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. 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. Instead, use a nonlinear material property expression that ramps from a very smooth function to a very nearly discontinuous one. Building on these topics, we will now address how to prepare your mesh for efficiently solving nonlinear finite element problems. It's brand new in the hmart plaza and I wish it was open back when I would hangout in the plaza after school (although they would have taken all my allowance money! Second, the continuation method will automatically take smaller load increments if a solution cannot be found. Why is there a voltage on my HDMI and coaxial cables? I am trying to solve the coupling between a waveguide and a microring resonator. The conditions on the geometric aspect ratio are relatively more strict. 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. An example model that combines the techniques of nonlinearity ramping and adaptive mesh refinement with multiple study steps is: COMSOL does not assume any legal liability for the accuracy of the data disclosed. An example model that combines the techniques of nonlinearity ramping and adaptive mesh refinement with multiple study steps is: Computational Fluid Dynamics (CFD), API Again, introduce a Global Parameter that gets ramped from exactly zero to one. Full text of the 'Sri Mahalakshmi Dhyanam & Stotram'. That is, within each outer Newton-type iteration, the segregated approach solves for each segregated group sequentially. Hello, I highly recommend this flower shop. Linear solvers. Use this parameter to modify the nonlinearity expressions in the model. so many cute little stationary items , hair". The default solver for most 3D models is an iterative solver, which is more sensitive to ill-conditioned problems. The fully coupled and segregated approaches are discussed below. Using a predictor of type Constant will take the solution from the iteration and use it as the initial value for the iteration. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. This parameter is used within the physics interfaces to multiply one, some, or all of the applied loads. 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. 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. The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). SGP handled 7 different prints for me at once and they all came out perfectly, in a timely manner. I am solving a linear stationary finite element model but the software is not solving. 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. 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. 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. 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. 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. That is, the material property changes instantaneously from 10W/m/K to 20W/m/K at 400K. Dun & Bradstreet gathers Office Supplies, Stationery, and Gift Retailers business information from trusted . k(T,P) = 10[W/m/K]*((1-P)+P*exp(-(T-293[K])/100[K])) 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. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. 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 settings controlling the predictor type. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. Multiphysics problems are often nonlinear. 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. She opened prepackaged 6-packs of Seegars to make ", All "stationary stores" results in Brea, CA, Search stationary stores in popular locations. The Fully Coupled solution approach, with the Plot While Solving enabled. "I chose this print shop based off yelp reviews and was very happy with the outcome! (Frequency Domain should be the last step) listed if standards is not an option). 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. This guide applies solely to nonlinear stationary models. 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. 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. Each physics is thus solved as a standalone problem, using the solution from any previously computed steps as initial values and linearization points. One of the key concepts there was the idea of mesh convergence as you refine the mesh, the solution will become more accurate. 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 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. 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. 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. As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. Not entering required material parameters. Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? In the extreme case, suppose one wants to model an instantaneous change in properties, such as: 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. Different physics have different default solvers. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. Find centralized, trusted content and collaborate around the technologies you use most. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. Cooling and Solidification of Metal. The algorithm is, generally speaking, a Newton's method approach. This guide applies solely to nonlinear stationary models. This can arise as a consequence of extreme variations in the material properties, or high aspect ratio geometry. Reply . You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version 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. This is for COMSOL 5.2, but should be similar for 4.2: Create the stationary study. I personally liked emailing them the file, ", "This flower shop is the best! It is also possible to manually refine the mesh. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. 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. k(T) = 10[W/m/K]*exp(-(T-293[K])/100[K]) P&S Comsol Team: Yannik Horst, Manuel Kohli, Xinzhi Zhang. Repeat this for every nonlinearity of the model. Your internet explorer is in compatibility mode and may not be displaying the website correctly. 