3D nanomagnetic

Posted 25.06.2024, 18:45 GMT-4 Electromagnetics, Low-Frequency Electromagnetics Version 6.2 1 Reply

Mohammad Alneari

Send Private Message Flag post as spam

Please login with a confirmed email address before reporting spam

Dear all, I do have a 2D model to study the magnetization dynamics induced by external current density applied normal to the surface that makes the magnetization rotating, however, when I extended it to 3D the simulation works but with a warning meesage; nonsymmatric matrix found and then ends up by saying singular matrix. i also plot the normal magnetization and found straigt lines for 2D while it is not for the 3D.

Reply

1 Reply Last Post 25.10.2024, 02:32 GMT-4

COMSOL Moderator

Hello Mohammad Alneari

Your Discussion has gone 30 days without a reply. If you still need help with COMSOL and have an on-subscription license, please visit our Support Center for help.

If you do not hold an on-subscription license, you may find an answer in another Discussion or in the Knowledge Base.

Sweta sarita Sarangi

Send Private Message Flag post as spam

Please login with a confirmed email address before reporting spam

Posted: 4 weeks ago

In COMSOL, the error you are encountering—related to a "nonsymmetric matrix" and a "singular matrix"—typically arises due to issues with the setup or numerical solution of the partial differential equations (PDEs) in 3D.

Here's a step-by-step guide to troubleshooting and fixing this issue in COMSOL for your magnetization dynamics simulation:

Check Mesh Quality Reason: The 3D model typically requires a finer and more structured mesh compared to 2D. Poor mesh quality can lead to instability in the matrix solver, resulting in nonsymmetric or singular matrices.

Solution: In COMSOL, use Mesh > Statistics to check for distorted or low-quality elements in your 3D mesh. Refine the mesh where needed, especially in regions where the magnetization or current density gradients are large. You may also switch to a finer mesh or adaptive mesh refinement.

Solver Settings Reason: The solver might be inappropriate for the complexity of your 3D model, which may include complex boundary conditions or anisotropy.

Solution: Direct Solver: Go to Study > Solver Configurations > Solver. Try switching to a direct solver (e.g., MUMPS) instead of iterative solvers like GMRES. Direct solvers are more robust for ill-conditioned systems.

Iterative Solver Settings: If using an iterative solver, enable preconditioning and increase the number of iterations to help with convergence. Tolerance: Lower the relative tolerance in the solver settings to improve accuracy. Symmetric Solver Option: In some cases, enabling or forcing the symmetry option in the Advanced Solver Settings might help, but this depends on whether your problem is fundamentally symmetric.

Check Boundary and Initial Conditions Reason: Boundary and initial conditions in 3D are more complex than in 2D. Incorrect or inconsistent boundary conditions can lead to singular matrices. Solution: Revisit the boundary conditions and ensure they are physically meaningful and properly defined for all the 3D boundaries. Ensure that initial conditions for the magnetization field are realistic, especially for 3D, where small inconsistencies can lead to large numerical issues.
Material Properties

Reason: In 3D, the material properties such as magnetic permeability or electrical conductivity may need to be defined more precisely. Any anisotropy in the material might be incorrectly represented, leading to matrix issues.

Solution: Double-check that the magnetic permeability and conductivity tensors (if anisotropic) are defined correctly for the 3D geometry. Also, check that material properties vary smoothly throughout the 3D domain.

Equation Formulation Reason: Extending from 2D to 3D can introduce additional terms or complexities (like demagnetizing fields) in the Landau-Lifshitz-Gilbert (LLG) equations or other governing equations.

Solution: Re-check the formulation of the magnetization dynamics equations in COMSOL. Ensure that all terms are correctly extended to 3D (e.g., including the demagnetizing fields and stray fields). If necessary, enable or explicitly define terms for anisotropy, exchange energy, and demagnetizing field in the 3D domain, which may not be as crucial in the 2D case but are essential in 3D simulations.

