Quantum mechanics

Control (management)

Discretization

Engineering

Transient (computer programming)

Materials science

Transient response

Transient analysis

Applied mathematics

Operating system

Computer science

Mathematical optimization

Thermodynamics

Physics

Finite element method

Nonlinear system

Mathematics

Mathematical analysis

Artificial intelligence

Isogeometric analysis

Thermal conduction

Control theory (sociology)

Mechanics

Newton's method

Electrical engineering

Numerical Heat Transfer Part A Applications

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.

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