Curvilinear coordinate adaptive method in COMSOL

  • #1
EdgarasM
Hello everyone,

In the COMSOL v5.1 doc i haven't found the mathematical description on how does the automatic geometry analysis or the curvilinear coordinates adaptive method (it is mentioned that they are similar) works.

It would be convenient to have an idea about how does the Ecoil vector field is derived in a mathematical sense, precisely for the research purposes.

What i have managed to find out is that there are weak expressions used by the name of cc.adap1.weak1 and cc.adap1.weak2 in the domain region and cc.adap1.inl1.weak1 at the inlet, and at the outlet the constrain cc.adap1.out1.constr is prescribed.

In most other physics interfaces weak expressions are shown in terms of the variables and the mathematical background could be understood.

Thank you in advance,

Edgaras
 
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  • #2

Hello Edgaras,

Thank you for your question about the mathematical description of the automatic geometry analysis and curvilinear coordinates adaptive method in COMSOL v5.1. I'm glad to see that you are doing research and looking for a deeper understanding of these methods.

To begin, the automatic geometry analysis in COMSOL v5.1 uses a combination of algorithms and mathematical techniques to analyze and adapt the geometry of a model. This involves identifying and refining areas of high curvature or complexity, while simplifying or coarsening areas with lower curvature or complexity. This is done in an automated way to improve the accuracy and efficiency of the simulation.

The curvilinear coordinates adaptive method is a specific technique used in the automatic geometry analysis. It involves transforming the coordinate system of the model to better match the geometry, which can improve the accuracy of the simulation.

In terms of the Ecoil vector field, its derivation involves solving the equations of motion for the electric and magnetic fields, as well as the material properties and boundary conditions of the model. This is a complex mathematical process and involves the use of weak expressions, which are mathematical formulations used to describe the behavior of a physical system.

The specific weak expressions you mentioned, cc.adap1.weak1 and cc.adap1.weak2, are used to describe the behavior of the electric and magnetic fields in the domain region. Similarly, cc.adap1.inl1.weak1 is used to describe the behavior at the inlet and cc.adap1.out1.constr is used to prescribe a constraint at the outlet. These weak expressions are derived from the underlying equations and boundary conditions of the model.

I hope this helps to give you a better understanding of the mathematical background behind the automatic geometry analysis and curvilinear coordinates adaptive method in COMSOL v5.1. If you have any further questions, please don't hesitate to ask.


 

1. What is a curvilinear coordinate adaptive method in COMSOL?

A curvilinear coordinate adaptive method in COMSOL is a numerical algorithm that is used to solve partial differential equations in complex geometries. It allows for the use of curvilinear coordinates, which are coordinate systems that conform to the shape of the problem domain, making it easier to model and solve problems with curved boundaries or irregular shapes.

2. How does the curvilinear coordinate adaptive method work in COMSOL?

The curvilinear coordinate adaptive method works by first discretizing the problem domain into a mesh of elements. It then adapts the mesh by refining or coarsening the elements in areas where the solution needs to be more accurate. This is done based on a local error estimate, which is calculated using the residuals of the equations being solved. The adapted mesh is then used to solve the equations and the process is repeated until the desired level of accuracy is achieved.

3. What are the advantages of using the curvilinear coordinate adaptive method in COMSOL?

There are several advantages to using the curvilinear coordinate adaptive method in COMSOL. These include the ability to model and solve problems with complex geometries more accurately and efficiently, as well as the ability to easily incorporate boundary conditions on curved boundaries. It also allows for a more efficient use of computational resources by only refining the mesh where it is necessary for accurate results.

4. Are there any limitations to using the curvilinear coordinate adaptive method in COMSOL?

While the curvilinear coordinate adaptive method is a powerful tool, it does have some limitations. It may not be suitable for problems with highly anisotropic solutions or problems with sharp gradients in the solution. Additionally, it may require more computational resources and time compared to other numerical methods, especially for problems with highly non-linear behavior.

5. How can I learn more about using the curvilinear coordinate adaptive method in COMSOL?

There are various resources available for learning more about the curvilinear coordinate adaptive method in COMSOL. The COMSOL website offers tutorials, videos, and user guides on this topic. Additionally, attending workshops or training courses on COMSOL can provide hands-on experience and guidance from experts. Finally, consulting with other scientists or engineers who have experience with this method can also be helpful in understanding its applications and limitations.

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