Hybrid 3D-plane finite element modeling for elastodynamics

Many engineering applications require the numerical solution of a large scale three dimensional (3D) or two-dimensional (2D) problem, which consists of a large number of degrees-of-freedom (DOF). Mixed-dimensional modeling suggests the reduction of a part of the domain in which the solution is expected to exhibit a lower-dimensional (lowD) behavior to a domain of lower dimension. The motivation in constructing a mixeddimensional model comes from the fact that solving the problem in its high-dimensional (highD) form everywhere may require a very large computational effort. The idea is thus to partly reduce the spatial dimension of the problem in order to obtain a hybrid model which is much more efficient, without a significant loss of accuracy in the region of interest. The saving manifests itself in that there is a significant reduction in the total number of degrees of freedom of the model, and moreover there is a significant decrease in the bandwidth of the mass and stiffness matrices. Fields of application where mixed-dimensional modeling is of special interest include, among others, hydrological and geophysical flow models, blood-flow analysis, and elastic structures. The present research is motivated by the latter application, and demonstrates the applicability of the Panasenko coupling method to a hybrid 3D-2D elastodynamics problem with finiteelements (FE) analysis.