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Gauss-Galerkin quadrature rules for quadratic and cubic spline spaces and their application to isogeometric analysis
We introduce Gaussian quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. By definition, these spaces are of even degrees. The optimal quadrature ...
Towards efficient 5-axis flank CNC machining of free-form surfaces via fitting envelopes of surfaces of revolution
We introduce a new method that approximates free-form surfaces by envelopes of one-parameter motions of surfaces of revolution. In the context of 5-axis computer numerically controlled (CNC) machining, we propose a flank ...
Optimal quadrature rules for odd-degree spline spaces and their application to tensor-product-based isogeometric analysis
We introduce optimal quadrature rules for spline spaces that are frequently used in Galerkin discretizations to build mass and stiffness matrices. Using the homotopy continuation concept (Barton and Calo, 2016) that ...