data-driven numerical solver

Krylov-subspace recycling via the POD-augmented conjugate-gradient method

This work presents a new Krylov-subspace-recycling method for efficiently solving sequences of linear systems of equations characterized by varying right-hand sides and symmetric-positive-definite matrices. As opposed to typical truncation strategies …

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most …

An adaptive POD-Krylov reduced-order model for structural optimization

We present an adaptive proper orthogonal decomposition (POD)-Krylov reduced-order model (ROM) for structural optimization. At each step of the optimization loop, we compute approximate solutions to the structural state and sensitivity equations using …