The algorithm is, generally speaking, a Newton's method approach. - Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. In particular, choosing an improper initial condition or setting up a problem without a solution will simply cause the nonlinear solver to continue iterating without converging. Posted 26 set 2019, 11:57 GMT-4 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. "I chose this print shop based off yelp reviews and was very happy with the outcome! To switch between these solver types, go to the Stationary Solver node within the Study sequence. SGP handled 7 different prints for me at once and they all came out perfectly, in a timely manner. Why? 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. Multiphysics problems are often nonlinear. 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. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Connect and share knowledge within a single location that is structured and easy to search. This approach is known as a Continuation Method with a Constant predictor. 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. Using a predictor of type Constant will take the solution from the iteration and use it as the initial value for the iteration. From there, if an additional small load increment is applied, the previously computed solution is a reasonable initial condition. Not entering required material parameters. Check the solver log to see if the continuation method is backtracking. About the Stationary Solver The following background information about the Stationary Solver discusses these topics: Damped Newton Methods, Termination Criterion for the Fully Coupled and Segregated Attribute Nodes, Linear Solvers versus Nonlinear Solvers, and Pseudo Time Stepping. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. Making statements based on opinion; back them up with references or personal experience. The exceptions are the Heat Transfer interfaces, which have a default Initial Value of 293.15K, or 20C, for the temperature fields. Cooling and Solidification of Metal. 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. 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. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. 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. - Feature: Stationary Solver 1 (sol1/s1) 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. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. To start a new discussion with a link back to this one, click here. As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. If your matrix is singular than no solver in the world can solve Ax=B. 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. 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. 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. With the exception of some thermal problems however, it is often difficult to estimate the solution, so alternative approaches are needed. Again, introduce a Global Parameter that gets ramped from exactly zero to one. There will also be a red cross over the Materials branch icon. Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. Multiphysics problems are often nonlinear. If instead the model is linear, see: Knowledgebase 1260: What to do when a linear stationary model is not solving. 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. Use this parameter to modify the nonlinearity expressions in the model. Using a predictor of type Constant will take the solution from the iteration and use it as the initial value for the iteration. The segregated approach, on the other hand, solves sets of unknowns separately. Repeat this for every nonlinearity of the model. This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. - You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version 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. The objective here is to simplify the model to a state where the model will solve, with linear approximations. GCRO-DR is a method for Krylov subspace recycling. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. It may also reveal that the model itself is ill-posed in some way. 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. Consult your product manuals for complete trademark details. Perhaps this approach could be adapted to represent your model. Linear solvers. Trying to understand how to get this basic Fourier Series. Repeat this for every nonlinearity of the model. k(T) = 10[W/m/K]+10[W/m/K]*(T>400[K]) There will always already be either a Segregated or Fully Coupled feature beneath this. 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. See Knowledge Base 1240: Manually Setting the Scaling of Variables. Not meshing all the domains. 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 settings controlling the predictor type. listed if standards is not an option). You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version Your internet explorer is in compatibility mode and may not be displaying the website correctly. There will always already be either a Segregated or Fully Coupled feature beneath this. The objective here is to simplify the model to a state where the model will solve, with linear approximations. Consult your product manuals for complete trademark details. Review the model setup to resolve these. An example model that combines the techniques of nonlinearity ramping and adaptive mesh refinement with multiple study steps is: The Auxiliary Sweep can be used to implement ramping of any Global Parameter. The unknowns are segregated into groups, usually according the physics that they represent, and these groups are solved one after another. This guide applies solely to nonlinear stationary models. Not entering required material parameters. It may also reveal that the model itself is ill-posed in some way. 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. Any trademarks referenced in this document are the property of their respective owners. Mesh 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 Fully Coupled solution approach, with the Plot While Solving enabled. The settings controlling the predictor type. 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. Solving for laminar flow using Comsol - YouTube Comsol help video number 2: Solving a laminar flow problem in a slit. I am trying to solve the coupling between a waveguide and a microring resonator. That is, they are tuned to achieve convergence in as many cases as possible. Learn how your comment data is processed. The other low-level default settings within the Stationary Solver are chosen for robustness. COMSOL makes every reasonable effort to verify the information you view on this page. (Frequency Domain should be the last step) 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. It is also possible to manually refine the mesh. P&S: COMSOL Design Tool for Photonic Devices. COMSOL makes every reasonable effort to verify the information you view on this page. Not assigning proper boundary conditions: Especially if you have ports. Each physics is thus solved as a standalone problem, using the solution from any previously computed steps as initial values and linearization points. Your internet explorer is in compatibility mode and may not be displaying the website correctly. Feature: Stationary Solver 1 (sol1/s1)" . How do/should administrators estimate the cost of producing an online introductory mathematics class? I highly recommend this flower shop. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. The algorithm is, generally speaking, a Newton's method approach. 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. That is, the material property changes instantaneously from 10W/m/K to 20W/m/K at 400K. 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. That is, within each outer Newton-type iteration, the segregated approach solves for each segregated group sequentially. This guide applies solely to nonlinear stationary models. The other low-level default settings within the Stationary Solver are chosen for robustness. The stationary solver is used both for Stationary (time-invariant) and Frequency Domain (time-harmonic) study types. This involves a systematic reduction in the model complexity. If it does so, use a finer increment in that range. Starting from zero initial conditions, the nonlinear solver will most likely converge if a sufficiently small load is applied. Understanding the Fully Coupled vs. 