A non-intrusive reduced basis method for elastoplasticity problems in geotechnics

摘要

This work aims at investigating the use of reduced basis (RB) methods to diminish the cost of numerical simulation of elastoplasticity problems arising from geotechnics modeling, and involving parameter-dependent partial differential equations (PDEs). Computation times for large three-dimensional analysis commonly take tens of hours, making optimization procedures or sensitivity analysis, relying on repeated simulations, hardly feasible. In many cases the geotechnical analysis requires very specific features such as highly non-linear constitutive laws, making the necessary modification of the FE calculation code for a standard RB method impossible. An approach making it possible to use the reduced basis framework without having to modify the code gives the so-called non-intrusive reduced basis method a versatility of great practical interest. Our approach involves the computation of less expensive (but less accurate) FE approximation during the online stage and improvement of those solutions using a RB-based rectification method.