# COMSOL Blog

## Nonlinearity Ramping for Improving Convergence of Nonlinear Problems

##### Walter Frei | 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

##### Walter Frei | 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.

### Solving Nonlinear Static Finite Element Problems

##### Walter Frei | November 19, 2013

Here, we begin an overview of the algorithms used for solving nonlinear static finite element problems. This information is presented in the context of a very simple 1D finite element problem, and builds upon our previous entry on Solving Linear Static Finite Element Models.

### Solutions to Linear Systems of Equations: Direct and Iterative Solvers

##### Walter Frei | November 11, 2013

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. This information is relevant both for understanding the inner workings of the solver and for understanding how memory requirements grow with problem size.

### Meshing your Geometry: When to Use the Various Element Types

##### Walter Frei | November 4, 2013

In a previous blog entry, we introduced meshing considerations for linear static problems. One of the key concepts there was the idea of mesh convergence — as you refine the mesh, the solution will become more accurate. In this post, we will delve deeper into how to choose an appropriate mesh to start your mesh convergence studies for linear static finite element problems.

### How to Identify and Resolve Singularities in the Model when Meshing

##### Walter Frei | October 29, 2013

In our previous post on Meshing Considerations for Linear Static Problems, we found that, in the limit of mesh refinement, the solution to the finite element model would converge toward the true solution. We also saw that adaptive mesh refinement could be used to generate a mesh that would have smaller elements in regions where the error was higher, rather than simply using smaller elements everywhere in the model. In this post, we will examine a couple of common pitfalls […]

### Meshing Considerations for Linear Static Problems

##### Walter Frei | October 22, 2013

In this blog entry, we introduce meshing considerations for linear static finite element problems. This is the first in a series of postings on meshing techniques that is meant to provide guidance on how to approach the meshing of your finite element model with confidence.

### Solving Linear Static Finite Element Models

##### Walter Frei | October 15, 2013

In this first blog entry of our new solver series, we describe the algorithm used to solve all linear static finite element problems. This information is presented in the context of a very simple 1D finite element problem, but is applicable for all cases, and is important for understanding more complex nonlinear and multiphysics solution techniques to be discussed in upcoming blog posts.

### Using Global Equations: Modeling Room Air Temperature in a House

##### Walter Frei | September 20, 2013

An interesting question came up the other day that I felt would make an excellent blog post since it allows us to discuss one of the very powerful, and often underutilized, features of COMSOL Multiphysics: the Global Equation. In this post, we will look at using global equations to introduce an additional degree of freedom to a model. This additional degree of freedom will represent something we do not want to model explicitly.

### Which Turbulence Model Should I Choose for my CFD Application?

##### Walter Frei | September 16, 2013

COMSOL Multiphysics offers several different formulations for solving turbulent flow problems: the L-VEL, yPlus, Spalart-Allmaras, k-epsilon, k-omega, Low Reynolds number k-epsilon, and SST models. All of these formulations are available in the CFD Module, and the k-epsilon and Low Reynolds number k-epsilon are available in the Heat Transfer Module. This posting outlines the reasons why we want to use these various turbulence models, how to choose between them, and how to use them effectively. Throughout the post, you’ll find links […]