stationary solver comsol
Review the model setup to resolve these. How do/should administrators estimate the cost of producing an online introductory mathematics class? The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). Dr.S.Ravindran Cite 1 Recommendation Popular answers (1). Using a predictor of type Constant will take the solution from the iteration and use it as the initial value for the iteration. replace it with the expression: The Fully Coupled solution approach, with the Plot While Solving enabled. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. This segregated approach is used by default for most 3D multiphysics models, and the software will automatically segregate the problem into appropriate groups. Starting from zero initial conditions, the nonlinear solver will most likely converge if a sufficiently small load is applied. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. 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. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. This information is relevant both for understanding the inner workings of the solver and for understanding how memory requirements grow with problem size. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. rev2023.3.3.43278. This involves a systematic reduction in the model complexity. Computational Fluid Dynamics (CFD), API For example, in Solid Mechanics, if the Poisson Ratio set to 0.5, then the model will not solve, as this value in incompatible with the theory of linear elasticity. The Fully Coupled solution approach, with the Plot While Solving enabled. The advantages of the continuation method are two-fold. k(T,P) = 10[W/m/K]*((1-P)+P*exp(-(T-293[K])/100[K])) Nonlinearity ramping is an especially useful technique if any of the nonlinear terms in the model are very abrupt. The default Initial Values for the unknowns in most physics interfaces are zero. This guide applies solely to nonlinear stationary models. Once a simplified solvable version of the model has been found, gradually increase the model complexity again, re-introducing nonlinearities and multiphysics couplings. With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? These are some cards & stationery with a large number of reviews in Brea, CA. This is relatively expensive to do, but will lead to the most robust convergence. thanks for reply Alle Rechte vorbehalten. There will always already be either a Segregated or Fully Coupled feature beneath this. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. To switch between these solver types, go to the Stationary Solver node within the Study sequence. Linear solvers. Have you taken a look at this [blog post](https://www.comsol.com/blogs/modeling-fluid-structure-interaction-in-multibody-mechanisms/)? The conditions on the geometric aspect ratio are relatively more strict. P&S Comsol Team: Yannik Horst, Manuel Kohli, Xinzhi Zhang. Can I tell police to wait and call a lawyer when served with a search warrant? 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: 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. Stationary (time-invariant) models with nonlinearities may converge very slowly. It can be useful while solving sequences of linear systems arising from, for example, nonlinear problems. Posted Sep 9, 2020, 1:44 p.m. EDT I am solving a linear stationary finite element model but the software is not solving. 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. 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. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. In such cases, use the same continuation method, but instead ramp the nonlinearities 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. Full text of the 'Sri Mahalakshmi Dhyanam & Stotram'. 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. Second, the continuation method will automatically take smaller load increments if a solution cannot be found. They are usually called comp1.u, comp1.v, and comp1.w though. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. 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. This approach is known as a Continuation Method with a Constant predictor. Consult your product manuals for complete trademark details. Such a case would be better to address instead with the Shell physics interface, which is specially formulated for handling thin-walled structural parts. 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. 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. One of the key concepts there was the idea of mesh convergence as you refine the mesh, the solution will become more accurate. listed if standards is not an option). Linear solvers. Stationary Solver Use the Stationary Solver () to find the solution to linear and nonlinear stationary problems (also called static or steady-state problems). Any trademarks referenced in this document are the property of their respective owners. Direct PARDISO Solver , PARDISO . This is relatively expensive to do, but will lead to the most robust convergence. Feature: Stationary Solver 1 (sol1/s1)" . Again, introduce a Global Parameter that gets ramped from exactly zero to one. For example, in an Electric Currents problem, you may want to consider a system of materials including a good conductor such as copper (with an electric conductivity of ~6e7 S/m) and an insulative material such as glass (which can have electric conductivity of ~1e-14 S/m.) You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version For example, if there is a temperature-dependent material property such as: The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. The technique of load ramping is not always reasonable for all problems. If the material properties entered are incorrect for the governing equation, the model will generate an error at runtime, usually a Singular Matrix error. See Knowledge Base 1240: Manually Setting the Scaling of Variables. In such cases it will be particularly helpful to ramp the load gradually in time, from consistent initial values. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. listed if standards is not an option). The memory requirements will always be lower than with the fully coupled approach, and the overall solution time can often be lower as well. 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. These are some highly rated cards & stationery in Brea, CA: What are some cards & stationery with a large number of reviews in Brea, CA? See Knowledge Base 1240: Manually Setting the Scaling of Variables. