  This work explores the application of the fast assembly and formation
strategy from [8, 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-weightedquadrature has
potential for high degrees, in particular, if the related weights are computed
in parallel.
