Fast Formation and Assembly of Isogeometric Galerkin Matrices for Trimmed Patches

This work explores the application of fast assembly and formation strategy from [9, 17] to trimmed bi-variate parameter spaces. Two concepts for treatment basis functions cut by trimming curve are investigated: one employs a hybrid Gauss-point-based approach, other computes discontinuous weighted quadrature rules. The concepts’ accuracy efficiency examined mass matrices their $$L^2$$ -projection. Significant speed-ups compared standard element finite observed. There is no clear preference between proposed. While scheme scales favorably with degree basis, it also requires additional effort computing weights. Gauss approach does not have this overhead, which determined complexity curve. Hence, well-suited moderate degrees, whereas discontinuous-weighted-quadrature has potential high in particular, if related weights computed parallel.