«Excalibur» is the actual code name for the algorithmic engine. The corresponding software package is being developed for numerical modeling and analysis of the equilibrium states of magnetic and superconducting systems.

Main features:

- The software runs on computers equipped with NVIDIA graphics card.
- The algorithmic engine finds stationary configurations by minimizing the total free energy of the systems such as micro-magnets, superconductors, and hybrid devices made of magnets and superconductors.
- The program has three-dimensional graphics.
- The program allows influencing the system in real-time by using a mouse.

Technical and algorithmic implementation:

- All time-consuming subroutines are highly optimized and parallelized for CUDA architecture.
- The minimization algorithm is based on the nonlinear conjugate gradient method.
- Discretization is carried out by the finite-difference methods with optimal correction coefficients for the points on the interfaces. Thus, the samples are calculated as tunable sets of rectangular cuboids.
- Accurate accounting of the nonlocal magnetic fields based on the canonical Hamiltonians (Asselin & Thiele 1986, IEEE Trans. Magn. 22, p. 1876; Du & Wu 1999, SIAM J. Numer. Anal. 36, p. 1482; Di Fratta et al. 2020, SIAM J. Math. Anal. 52, p. 3580) and advanced algorithms.

Real-time simulations of magnetic bubbles in 60-nm-thickness cobalt film. An external magnetic field of 1 Tesla is applied. The mesh: 300x150x31. The outcome corresponding to the infinitely wide film is achieved due to periodic boundary conditions along X and Y.

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