Miscellaneous

# What is weak form in COMSOL?

## What is weak form in COMSOL?

The weak formulation turns the differential equation for the heat transfer physics into an integral equation, with a test function as a localized sampling function within the integrand to clamp down the solution. Integrating the weak form by parts provides the numerical benefit of reduced differentiation order.

### What is the weak form of an equation?

Weak form – an integral expression such as a functional which implicitly contains a differential equations is called a weak form. The strong form states conditions that must be met at every material point, whereas weak form states conditions that must be met only in an average sense.

#### How do I enable equation view in COMSOL?

You can access the equations and variables used internally by COMSOL Multiphysics® by enabling the Equation View nodes to display in the model tree. Through the Model Builder toolbar, you can open the menu for showing more options, and then select the check box next to Equation View and click OK.

What is a weak form?

Weak forms are syllable sounds that become unstressed in connected speech and are often then pronounced as a schwa. In the sentence below the first ‘do’ is a weak form and the second is stressed.

How do I add weak contributions to Comsol?

Then, in the Model Builder, right-click the main interface node and, depending on the geometric entity level, select More>Weak Contribution at the domain or boundary level, Edges>Weak Contribution, Points>Weak Contribution, or Global>Weak Contribution.

## How do I change equations in COMSOL?

You should be able to edit the equation when clicking on the “Equation View” branch of the related physics node. As an alternative, you may input 0, 1 or a function in the value field of that variable which you want to simplify/modify.

### How can I write expression in COMSOL?

Click the Insert Expression button ( ) at the bottom of the section or press Ctrl+Space to insert a predefined expression or variable into the selected cell in the Value column.

#### How do I write expressions in Comsol?

How do I change equations in Comsol?

What are the advantages of weak formulation?

The weak formulation turns a differential equation into an integral equation. Integration by parts reduces the order of differentiation to provide numerical advantages, and generates natural boundary conditions for specifying fluxes at the boundaries.

## What is test function in Comsol?

While the test function, mathematically, is definded as a more-or-less often differentiable hat-function on a given region, it is displayed in most COMSOL models as something like this. rest_of_equation*(test(uTx) + test(u) + test(vty)) or similar.

### Why are weak forms important?

Why are weak forms important? For at least two reasons: English has a tendency to make the important words for the message one wants to get across stand out. Second, shortening of some, less important words is essential to the rhythm characteristic of the English language.

#### What are examples of weak verbs?

With weak verbs, the stem vowel does not change in the past or past participle tense….Examples of Weak Verbs

• Beg > begged.
• Call > called.
• Damage > damaged.
• Earn > earned.
• Mark > marked.
• Taste > tasted.
• Yell > yelled.

Why do we need weak formulation?

Weak formulations are important tools for the analysis of mathematical equations that permit the transfer of concepts of linear algebra to solve problems in other fields such as partial differential equations.

How do I write variables in COMSOL?

Right-click Global Definitions and choose Variables. Under Component right-click Definitions and choose Variables, or click Local Variables in the Definitions toolbar (Windows users). Use the Variables node to define expressions as user-defined variables.

## Can We Solve weak form equations in COMSOL Multiphysics?

In the previous post, we implemented and solved an exemplary weak form equation in the COMSOL Multiphysics software. The result was validated with simple physical arguments.

### Is it possible to solve the weak form matrix equation efficiently?

The resulting matrix equation is sparse, which can be solved efficiently using a computer. In the previous blog post, when we implemented the weak form equation using COMSOL Multiphysics, the discretization was done under the hood without needing the user’s help.

#### How do you discretize the weak form equation in two steps?

Discretizing the Weak Form Equation in Two Steps. With the new set of basis functions defined above, we proceed to discretize the weak form equation (1) in two steps. First, the temperature function, T(x), can be approximated by the set of basis functions in the same way as in Eq.

How do I use Lambda2 in COMSOL?

We enter lambda2 for the Field variable name in the subnode and then enter the weak expression as the two terms in Eq. (1): -lambda2*test (T)-test (lambda2)* (T-9) The COMSOL software discretizes the domain by creating a mesh. Let’s right-click the Mesh 1 node and select Edge and then right-click Edge 1 and select Distribution.