Higher order stray field computation on tensor product domains

TL;DR

This paper introduces a higher-order tensor grid method for stray field computation on rectangular domains, utilizing B-spline bases and a super-potential formulation to achieve high accuracy, efficiency, and mesh-free continuous field evaluation.

Contribution

It extends tensor grid methods by incorporating higher-order basis functions and a super-potential approach, enabling more accurate and efficient stray field calculations on tensor product domains.

Findings

Exponential convergence of the energy demonstrated

Linear computational scaling with expansion rank

High accuracy and smoothness achieved with B-spline bases

Abstract

We present an extension of the tensor grid method for stray field computation on rectangular domains that incorporates higher-order basis functions. Both the magnetization and the resulting magnetic field are represented using higher-order B-spline bases, which allow for increased accuracy and smoothness. The method employs a super-potential formulation, which circumvents the need to convolve with a singular kernel. The field is represented with high accuracy as a functional Tucker tensor, leveraging separable expansions on the tensor product domain and trained via a multilinear extension of the extreme learning machine methodology. Unlike conventional grid-based methods, the proposed mesh-free approach allows for continuous field evaluation. Numerical experiments confirm the accuracy and efficiency of the proposed method, demonstrating exponential convergence of the energy and linear computational scaling with respect to the multilinear expansion rank.