A subspace-accelerated method for solving nonlinear thermoacoustic eigenvalue problems

We propose a method to accelerate the solution of 3D FEM-discretized nonlinear eigenvalue problems by drastically reducing the problem dimension. Our method yields a reduced order model (ROM) via a projection onto a suitable subspace, with eigenpairs identical to the full problem in a region of the complex plane. The subspace is automatically constructed by solving the full problem at a few random points inside the region of interest. The method requires minimal user input and, although exemplified for with a thermoacoustic application, readily generalizes to applications dealing with other vibrational problems.