Equation-Based Modeling Blog Posts
Integrals with Moving Limits and Solving Integro-Differential Equations
Learn how to analyze spatial integrals over variable limits, whether they are prescribed explicitly or defined implicitly. (Part 2 of 2)
Guidelines for Equation-Based Modeling in Axisymmetric Components
Here’s your comprehensive guide to equation-based modeling for problems with cylindrical coordinates and axisymmetric components.
Investigating Turing’s Theory of Morphogenesis
Ever wonder how a tiger gets its stripes? Alan Turing’s theory of morphogenesis explains how patterns, such as stripes, develop naturally from initially homogeneous states.
Thermal Modeling of Phase-Change Materials with Hysteresis
Hysteresis occurs when the melting temperature of a material is different from the solidification temperature. We demonstrate the thermal modeling of such a material here.
Modeling the Thermal Curing Process
Polymerization of a thermoset resin is one example of thermal curing, a process in which temperature-induced chemical change occurs in a material.
Analyze the Spread of Epidemic Diseases with Simulation
Did you know that public health officials use mathematical modeling techniques to study the flu and other infectious diseases to predict their spread and make informed decisions?
Verify Simulations with the Method of Manufactured Solutions
The Method of Manufactured Solutions involves assuming a solution, obtaining source terms, solving the problem, and comparing the results with the assumed solution. Use it to verify your models.
Implementing the Weak Form with a COMSOL App
First we implement the weak form equation and examine its matrices. Then we create a simulation app that displays all relevant matrices at once, arranged logically on one screen.
Can We Hear the Shape of a Drum?
Over half a century ago, Mark Kac gave an interesting lecture on a question that he had heard from Professor Bochner ten years earlier: “Can one hear the shape of a drum?”
Discretizing the Weak Form Equations
In another installment of our blog series on the weak form equations, get an overview of how these equations are discretized and solved numerically in the COMSOL® software.
Implementing the Weak Form in COMSOL Multiphysics
In Part 2 of our series on the weak form equations, we demonstrate how to implement and solve these equations numerically using COMSOL Multiphysics®.
A Brief Introduction to the Weak Form
Whether or not you use finite element analysis and vector calculus in your daily life, you’ll appreciate this introduction to the weak form equations.