Efficient implementation of the hybridized Raviart-Thomas mixed method by converting flux subspaces into stabilizations-Reference-Cited by-同舟云学术

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

Published:2024 Issue:2 Volume:6 Page:221-237
ISSN:2640-3501
Container-title:Mathematics in Engineering
language:
Short-container-title:MINE

Author:

Anantharamu Sreevatsa¹,Cockburn Bernardo²

Affiliation:

1. Senior Applications Engineer, X-ScaleSolutions, LLC, USA

2. School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Abstract

<abstract><p>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.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

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