An isogeometric independent coefficients (IGA-IC) reduced order method for accurate and efficient transient nonlinear heat conduction analysis

Abstract

This article develops an isogeometric independent coefficients (IGA-IC) reduced order method for transient nonlinear heat conduction analysis. Herein, we first exactly represent the geometric model via isogeometric analysis (IGA), and therein provide an accurate solution for the semi-discretized equations. Next, our proposed GSSSS-1 time-stepping framework is employed to solve the transient nonlinear temperature in space and time domains. We advance our independent coefficients (IC) reduced order method to efficiently solve IGA-based transient nonlinear heat conduction problems. We extend the IC method to significantly reduce the original full IGA-discretized formulations and calculate the reduced equilibrium formulations in each Newton–Raphson iteration. Thereby, hugely improving the efficiency and guaranteeing the accuracy simultaneously. Illustrative numerical examples validate this proposed IGA-IC method is reliable, accurate, and efficient; especially, the larger the scale of the problem, the more advantages the proposed IGA-IC will inherit.

Additional information

Funding

This work was supported by the State Key Program of National Natural Science of China [61232014]; National Science Foundation of China [11472101]; Hunan Provincial Innovation Foundation for Postgraduate [CX2016B079]; and China Scholarship Council [201606130079].