Open this publication in new window or tab >>2025 (English)In: BIT Numerical Mathematics, ISSN 0006-3835, E-ISSN 1572-9125, Vol. 65, no 1, article id 8Article in journal (Refereed) Published
Abstract [en]
The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provides a systematic error analysis for IBIMs on uniform Cartesian grids for boundaries with different degrees of regularity. First, it is shown that the quadrature error gains an additional order of d-12 from the curvature for a strongly convex smooth boundary due to the “randomness” in the signed distances. This gain is discounted for degenerated convex surfaces. Then the extension of error estimate to general boundaries under some special circumstances is considered, including how quadrature error depends on the boundary’s local geometry relative to the underlying grid. Bounds on the variance of the quadrature error under random shifts and rotations of the lattices are also derived.
Place, publisher, year, edition, pages
Springer Nature, 2025
Keywords
Error analysis, Implicit boundary integral method, Level set, Solvent-excluded surface
National Category
Computational Mathematics
Identifiers
urn:nbn:se:kth:diva-360580 (URN)10.1007/s10543-024-01051-8 (DOI)001400048000001 ()2-s2.0-85217806551 (Scopus ID)
Note
QC 20250227
2025-02-262025-02-262025-02-27Bibliographically approved