We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary Method for spatial discretization is combined with an explicit predictor/multi-corrector time integration to integrate in time the numerical solutions to the shallow water equations, both for the full and reduced-order model. In order to improve the approximation of the solution manifold also for geometries that are untested during the offline stage, the snapshots have been pre-processed by means of an interpolation procedure that precedes the reduced basis computation. The methodology is tested on geometrically parametrized shapes with varying size and position.

翻译：我们考虑了浅水双曲问题及其减序模型的完全离散嵌入的有限元素近似值。我们的方法基于固定的背景网格和嵌入的缩小基数。空间分解的改变边界方法与明确的预测/多校正时间集成相结合,以便及时整合完整和减序模型的浅水方程的数字解决方案。为了提高在离线阶段未测试的地理比例的解决方案多重值的近近似度,通过在降低基数计算之前的内插程序预先处理了近似值。该方法以不同大小和位置的几何对称形状进行测试。