2022/10/29 by Steffen Börm, Börm, Steffen, Janne Henningsen +1 · 1 citation
Engineering · Physics and Astronomy · #41A10 #65D05 #65N38 #65R20 #Electromagnetic Scattering and Analysis #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
paper · pdf · doi:10.48550/arxiv.2210.16609
openalex publication_date 2022/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Boundary element methods for elliptic partial differential equations typically lead to boundary integral operators with translation-invariant kernel functions. Taking advantage of this property is fairly simple for particle methods, e.g., Nystrom-type discretizations, but more challenging if the supports of basis functions have to be taken into account. In this article, we present a modified construction for H2-matrices that uses translation-invariance to significantly reduce the storage requirements. Due to the uniformity of the boxes used for the construction, we need only a few uncomplicated assumptions to prove estimates for the resulting storage complexity.