Adaptive parameter space sampling in matrix interpolatory pMOR

Abstract

Standard order reduction techniques are not robust to parameter variations and as such a new reduced model needs to be generated each time a parameter is varied in the system under study. The problem is further compounded in large systems with analytically inexpressible parametric dependencies wherein the large scale itself may need to be generated repetitively making design cycles almost unachievable in real time. For such systems, Matrix Interpolatory parametric reduction framework is used in which the reduced model corresponding to a specific parameter value is obtained by interpolating the matrices of reduced models obtained via direct reduction at suitable points in the parametric space. However, one of the main issues in this approach is the efficient sampling of the parametric space. In this work, this issue is taken up and a measure based on subspace angles is proposed for efficient and adaptive sampling of the parameter space. Numerical results are shown for a benchmark model.