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. Use this parameter to modify the nonlinearity expressions in the model. Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. Find centralized, trusted content and collaborate around the technologies you use most. there is no defined multiphysics for it as I know, I have a standing accoustic wave and a flow in the background but I don't see their connection. Not assigning proper boundary conditions: Especially if you have ports. See also: Knowledge Base 1254: Controlling the Time Dependent solver timesteps. The issue here has do with the iterative algorithm used to solve nonlinear stationary models. 3. November 11, 2013. Some models are numerically ill-conditioned due to the setup. This algorithm was also useful for understanding what happens near a failure load. Using this technique systematically, along with the techniques described previously, will usually identify the nonlinearities in the model that are leading to issues. Wish you all the best. 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. 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. It is thus always advised to start this procedure with a simplified 2D, or 2D-axisymmetric model. That is: Even if the forces on a part are opposite and equal, this is not sufficient information to say where the part is, so you must add some other condition, such as as Fixed Constraint to constrain displacement. If the model is nonlinear, see: Improving Convergence of Nonlinear Stationary Models. replace it with the expression: I am following the same model as Comsol provide us on the web. 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. The difference between the phonemes /p/ and /b/ in Japanese. This guide applies solely to nonlinear stationary models. Linear solvers. Again, introduce a Global Parameter that gets ramped from exactly zero to one. Nonlinearities arise as a consequence of the governing equation, as a material nonlinear expression, or as a coupling term between physics. 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. Not entering required material parameters. 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. Dr.S.Ravindran Cite 1 Recommendation Popular answers (1). 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. There will always already be either a Segregated or Fully Coupled feature beneath this. For example, if there is a temperature-dependent material property such as: Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. Segregated approach and Direct vs. Iterative linear solvers, About the time step setting of the solver, Introducing Goal Seeking into the Segregated Solver. 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. $140,000.00, $120,000.00 Different physics have different default solvers. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. This can arise as a consequence of extreme variations in the material properties, or high aspect ratio geometry. Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. Convergence can be poor when the initial values do not provide a good starting point for this iterative approach. The unknowns are segregated into groups, usually according the physics that they represent, and these groups are solved one after another. Segregated approach and Direct vs. Nonlinearities arise as a consequence of the governing equation, as a material nonlinear expression, or as a coupling term between physics. Alternatively, delete and re-create the study. 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. As P is ramped up, the continuation method uses the previous solutions to compute initial conditions for the more nonlinear cases. Check the solver log to see if the continuation method is backtracking. By creating this job alert, you agree to the LinkedIn User Agreement and Privacy Policy. How can I check before my flight that the cloud separation requirements in VFR flight rules are met? listed if standards is not an option). Any trademarks referenced in this document are the property of their respective owners. Does ZnSO4 + H2 at high pressure reverses to Zn + H2SO4? This approach is used by default for most 1D, 2D, and 2D-axisymmetric models. If both load ramping and nonlinearity ramping are still leading to slow convergence, refine the mesh. What are some highly rated cards & stationery in Brea, CA? COMSOL does not assume any legal liability for the accuracy of the data disclosed. A Global Parameter has to be introduced (in the above screenshot, P) and is ramped from a value nearly zero up to one. That is, when solving, the software starts with the user-specified initial values to evaluate all solution-dependent terms. Stationary (time-invariant) models with nonlinearities may converge very slowly. 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. If these settings have been manually changed, you will see a small star symbol on the Solution feature, as shown in the screenshot below. $125,000.00, Project Engineer (In-person/Hybrid/Remote), $100,000.00 - Variable: B1 - Defined as: 1/ ( ( (comp1.cH2 (unit_m_cf^3))/unit_mol_cf)^2.5) Failed to evaluate variable. Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems. 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. 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. Dun & Bradstreet gathers Office Supplies, Stationery, and Gift Retailers business information from trusted . Hello, That is, start by first solving a model with a small, but non-zero, load. My comment is perhaps a bit nave but it seems to me that you could simply deactivate the \frac{\partial \cdot}{\partial t} term of the background field equation but keep its connexion to the solid to get what you want. This doesn't seem to me the most elegant of methods, since I am essentially solving a stationary solution using a time dependent Nonlinearity ramping is an especially useful technique if any of the nonlinear terms in the model are very abrupt. Consult your product manuals for complete trademark details. Save my name, email, and website in this browser for the next time I comment. This segregated approach is used by default for most 3D multiphysics models, and the software will automatically segregate the problem into appropriate groups. This is useful since the software will then return an estimation of the maximum possible loadcase for which the solver can converge. Acidity of alcohols and basicity of amines. Reply . (Frequency Domain should be the last step) Your internet explorer is in compatibility mode and may not be displaying the website correctly. 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. The segregated approach, on the other hand, solves sets of unknowns separately. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. With respect to any nonlinearities, replace them by a reasonable linearized term. That is, they are tuned to achieve convergence in as many cases as possible. 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. Not the answer you're looking for? Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. 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. Right-click on the Stationary Solver node and add either the Segregated or Fully Coupled feature. Perhaps this approach could be adapted to represent your model. - Therefore, an initial value of zero is almost always reasonable if a very small load is applied. 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. Once a simplified solvable version of the model has been found, gradually increase the model complexity again, re-introducing nonlinearities and multiphysics couplings. The default solver for most 3D models is an iterative solver, which is more sensitive to ill-conditioned problems. Cooling and Solidification of Metal. 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. Wrong ordering of study steps. thanks for reply Is there a way to use the stationary solution obtained in Comsol 4.2 as the initial conditions in a time dependent model? Ramping the nonlinearities over time is not as strongly motivated, but step changes in nonlinearities should be smoothed out throughout the simulation. 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.