Fast and Multiscale Formation of Isogeometric matrices of Microstructured Geometric Models

TL;DR

This paper introduces a multiscale assembly method for isogeometric matrices that significantly reduces computation time for complex microstructured geometries by combining polynomial approximation and lookup tables, enhancing efficiency in finite element analysis.

Contribution

It presents a novel multiscale assembly procedure that accelerates matrix formation in isogeometric analysis of microstructured models using polynomial approximation and pre-computed lookup tables.

Findings

Reduces assembly time for high-order discretizations.

Enables fast computation of sensitivities and other quantities.

Demonstrates efficiency through numerical examples.

Abstract

The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly time in the context of isogeometric linear elasticity of complex microstructured geometries modeled via spline compositions. The developed isogeometric approach involves a polynomial approximation occurring at the macro-scale and the use of lookup tables with pre-computed integrals incorporating the micro-scale information. We provide theoretical insights and numerical examples to investigate the performance of the procedure. The strategy turns out to be of great interest not only to form finite element operators but also to compute other quantities in a fast manner as for instance sensitivity analyses commonly used in design optimization.