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); This site uses Akismet to reduce spam. 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. Each physics is thus solved as a standalone problem, using the solution from any previously computed steps as initial values and linearization points. The stationary solver is used both for Stationary (time-invariant) and Frequency Domain (time-harmonic) study types. 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. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. If the model is nonlinear, see: Improving Convergence of Nonlinear Stationary Models. Cooling and Solidification of Metal. The problem is that when I run my model this message appear: Undefined value found. To start a new discussion with a link back to this one, click here. However, it is usually not possible to know this ahead of time. There are also cases when an extremely poor quality mesh leads to an ill-conditioned problem, This issue often arises in combination with, and as a consequence of, geometries that have extreme aspect ratios. 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 solver is automatically used when a Stationary or Frequency Domain study is added to the model. This algorithm was also useful for understanding what happens near a failure load. Discussion Closed This discussion was created more than 6 months ago and has been closed. Segregated approach and Direct vs. Iterative linear solvers, About the time step setting of the solver, Introducing Goal Seeking into the Segregated Solver. Hi ! Second, the continuation method will automatically take smaller load increments if a solution cannot be found. 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 other low-level default settings within the Stationary Solver are chosen for robustness. Name: actdep_int1, Your email address will not be published. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. Repeat this for every nonlinearity of the model. Your internet explorer is in compatibility mode and may not be displaying the website correctly. They worked with me. 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. Set initial conditions in the physics to the appropriate dependent model variable names rather than the default 0. Asking for help, clarification, or responding to other answers. To learn more, see our tips on writing great answers. Again, introduce a Global Parameter that gets ramped from exactly zero to one. Nonlinearity ramping is an especially useful technique if any of the nonlinear terms in the model are very abrupt. Have you taken a look at this blog post? 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. However, it is usually not possible to know this ahead of time. 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 Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. I highly recommend this flower shop. 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. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. However, it is usually not possible to know this ahead of time. With respect to any nonlinearities, replace them by a reasonable linearized term. Note that while COMSOL employees may participate in the discussion forum, COMSOL software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team. Hello, The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. The default Initial Values for the unknowns in most physics interfaces are zero. Using a predictor of type Constant will take the solution from the iteration and use it as the initial value for the iteration. The algorithm is, generally speaking, a Newton's method approach. 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. The objective here is to simplify the model to a state where the model will solve, with linear approximations. so many cute little stationary items , hair". Wrong ordering of study steps. 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. P&S: COMSOL Design Tool for Photonic Devices. 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 can arise as a consequence of extreme variations in the material properties, or high aspect ratio geometry. This approach is known as a Continuation Method with a Constant predictor. Note that while COMSOL employees may participate in the discussion forum, COMSOL software users who are on-subscription should submit their questions via the Support Center for a more comprehensive response from the Technical Support team. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version It is sometimes necessary to manually scale the dependent variables. If one particular material is missing one property, that material will also be highlighted with a red cross over that material icon in the Model Builder. This will use the initial conditions you specified in your physics setting (usually 0 is used in the physics settings). Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. Consult your product manuals for complete trademark details. 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. Stationary (time-invariant) models with nonlinearities may converge very slowly. The issue here has do with the iterative algorithm used to solve nonlinear stationary models. Function: / Failed to evaluate expression. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. That is, start by first solving a model with a small, but non-zero, load. k(T) = 10[W/m/K]+10[W/m/K]*(T>400[K]) With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. That is, they are tuned to achieve convergence in as many cases as possible. In this posting, we introduce the idea of ramping the nonlinearities in the problem to improve convergence. Under Initial values of variables solved for, the default value of the Settingslist is Physics controlled. The issue here has do with the iterative algorithm used to solve nonlinear stationary models. The other low-level default settings within the Stationary Solver are chosen for robustness. Such problems must solved in the time domain. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. Also, keep in mind that a linear stationary model should solve regardless of how coarse the mesh is (albeit to a low accuracy) so you can always start with as coarse a mesh as possible, and refine the mesh (See also: Knowledgebase 1030: Performing a Mesh Refinement Study. Most multiphysics problems are nonlinear. For example, if there is a temperature-dependent material property such as: 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.
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