Non intrusive method for parametric model order reduction using a bi-calibrated interpolation on the Grassmann manifold

Approximating solutions of non-linear parametrized physical problems by interpolation presents a major challenge in terms accuracy. In fact, pointwise such is rarely efficient and generally leads to incorrect predictions. To overcome this issue, instead interpolating directly straightforward approach, reduced order models (ROMs) can be efficiently used. end, the ITSGM (Interpolation On Tangent Space Grassmann Manifold) an technique used interpolate parameterized POD (Proper Orthogonal Decomposition) bases. The temporal dynamics afterwards determined Galerkin projection predicted basis onto high fidelity model. However, interpolated ROMs based on ITSGM/Galerkin are intrusive, given fact that their construction requires access equations underlying present paper non-intrusive approach (Galerkin free) for proposed. This method, referred as Bi-CITSGM (Bi-Calibrated ITSGM) consists two steps. First, untrained spatial bases method eigenvalues spline cubic. Then, orthogonal matrices, analytical optimization problems, introduced calibrate with corresponding eigenvalues. Results flow problem past circular cylinder where parameter Reynolds number, show new number values, developed produces sufficiently accurate real-computational time.