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. Your internet explorer is in compatibility mode and may not be displaying the website correctly. With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. That is, start by first solving a model with a small, but non-zero, load. k(T,P) = 10[W/m/K]*((1-P)+P*exp(-(T-293[K])/100[K])) Here we introduce a more robust approach to solving nonlinear problems. If you do not hold an on-subscription license, you may find an answer in another Discussion or in the Knowledge Base. Numerically ill-conditioned means that the system matrix is nearly singular and that it will be difficult to solve on a finite-precision computer. 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. 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. $140,000.00, $120,000.00 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. I use comsol multiphysics 5.2a and . $125,000.00, Project Engineer (In-person/Hybrid/Remote), $100,000.00 Wrong ordering of study steps. For example, if there is a temperature-dependent material property such as: Get notified about new Stationary Engineer jobs in Brea, California, United States. 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. A Global Parameter has to be introduced (in the above screenshot, P) and is ramped from a value nearly zero up to one. Any trademarks referenced in this document are the property of their respective owners. Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. We use COMSOL Multiphysics for solving distributed optimal control of un-steady Burgers equation without constraints and with pointwise control constraints. ", "Absolutely the best place to shop for flowers and greenery, I spent an hour just looking around for fun prior to purchasing a bouquet, they have the best customer service people all over the place and it's a huge place", "Recently came in here to pick up 45 chocolate Seegars (cigars) for a dinner banquet in honor of my baby nephew. First, it is physically intuitive, often matching how one would perform an experiment. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. Use this parameter to modify the nonlinearity expressions in the model. 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. Direct PARDISO Solver , PARDISO . The objective here is to simplify the model to a state where the model will solve, with linear approximations. Such a large difference in the materials properties can be challenging. Create the time-dependent step or study. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. November 11, 2013. Stationary Solver Use the Stationary Solver () to find the solution to linear and nonlinear stationary problems (also called static or steady-state problems). Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. In our previous blog entry, we introduced the Fully Coupled and the Segregated algorithms used for solving steady-state multiphysics problems in COMSOL. (I am begginer in comsol) Thank you. The unknowns are segregated into groups, usually according the physics that they represent, and these groups are solved one after another. 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. 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 it does so, use a finer increment in that range. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. It may also reveal that the model itself is ill-posed in some way. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. This solver is automatically used when a Stationary or Frequency Domain study is added to the model. If the material properties entered are incorrect for the governing equation, the model will generate an error at runtime, usually a Singular Matrix error. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. 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. Near the top of the Stationary Solver log, the software will report if a linear or nonlinear solver is being 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. The advantages of the continuation method are two-fold. What sort of strategies would a medieval military use against a fantasy giant? Improving Convergence of Nonlinear Stationary Models, Knowledgebase 1030: Error: "Out of memory", Knowledgebase 1030: Performing a Mesh Refinement Study, Understanding the Fully Coupled vs. Your internet explorer is in compatibility mode and may not be displaying the website correctly. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. Instead, use a nonlinear material property expression that ramps from a very smooth function to a very nearly discontinuous one. Again, introduce a Global Parameter that gets ramped from exactly zero to one. 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. replace it with the expression: That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. Singular matrix., Make sure you defined your ports correctly:Boundary selectionType of port: e.g. The segregated approach, on the other hand, solves sets of unknowns separately. This approach is known as a Continuation Method with a Constant predictor. - Function: ^ Failed to evaluate variable. Tutti i diritti sono riservati. 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. This algorithm was also useful for understanding what happens near a failure load. Nonlinearity ramping is an especially useful technique if any of the nonlinear terms in the model are very abrupt. Using the first order optimality. Any trademarks referenced in this document are the property of their respective owners. Segregated approach and Direct vs. Iterative linear solvers, About the time step setting of the solver, Introducing Goal Seeking into the Segregated Solver. 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. If instead the model is linear, see: Knowledgebase 1260: What to do when a linear stationary model is not solving. 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. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Not assigning proper boundary conditions: Especially if you have ports.