Efficient implementation of the hybridized Raviart-Thomas mixed method by converting flux subspaces into stabilizations

TL;DR

This paper presents a new implementation of the Raviart-Thomas mixed method that significantly reduces computational time by transforming certain flux subspaces into stabilization functions, demonstrated through numerical experiments.

Contribution

It introduces a novel implementation approach that converts flux subspaces into stabilizations, leading to 10-20% faster computations for the Raviart-Thomas method.

Findings

Achieved 10-20% reduction in computational time

Validated the approach on a model elliptic problem

Applicable for Raviart-Thomas index k from 1 to 20

Abstract

We show how to reduce the computational time of the practical implementation of the Raviart-Thomas mixed method for second-order elliptic problems. The implementation takes advantage of a recent result which states that certain local subspaces of the vector unknown can be eliminated from the equations by transforming them into stabilization functions; see the paper published online in JJIAM on August 10, 2023. We describe in detail the new implementation (in MATLAB and a laptop with Intel(R) Core (TM) i7-8700 processor which has six cores and hyperthreading) and present numerical results showing 10 to 20% reduction in the computational time for the Raviart-Thomas method of index $k$, with $k$ ranging from 1 to 20, applied to a model problem.