Magnetic Vector Potential vs. Scalar Potential Reason: In 3D, the choice between using a magnetic vector potential formulation (for transient magnetic fields) versus a magnetic scalar potential formulation (for static fields) can affect stability and convergence. Solution: Verify the potential formulation used in your simulation: Use magnetic vector potential for dynamic simulations involving currents and moving magnetization.

Use magnetic scalar potential for simpler static field calculations. In COMSOL, you can adjust this under Physics > Magnetic Fields.

Singular Matrix and Regularization

Reason: Singular matrices often indicate that the system of equations is not properly constrained or ill-posed.

Solution: In COMSOL, you can use regularization techniques to handle singular matrices. Check the options in Physics > Magnetic Fields to add regularization terms, particularly for ill-posed boundary conditions or problematic initial conditions.

Current Density Distribution Reason: In 3D, the current density distribution applied to the model may differ significantly from the 2D case, leading to unexpected behavior.

Solution: Ensure that the current density is applied correctly in 3D. If the current is distributed non-uniformly, increase the resolution of the applied current and check for regions with high gradients.

Plotting and Post-Processing Reason: The fact that your normal magnetization plot shows straight lines in 2D but not in 3D suggests that the magnetization is behaving differently in 3D, which is expected due to additional degrees of freedom.

Solution: Use Post-processing in COMSOL to visualize the magnetic fields, current density, and magnetization dynamics in the 3D model. Compare the 2D and 3D results to understand where the magnetization dynamics differ and adjust parameters accordingly.

By following these steps, you should be able to address the matrix singularity and nonsymmetric matrix warnings in COMSOL, improving the accuracy and stability of your 3D magnetization dynamic sitution.

In COMSOL, the error you are encountering—related to a "nonsymmetric matrix" and a "singular matrix"—typically arises due to issues with the setup or numerical solution of the partial differential equations (PDEs) in 3D. Here's a step-by-step guide to troubleshooting and fixing this issue in COMSOL for your magnetization dynamics simulation: 1. Check Mesh Quality Reason: The 3D model typically requires a finer and more structured mesh compared to 2D. Poor mesh quality can lead to instability in the matrix solver, resulting in nonsymmetric or singular matrices. Solution: In COMSOL, use Mesh > Statistics to check for distorted or low-quality elements in your 3D mesh. Refine the mesh where needed, especially in regions where the magnetization or current density gradients are large. You may also switch to a finer mesh or adaptive mesh refinement. 2. Solver Settings Reason: The solver might be inappropriate for the complexity of your 3D model, which may include complex boundary conditions or anisotropy. Solution: Direct Solver: Go to Study > Solver Configurations > Solver. Try switching to a direct solver (e.g., MUMPS) instead of iterative solvers like GMRES. Direct solvers are more robust for ill-conditioned systems. Iterative Solver Settings: If using an iterative solver, enable preconditioning and increase the number of iterations to help with convergence. Tolerance: Lower the relative tolerance in the solver settings to improve accuracy. Symmetric Solver Option: In some cases, enabling or forcing the symmetry option in the Advanced Solver Settings might help, but this depends on whether your problem is fundamentally symmetric. 3. Check Boundary and Initial Conditions Reason: Boundary and initial conditions in 3D are more complex than in 2D. Incorrect or inconsistent boundary conditions can lead to singular matrices. Solution: Revisit the boundary conditions and ensure they are physically meaningful and properly defined for all the 3D boundaries. Ensure that initial conditions for the magnetization field are realistic, especially for 3D, where small inconsistencies can lead to large numerical issues. 4. Material Properties Reason: In 3D, the material properties such as magnetic permeability or electrical conductivity may need to be defined more precisely. Any anisotropy in the material might be incorrectly represented, leading to matrix issues. Solution: Double-check that the magnetic permeability and conductivity tensors (if anisotropic) are defined correctly for the 3D geometry. Also, check that material properties vary smoothly throughout the 3D domain. 5. Equation Formulation Reason: Extending from 2D to 3D can introduce additional terms or complexities (like demagnetizing fields) in the Landau-Lifshitz-Gilbert (LLG) equations or other governing equations. Solution: Re-check the formulation of the magnetization dynamics equations in COMSOL. Ensure that all terms are correctly extended to 3D (e.g., including the demagnetizing fields and stray fields). If necessary, enable or explicitly define terms for anisotropy, exchange energy, and demagnetizing field in the 3D domain, which may not be as crucial in the 2D case but are essential in 3D simulations. 6. Magnetic Vector Potential vs. Scalar Potential Reason: In 3D, the choice between using a magnetic vector potential formulation (for transient magnetic fields) versus a magnetic scalar potential formulation (for static fields) can affect stability and convergence. Solution: Verify the potential formulation used in your simulation: Use magnetic vector potential for dynamic simulations involving currents and moving magnetization. Use magnetic scalar potential for simpler static field calculations. In COMSOL, you can adjust this under Physics > Magnetic Fields. 7. Singular Matrix and Regularization Reason: Singular matrices often indicate that the system of equations is not properly constrained or ill-posed. Solution: In COMSOL, you can use regularization techniques to handle singular matrices. Check the options in Physics > Magnetic Fields to add regularization terms, particularly for ill-posed boundary conditions or problematic initial conditions. 8. Current Density Distribution Reason: In 3D, the current density distribution applied to the model may differ significantly from the 2D case, leading to unexpected behavior. Solution: Ensure that the current density is applied correctly in 3D. If the current is distributed non-uniformly, increase the resolution of the applied current and check for regions with high gradients. 9. Plotting and Post-Processing Reason: The fact that your normal magnetization plot shows straight lines in 2D but not in 3D suggests that the magnetization is behaving differently in 3D, which is expected due to additional degrees of freedom. Solution: Use Post-processing in COMSOL to visualize the magnetic fields, current density, and magnetization dynamics in the 3D model. Compare the 2D and 3D results to understand where the magnetization dynamics differ and adjust parameters accordingly. By following these steps, you should be able to address the matrix singularity and nonsymmetric matrix warnings in COMSOL, improving the accuracy and stability of your 3D magnetization dynamic sitution.

