithm used to solve nonlinear stationary models. Comsol help video number 2: Solving a laminar flow problem in a slit.. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. It is also possible to manually refine the mesh. Once the error estimate is small enough, as determined by the convergence criterion (20-16) the software terminates the computations and returns a solution. There are two approaches that can be used when iteratively solving the nonlinear system of equations: a Fully Coupled or a Segregated approach. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. Hi Jason, With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. 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. The exceptions are the Heat Transfer interfaces, which have a default Initial Value of 293.15K, or 20C, for the temperature fields. The stationary solver is used both for Stationary (time-invariant) and Frequency Domain (time-harmonic) study types. Improving Convergence of Nonlinear Stationary Models, Knowledgebase 1030: Error: "Out of memory", Knowledgebase 1030: Performing a Mesh Refinement Study, Understanding the Fully Coupled vs. k(T) = 10[W/m/K]+10[W/m/K]*(T>400[K]) This is for COMSOL 5.2, but should be similar for 4.2: Create the stationary study. 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. 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. What is the purpose of this D-shaped ring at the base of the tongue on my hiking boots? 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. First, it is physically intuitive, often matching how one would perform an experiment. The algorithm is, generally speaking, a Newton's method approach. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. Near the top of the Stationary Solver log, the software will report if a linear or nonlinear solver is being used. 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. 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. 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. $130,000.00. 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. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version I am solving a linear stationary finite element model but the software is not solving. Reply . Segregated approach and Direct vs. 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. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. 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. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. I use comsol multiphysics 5.2a and . This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. Singular matrix., Make sure you defined your ports correctly:Boundary selectionType of port: e.g. - the incident has nothing to do with me; can I use this this way? Your internet explorer is in compatibility mode and may not be displaying the website correctly. Not entering required material parameters. 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. k(T) = 10[W/m/K]+10[W/m/K]*(T>400[K]) COMSOL does not assume any legal liability for the accuracy of the data disclosed. 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. Feature: Stationary Solver 1 (sol1/s1)" . Sign in to create your job alert for Stationary Engineer jobs in Brea, California, United States. Multiscale Modeling in High-Frequency Electromagnetics. If your matrix is singular than no solver in the world can solve Ax=B. With respect to any nonlinearities, replace them by a reasonable linearized term. 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. Not assigning proper boundary conditions: Especially if you have ports. The solver settings are stored at Study > Solver Configurations > Solution. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. Hello guys. That is, the material property changes instantaneously from 10W/m/K to 20W/m/K at 400K. I have searched all over comsol forum to fix this stationary solver configuration and still doesn't work because I don't know the logic behind the solver system. Consult your product manuals for complete trademark details. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help. Therefore, an initial value of zero is almost always reasonable if a very small load is applied. 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. COMSOL does not assume any legal liability for the accuracy of the data disclosed. Segregated approach and Direct vs. Iterative linear solvers, About the time step setting of the solver, Introducing Goal Seeking into the Segregated Solver. I want to conduct a simulation to find a solution (u) and its first derivative (ux) using a 3D stationary model. listed if standards is not an option). k(T,P) = 10[W/m/K]*((1-P)+P*exp(-(T-293[K])/100[K])) 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 people saying about cards & stationery in Brea, CA? Create the time-dependent step or study. If you see this, right-click on the Solution feature and select Reset Solver to Default. The Fully Coupled solution approach, with the Plot While Solving enabled. replace it with the expression: In this posting, we introduce the idea of ramping the nonlinearities in the problem to improve convergence. Thanks for contributing an answer to Stack Overflow! 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. I am following the same model as Comsol provide us on the web. rev2023.3.3.43278. This algorithm was also useful for understanding what happens near a failure load.
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