TY - JOUR
T1 - Bootstrap Algebraic Multigrid: Status Report, Open Problems, and Outlook
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 1
SP - 112
EP - 135
PY - 2015
DA - 2015/08
SN - 8
DO - http://doi.org/10.4208/nmtma.2015.w06si
UR - https://global-sci.org/intro/article_detail/nmtma/12402.html
KW - 
AB - <p style="text-align: justify;">This paper provides an overview of the main ideas driving the bootstrap
algebraic multigrid methodology, including compatible relaxation and algebraic distances for defining effective coarsening strategies, the least squares method for computing accurate prolongation operators and the bootstrap cycles for computing the
test vectors that are used in the least squares process. We review some recent research in the development, analysis and application of bootstrap algebraic multigrid
and point to open problems in these areas. Results from our previous research as
well as some new results for some model diffusion problems with highly oscillatory
diffusion coefficient are presented to illustrate the basic components of the BAMG
algorithm.</p>