## 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.

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### 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.

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### 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 […]

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### 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.

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### 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.

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### On Solvers: Benefits and Limits of Solution Methods

##### Wolfgang Joppich April 24, 2013

This week we have the honor of having Professor Wolfgang Joppich as a guest blogger. As you may know, COMSOL Multiphysics provides great default solvers for all applications. For the interested user, it is good to know that you can optionally tune or completely change the solver settings. We strongly recommend that you read this blog posting to get an experts’ perspective on the solver technologies offered by COMSOL. I am an avid reader of the COMSOL Blog and an […]

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#### Categorias

##### Bjorn Sjodin March 19, 2013

For a transient simulation, imagine if you could simply insert a virtual sensor in a model at a certain location and then monitor the evolution of a field value over time while solving. In COMSOL Multiphysics you can do just that by using Probes. You define a probe in the Model Builder tree right under the Model Definitions node. Measuring the value at a point is not the only thing you can do with probes, but in this blog post […]

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### On Solvers: The V-Cycle Multigrid

##### Valerio Marra February 13, 2013

As discussed previously on the blog, iterative methods efficiently eliminate oscillatory error components while leaving the smooth ones almost untouched (smoothing property). Multigrid methods, in particular, use the smoothing property, nested iteration, and residual correction to optimize convergence. Before putting all of the pieces of this proverbial puzzle together, we need to introduce residual correction and dive a bit deeper into nested iteration. Let’s begin with the latter of these elements.

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### On Solvers: Multigrid Methods

##### Valerio Marra February 8, 2013

Solution methods are a valuable tool for ensuring the efficiency of a design as well as reducing the overall number of prototypes that are needed. In today’s blog post, we introduce you to a particular type of method known as multigrid methods and explore the ideas behind their use in COMSOL Multiphysics.

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### Moore’s Law for Solvers

##### David Kan September 12, 2012

At the heart of any simulation software are the solvers. Those are things that take geometry/mesh/physics to the computational results. While it’s convenient to think about solvers in terms of the type of study (think time-dependent, parametric, or eigenvalue), there is a hierarchy of solvers that are usually employed. And at the foundational level of any simulation — and for every iteration — there is a linear solver.

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