The algorithm is, generally speaking, a Newton's method approach. We use COMSOL Multiphysics for solving distributed optimal control of un-steady Burgers equation without constraints and with pointwise control constraints. Solve the stationary study then the time dependent study. 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. Not meshing all the domains. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. Instead, use a nonlinear material property expression that ramps from a very smooth function to a very nearly discontinuous one. This case is generally difficult, or impossible, to solve since this material property is non-smooth. The Continuation method is enabled by default when using the Auxiliary sweep study extension, as shown below. 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 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 many physics areas there exist alternative physics formulations specifically meant for solving cases where the geometry has an extreme aspect ratio. However, it is usually not possible to know this ahead of time. If it does so, use a finer increment in that range. By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. Numerically ill-conditioned means that the system matrix is nearly singular and that it will be difficult to solve on a finite-precision computer. listed if standards is not an option). 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. If the model is nonlinear, see: Improving Convergence of Nonlinear Stationary Models. The Fully Coupled solution approach, with the Plot While Solving enabled. k(T) = 10[W/m/K]*exp(-(T-293[K])/100[K]) 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. In such cases, use the same continuation method, but instead ramp the nonlinearities in the model. This will use the initial conditions you specified in your physics setting (usually 0 is used in the physics settings). Despite this, the segregated approach can often converge very robustly, unless there are very strong couplings between the physics in the model. This is a review for cards & stationery in Brea, CA: "Love this store!!! The other low-level default settings within the Stationary Solver are chosen for robustness. 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. 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. 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. That is, within each outer Newton-type iteration, the segregated approach solves for each segregated group sequentially. 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. 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. 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. The Auxiliary Sweep can be used to implement ramping of any Global Parameter. Using this technique systematically, along with the techniques described previously, will usually identify the nonlinearities in the model that are leading to issues. Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. Site design / logo 2023 Stack Exchange Inc; user contributions licensed under CC BY-SA. The finite element mesh must be fine enough to resolve the spatial variations in the solution fields. (Frequency Domain should be the last step) Please dont hesitate to post comments below or send emails to us if you experience any other problems. 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. 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 solver for most 3D models is an iterative solver, which is more sensitive to ill-conditioned problems. Resources and documents are provided for your information only, and COMSOL makes no explicit or implied claims to their validity. Wrong ordering of study steps. That is, start by first solving a model with a small, but non-zero, load. 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. Nonlinearity ramping is an especially useful technique if any of the nonlinear terms in the model are very abrupt. By clicking Post Your Answer, you agree to our terms of service, privacy policy and cookie policy. In such cases it will be particularly helpful to ramp the load gradually in time, from consistent initial values. 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. I personally liked emailing them the file, ", "This flower shop is the best! Using the first order optimality. Is it possible to rotate a window 90 degrees if it has the same length and width? 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. The default Initial Values for the unknowns in most physics interfaces are zero. 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. The coupling terms between the different groups are thus neglected. The former approach solves for all unknowns in the problem at once, and considers all coupling terms between all unknowns within a single iteration. COMSOL makes every reasonable effort to verify the information you view on this page. 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 conditions on the geometric aspect ratio are relatively more strict. 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. See Knowledge Base 1240: Manually Setting the Scaling of Variables. 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. Thanks for contributing an answer to Stack Overflow! Use either a very fine mesh throughout the simulation domain or use adaptive mesh refinement. 3 Replies, Please login with a confirmed email address before reporting spam. What is \newluafunction? Not entering required material parameters. Using this technique systematically, along with the techniques described previously, will usually identify the nonlinearities in the model that are leading to issues. 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. 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. You can fix this by pressing 'F12' on your keyboard, Selecting 'Document Mode' and choosing 'standards' (or the latest version 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. 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. The "Values for dependent values" in study step settings should be set to the default ("Physics-controlled" in 5.2). Could you expand a little bit more why the coupling is impossible? Trying to understand how to get this basic Fourier Series. It is sometimes necessary to manually scale the dependent variables. Such problems must solved in the time domain. 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. If so, see: Knowledgebase 1030: Error: "Out of memory". 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. This is relatively expensive to do, but will lead to the most robust convergence. 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 assigning proper boundary conditions: Especially if you have ports. 140K views 8 years ago COMSOL Multiphysics Tutorial for Beginners Please note that an updated version of the content in this video can be found in the Modeling Workflow video in the COMSOL. If a good estimate to the solution field is known, this can be entered as an an expression in the Initial Value field. It can be useful while solving sequences of linear systems arising from, for example, nonlinear problems. Ideally, one would use small elements in regions where the solution varies quickly in space, and larger elements elsewhere. thanks for reply 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. That is, they are tuned to achieve convergence in as many cases as possible. A Global Parameter has to be introduced (in the above screenshot, P) and is ramped from a value nearly zero up to one. Few days back i was also facing this problem in . The objective here is to simplify the model to a state where the model will solve, with linear approximations. The settings controlling the predictor type.