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

TL;DR

This paper introduces a low-cost surrogate matrix method for isogeometric analysis that reduces quadrature costs by interpolating matrix entries, with an open-source implementation to facilitate adoption.

Contribution

It presents a novel surrogate matrix approach for IGA that minimizes quadrature computations and provides a reference implementation in GeoPDEs.

Findings

Significant reduction in quadrature costs for IGA matrices

Successful implementation demonstrated in open-source GeoPDEs library

Potential for widespread adoption in IGA software

Abstract

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.