Treecode solver for the calculation of demagnetizing field in general domains.

Area of Science:

• Computational physics
• Materials science
• Numerical analysis

Background:

• Demagnetizing field calculation is a bottleneck in micromagnetic simulations.
• Existing treecode algorithms struggle with O(Nlog_{8}N) complexity for general domains.

Purpose of the Study:

• To develop a robust and accurate O(Nlog_{8}N) treecode algorithm for micromagnetic simulations.
• To enhance the efficiency of calculating demagnetizing fields.

Main Methods:

• Utilized hierarchy geometry tree data structures for constructing non-neighbor element patches.
• Developed a p-adaptive method based on multipole expansion error analysis.

Main Results:

• Achieved O(Nlog_{8}N) complexity for treecode algorithms in general domains.
• Demonstrated improved simulation efficiency for magnetic skyrmions using the p-adaptive method.

Conclusions:

• The proposed treecode algorithm offers a significant improvement in computational efficiency for micromagnetics.
• The p-adaptive method shows promise for advanced simulations, including magnetic skyrmions.