|TITLE||Model Order Reduction for Solving Partial Differential Equations|
Model order reduction (MOR) is briefly a series of techniques that aim to reduce
the complexity of mathematical models and the computational cost without losing too much accuracy in numerical simulations. How does MOR work? Simply speaking, it captures the essential features by collecting data set from numerical simulations of the full model or operationally proceed a transform to the full model to build a reduced-order model. This lecture will introduce the so-called proper orthogonal decomposition (POD) method and the discrete empirical interpolation method (DEIM) that reduces the dimension of the numerical model during solving PDEs. The POD technique can avoid the rapid rise of computational cost corresponding to high-resolution mesh grid or higher-dimensional problems. At the same time, the DEIM estimates the contribution of the nonlinear terms from the full model to the reduced model. Several examples, including stationary and nonstationary PDEs, are presented to end this lecture.
Keywords: Model order reduction; Proper orthogonal decomposition; Discrete empirical interpolation; Numerical partial differential equations.