Relevance to WCCM–ECCOMAS

This short course introduces a novel class of multistep time-integration methods constructed using NURBS and Bézier curves. The primary objective is to present a unified framework for solving time-dependent problems within the method of lines paradigm, with particular emphasis on nonlinear and multiphysics applications.

Course description

This short course introduces a novel class of multistep time-integration methods constructed using NURBS and Bézier curves. The primary objective is to present a unified framework for solving time-dependent problems within the method of lines paradigm, with particular emphasis on nonlinear and multiphysics applications.

The course covers theoretical foundations, formulation, and implementation aspects of these methods. A key advantage of the proposed approach is that it avoids explicit linearization of the governing equations, making it particularly suitable for strongly nonlinear problems. In addition, the methods provide enhanced numerical stability and efficiency, enabling the use of larger time-step sizes while maintaining high accuracy.

Objectives and target groups

The course is intended for:

• Graduate students in computational mechanics
• Researchers in numerical methods and scientific computing
• Engineers working on transient and nonlinear simulations
• Practitioners interested in advanced time-integration techniques

Scientific and technical areas covered

• Fundamentals of multistep time-integration methods
• Construction of time-integration schemes using NURBS and Bézier bases
• Method of lines framework
• Stability, consistency, and convergence analysis
• Treatment of strongly nonlinear systems
• Coupling with isogeometric spatial discretization
• Applications in:
• Structural mechanics (plates, shells, and solids)
• Multiphysics problems
• Biomechanics
• Nonlinear thermo-mechanical analysis