Seminar Presentation: Zeta Expansion for Long-Range Interactions under Periodic Boundary Conditions with Applications to Micromagnetics

Kurzfassung

Seminar presentation on the efficient computation of power-law-based interaction potentials in micromagnetics under periodic boundary conditions. The talk addresses the challenge of computing infinite lattice sums for dipolar interactions and generalized Riesz power-law potentials in arbitrary cuboidal domains. We present a method that achieves machine precision by complementing direct summation with correction terms, with exponential convergence and negligible additional computational cost compared to the truncated summation scheme. The approach includes a superexponentially convergent algorithm in terms of generalized zeta functions which requires special functions such as incomplete Bessel functions.