The surrogate matrix methodology: A reference implementation for low-cost assembly in isogeometric analysis

A reference implementation of a new method in isogeometric analysis (IGA) is presented. It delivers low-cost variable-scale approximations (surrogates) of the matrices which IGA conventionally requires to be computed by element-scale quadrature. To generate surrogate matrices, quadrature must only be performed on a fraction of the elements in the computational domain. In this way, quadrature determines only a subset of the entries in the final matrix. The remaining matrix entries are computed by a simple B-spline interpolation procedure. We present the modifications and extensions required for a reference implementation in the open-source IGA software library GeoPDEs. The exposition is fashioned to help facilitate similar modifications in other contemporary software libraries.•The surrogate matrix methodology is implemented in GeoPDEs.•Poisson's problem is considered.•The matrix assembly time is significantly reduced at negligible cost to solution accuracy.