A Survey of Hierarchical Model (Hi-Mod) Reduction Methods for Elliptic Problems

Abstract

AbstractIn this work, we review the basic aspects of the so called Hierarchical Model (Hi-Mod) reduction approach, recently advocated to reduce the complexity of models for advection-diffusion-reaction phenomena in pipe-like domains featuring a prevalent axial dynamics. The Hi-Mod approach aims at reducing the computational costs still preserving a reliable approximation of the transverse components of the solution by properly combining finite elements and modal approximations. In particular, we consider the convergence of this approximation to the solution of the full problem and the different ways for selecting the number of transverse modes.KeywordsProper Orthogonal DecompositionModal IndexFull SolutionAdaptive ProcedureFinite Element SpaceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.