General Blog Posts
On Solvers: The V-Cycle Multigrid
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.
On Solvers: Multigrid Methods
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.
Equations: Who Needs Them?
Most of us take mathematical modeling for granted. After all, we’re taught physics and calculus almost hand-in-hand. But we owe a lot to the early pioneers like Isaac Newton, who demonstrated and strongly promoted interpreting natural phenomena through equations. Differential equations are especially useful since most things change as time marches on. Since we live in 3D space, partial differential equations (i.e., equations that express change in more than one “direction”) arise as the prominent tool to express continuum level […]
User Tip: All About Icons
I give a lot of COMSOL workshops — about 20 so far this year. These are great events and they include hands-on minicourses, which allow me to connect with the audience. One topic that I often spend a few minutes on might surprise you: icons. The icons, especially those found at the nodes in the Model Builder, are packed with useful information. They’re easy to miss because they’re small, but knowing what they mean can be a big help.
Moore’s Law for Solvers
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.
Multiphysics Makes Single-Physics Simulations Better
Coupled physics phenomena (like electrical heating, fluid structure interaction, and conjugate heat transfer) demand multiphysics, which I’ve written about previously in “What is Multiphysics?”. But what if you just have a simple analysis to do — one that has been simplified to the point where only a “single physics” (to coin a term) is considered? What benefits does multiphysics have for this?
What Is Multiphysics?
If you’re a cynic (like I am sometimes), the term “multiphysics” might irk you. There’s only one set of physical laws, after all. There’s nothing “multi” about it. So what is multiphysics?
Including Operators and Expressions in a Multiphysics Simulation Is Easier Than You Think
As most skilled COMSOL users, I am sure you know that you are not limited to just selecting what is in our drop-down lists. Say that you have invented your own measure of structural stress. You want it to be equal to the quadratic mean of the Tresca and von Mises stresses. Go to Plot Parameters to find out what these predefined stresses are called (trescasmsld and misessmsld if you are modeling in 3D with the Structural Mechanics Module). Now […]