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All posts by Walter Frei

Using Adaptive Meshing for Local Solution Improvement

December 27, 2013

One of the perennial questions in finite element modeling is how to choose a mesh. We want a fine enough mesh to give accurate answers, but not too fine, as that would lead to an impractical solution time. As we’ve discussed previously, adaptive mesh refinement lets the software improve the mesh, and by default it will minimize the overall error in the model. However, we often are only interested in accurate results over some subset of the entire model space. […]

Learning to Solve Multiphysics Problems Effectively

December 26, 2013

One of the questions we get asked often is how to learn to solve multiphysics problems effectively. Over the last several weeks, I’ve been writing a series of blog posts addressing the core functionality of the COMSOL Multiphysics software. These posts are designed to give you an understanding of the key concepts behind developing accurate multiphysics models efficiently. Today, I’ll review the series as a whole.

Improving Convergence of Multiphysics Problems

December 23, 2013

In our previous blog entry, we introduced the Fully Coupled and the Segregated algorithms used for solving steady-state multiphysics problems in COMSOL. Here, we will examine techniques for accelerating the convergence of these two methods.

Solving Multiphysics Problems

December 16, 2013

Here we introduce the two classes of algorithms used to solve multiphysics finite element problems in COMSOL Multiphysics. So far, we’ve 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.

Thermal Modeling of Surfaces with Wavelength-Dependent Emissivity

December 12, 2013

Whenever we are solving a thermal problem where radiation is significant, we need to know the emissivities of all of our surfaces. Emissivity is a measure of the ability of a surface to emit energy by radiation, and it can depend strongly upon the wavelength of the radiation. This is very relevant for thermal problems where the temperature variation is large or when there is exposure to a high-temperature source of radiation such as the sun. In this post on […]

Meshing Considerations for Nonlinear Static Finite Element Problems

December 10, 2013

As part of our solver blog series we have discussed solving nonlinear static finite element problems, load ramping for improving convergence of nonlinear problems, and nonlinearity ramping for improving convergence of nonlinear problems. 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. Building on these topics, we will now address how to prepare your mesh for efficiently solving nonlinear finite element problems.

Nonlinearity Ramping for Improving Convergence of Nonlinear Problems

December 3, 2013

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. This algorithm was also useful for understanding what happens near a failure load. However, load ramping will not work in all cases, or may be inefficient. In this posting, we introduce the idea of ramping the nonlinearities in the problem to improve convergence.

Load Ramping of Nonlinear Problems

November 22, 2013

As we saw previously in the blog entry on Solving Nonlinear Static Finite Element Problems, not all nonlinear problems will be solvable via the damped Newton-Raphson method. 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. Here we introduce a more robust approach to solving nonlinear problems.