This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. The work was partially supported by ARO under US Army Federal Grant # W911NF-15-1-0590.
Lecture Notes in Computational Science and Engineering
Least squares method, Partial differential equations -- Numerical solutions
This work considers the combined space-time discretization of time-dependent partial differential equations by using first order least square methods. We also impose an explicit constraint representing space-time mass conservation. To alleviate the restrictive memory demand of the method, we use dimension reduction via accurate element agglomeration AMG coarsening, referred to as AMGe upscaling. Numerical experiments demonstrating the accuracy of the studied AMGe upscaling method are provided.
Neumüller M., Vassilevski P.S., Villa U.E. (2017) Space-Time CFOSLS Methods with AMGe Upscaling. In: Lee CO. et al. (eds) Domain Decomposition Methods in Science and Engineering XXIII. Lecture Notes in Computational Science and Engineering, vol 116. Springer, Cham