Reply

Please read the discussion forum rules before posting.

Discussion Forum Rules and Guidelines

The goal of COMSOL Access is to provide a forum for you to communicate effectively with COMSOL as well as your colleagues within the multiphysics simulation community. This involves providing you with access to technical support and downloads of the latest {:comsol} software releases, as well as the ability to share your comments and work with other users of the {:comsol} software through forums such as the blog, discussion forum, and Application Exchange. In order to make this an efficient and pleasant experience for you and other members of COMSOL Access, we ask that you follow a few rules and guidelines.

When registering for COMSOL Access, you agree to provide your complete and truthful information for all fields requested on your COMSOL Access account registration page. You also agree to maintain the accuracy of all information associated with you on your COMSOL Access account. You agree to maintain your COMSOL Access account for use solely by you, not to share your username and password with anyone else, and to take appropriate precautions to restrict access to your username and password from others. Furthermore, you agree not to submit any information relating to your employer through your COMSOL Access account without your employer’s authorization. Should you use a COMSOL Access account associated with an employer, you agree to immediately discontinue using that account upon termination of that employment.

The moderators of the forums will remove any generally objectionable material as quickly as possible. You acknowledge that all posts made to these forums express the views and opinions of the author and not the administrators, moderators, or webmaster (except for posts by these people). Hence, they will not be held liable.

You agree not to post or link to any material that is abusive, obscene, vulgar, slanderous, hateful, threatening, sexually oriented, or that infringes upon or violates any third-party rights or any other material that may violate any applicable laws. You agree that you will not otherwise use your COMSOL Access account to violate or to assist anyone in violating any law. Engaging in any activity in violation of these COMSOL Access rules and guidelines may lead to you being immediately and permanently banned from COMSOL Access. The IP address of all posts is recorded to aid in enforcing these conditions. You agree that the webmaster, administrator, and moderators of the forums have the right to remove, move, or close any topic at any time as they see fit. As a user of COMSOL Access, you agree to any information you have entered into any of the forums being stored in a database.

