TY - JOUR
T1 - A multigrid local smoother approach for a domain decomposition solver over non-matching grids
AU - Bornia, Giorgio
AU - Chierici, Andrea
AU - Chirco, Leonardo
AU - Giovacchini, Valentina
AU - Manservisi, Sandro
N1 - Publisher Copyright:
© 2021 Wiley Periodicals LLC.
PY - 2022/11
Y1 - 2022/11
N2 - In this paper we consider a multigrid approach for solving elliptic equations over non-matching grids with domain decomposition methods. The domain is partitioned into subdomains with different mesh levels that do not match at the interface. The proposed algorithm searches for the global solution over different levels by projecting the residuals on the overlap region. This method is used in conjunction with a domain decomposition solver which only requires, in each iteration step, the solutions of several small local subproblems over finite element blocks. This algorithm is shown to converge to the solution of the corresponding Lagrange multiplier problem for non-matching grids. The convergence properties of the algorithms are analyzed and numerical examples are presented. When the multigrid and domain decomposition approaches are combined, the method is shown to be reliable and easy to implement. Furthermore the local nature of the solver allows for a straightforward implementation on multiple parallel computers and graphics processing unit (GPU) clusters.
AB - In this paper we consider a multigrid approach for solving elliptic equations over non-matching grids with domain decomposition methods. The domain is partitioned into subdomains with different mesh levels that do not match at the interface. The proposed algorithm searches for the global solution over different levels by projecting the residuals on the overlap region. This method is used in conjunction with a domain decomposition solver which only requires, in each iteration step, the solutions of several small local subproblems over finite element blocks. This algorithm is shown to converge to the solution of the corresponding Lagrange multiplier problem for non-matching grids. The convergence properties of the algorithms are analyzed and numerical examples are presented. When the multigrid and domain decomposition approaches are combined, the method is shown to be reliable and easy to implement. Furthermore the local nature of the solver allows for a straightforward implementation on multiple parallel computers and graphics processing unit (GPU) clusters.
KW - Schwarz alternating algorithms
KW - domain decomposition
KW - multigrid
UR - http://www.scopus.com/inward/record.url?scp=85114194660&partnerID=8YFLogxK
U2 - 10.1002/num.22835
DO - 10.1002/num.22835
M3 - Article
AN - SCOPUS:85114194660
SN - 0749-159X
VL - 38
SP - 1794
EP - 1822
JO - Numerical Methods for Partial Differential Equations
JF - Numerical Methods for Partial Differential Equations
IS - 6
ER -