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This work explores the application of the fast assembly and formationstrategy from [8, 17] to trimmed bi-variate parameter spaces. Two concepts forthe treatment of basis functions cut by the trimming curve are investigated:one employs a hybrid Gauss-point-based approach, and the other computesdiscontinuous weighted quadrature rules. The concepts' accuracy and efficiencyare examined for the formation of mass matrices and their application toL2-projection. Significant speed-ups compared to standard element by elementfinite element formation are observed. There is no clear preference between theconcepts proposed. While the discontinuous weighted scheme scales favorablywith the degree of the basis, it also requires additional effort for computingthe quadrature weights. The hybrid Gauss approach does not have this overhead,which is determined by the complexity of the trimming curve. Hence, it iswell-suited for moderate degrees, whereas discontinuous-weightedquadrature haspotential for high degrees, in particular, if the related weights are computedin parallel.

Fast formation and assembly of isogeometric Galerkin matrices for trimmed patches