You agree that you will not use your COMSOL Access account in violation of any applicable export control laws. You represent and warrant that you are not subject to any comprehensive sanction or embargo by the U.S. or any other country, nor are you identified on any list maintained by the U.S. government that identifies persons for which the U.S. maintains restrictions. Further, you represent and warrant that you are not subject to any restriction on the receipt of technology or products under the export control laws of the U.S. or any other country.

Basic Rules

Flaming: Do not post any messages that harass, insult, belittle, threaten, or flame another member or guest. Debates are fine, but argue with the point, not the person.
Trolling: Do not post with the purpose of starting a dispute. Note that a person disagreeing with your opinion is not considered trolling; keep it civil, even if you are sure that the other person is wrong. Anything seen as trolling will result in you being banned.
Spamming: Posts without content or containing nonsense waste space and everyone's time. Spam will be removed from the forum.
Offensive Posts, Links or Images: Do not use profanity, racial, ethnic, religious, or other slurs or any other offensive material.
Advertising: Posting of advertisements for products or services, links to auctions, affiliate links, links to promote websites, and so forth is not allowed.
Disclosure of Personal Information: Do not disclose any other member's email, real name, address, phone number, IP address, or other personal information. This includes posting contents of emails and private messages without the sender's consent. Do not bring personal disputes into the forums. Bans and warnings issued to other users are considered personal information.
Misleading Titles: The subject line of the post should be as informative as possible about the content of the post. This also reduces the amount of duplicate posts.
Thread Hijacking: Taking a thread off-topic to pursue one's own agenda is not permitted.
Piracy: Do not upload, post, email, transmit, or otherwise make available any content that infringes upon any patent, trademark, trade secret, copyright, or other proprietary rights ("Rights") of any party. This includes COMSOL model files created by a forged or illegitimate license.
Honesty: Users must provide truthful information in creating their COMSOL Access account.

These rules are subject to change. The moderators reserve the right to remove, edit, or move posts at their discretion. The COMSOL Access administrators will reserve the right to permanently remove a user account without notice if any of the rules are not followed. Particular services accessible with your COMSOL Access account may be subject to additional rules. You agree to comply with all rules applicable to each service you access through your COMSOL Access account.

Posting Guidelines

When posting, understand that you are trying to communicate with other people. Although many COMSOL Access members are not fluent in English, the official language of this forum is English.

Here are some important guidelines of language:

Write in English.
If you are familiar with LaTeX, please use this to write mathematical equations.
Always do a quick check for spelling/grammar mistakes.
Format your post in a legible manner. Use the Preview button often.
Be concise and articulate as much as possible.
Use the Enter key to create paragraphs.
Capitalize correctly. It is difficult to read posts that are written entirely in uppercase or lowercase.
Use correct punctuation. Avoid run-on sentences.
Try to avoid using “text speak”, “net speak”, or slang. The purpose of language is to be understood.
Never invent acronyms and use as few acronyms as possible. For example, write "COMSOL Multiphysics" and not "CMP".
Review your post before publishing it. Try to catch typos.
Please check to see if a topic has already been posted. Do not post multiple threads on the same topic.

Disclaimer

By submitting content to the forums, you hereby grant COMSOL a nonexclusive, royalty-free, perpetual, worldwide, and unrestricted license to reproduce, publicly display, publicly distribute, and prepare derivative works of the content. COMSOL hereby grants you a license to copy and/or use content from the forums solely for your own internal purposes. COMSOL provides the forum service for the benefit of our users to share content with the community. All content is provided "as is" without warranty of any kind, express or implied, including without limitation, warranties of merchantability, noninfringement, design, operation, and fitness for a particular purpose, and the entire risk as to the quality and performance of the programs is with you.

Neither COMSOL, the authors, nor the copyright owners of submitted materials warrant that the programs will be error-free, uninterrupted, virus-free, secure, and suitable for your needs, produce specific results, or that errors or failures will be corrected. Comments on supplied content should be sent to the author or copyright owner through the tools provided in the forums.

Please log in to post a reply.