Fast Formation and Assembly of Isogeometric Galerkin Matrices for Trimmed Patches

Benjamin Marussig*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference paperpeer-review


This work explores the application of the fast assembly and formation strategy from [9, 17] to trimmed bi-variate parameter spaces. Two concepts for the treatment of basis functions cut by the trimming curve are investigated: one employs a hybrid Gauss-point-based approach, and the other computes discontinuous weighted quadrature rules. The concepts’ accuracy and efficiency are examined for the formation of mass matrices and their application to L2-projection. Significant speed-ups compared to standard element by element finite element formation are observed. There is no clear preference between the concepts proposed. While the discontinuous weighted scheme scales favorably with the degree of the basis, it also requires additional effort for computing the quadrature weights. The hybrid Gauss approach does not have this overhead, which is determined by the complexity of the trimming curve. Hence, it is well-suited for moderate degrees, whereas discontinuous-weighted-quadrature has potential for high degrees, in particular, if the related weights are computed in parallel.
Original languageEnglish
Title of host publicationGeometric Challenges in Isogeometric Analysis
EditorsCarla Manni, Hendrik Speleers
Place of PublicationCham
Number of pages21
ISBN (Electronic)978-3-030-92313-6
ISBN (Print)978-3-030-92313-6
Publication statusPublished - 2022
Event2020 INdAM Workshop Geometric Challenges in Isogeometric Analysis - Rom, Italy
Duration: 27 Jan 202031 Jan 2020

Publication series

NameSpringer INdAM Series


Conference2020 INdAM Workshop Geometric Challenges in Isogeometric Analysis

ASJC Scopus subject areas

  • Mathematics(all)


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