Efficient assembly based on B-spline tailored quadrature rules for the IgA-SGBEM
For researchers in isogeometric analysis and boundary element methods, this work provides a more efficient assembly strategy for 2D elliptic problems.
This paper develops efficient quadrature rules tailored for B-splines in the IgA-SGBEM framework, achieving accurate integral evaluation and reducing computational cost and elapsed time compared to standard element-by-element assembly.
This paper deals with the discrete counterpart of 2D elliptic model problems rewritten in terms of Boundary Integral Equations. The study is done within the framework of Isogeometric Analysis based on B-splines. In such a context, the problem of constructing appropriate, accurate and efficient quadrature rules for the Symmetric Galerkin Boundary Element Method is here investigated. The new integration schemes, together with row assembly and sum factorization, are used to build a more efficient strategy to derive the final linear system of equations. Key ingredients are weighted quadrature rules tailored for B--splines, that are constructed to be exact in the whole test space, also with respect to the singular kernel. Several simulations are presented and discussed, showing accurate evaluation of the involved integrals and outlining the superiority of the new approach in terms of computational cost and elapsed time with respect to the standard element-by-element assembly.