Projects
Isogeometric Method for Partial Differential Equations (sole PI):
Duration: July 2009 to November 2013.
Funding: € 216,090, Austrian Science Fund (P21516-N18).
Personnel:
Stefan Kleiss (defended his Ph.D. thesis on February 6, 2014).
Krishan Gahalaut (defended his PhD thesis on June 20, 2013).
Publications:
IETI - Isogeometric Tearing and Interconnecting (with B.J. Juettler, S.K. Kleiss and C. Pechstein). Comput. Methods Appl. Mech. Engrg., 247-248, 201-215, 2012.
Multigrid Methods for Isogeometric Discretization (with K.P.S. Gahalaut and J. Kraus). Comput. Methods Appl. Mech. Engrg., 253, 413-425, 2013.
Condition number study of graph theory based preconditioners for isogeometric discretization of Poisson equation (with K.P.S. Gahalaut). RICAM Report, 2012-14.
Algebraic multilevel preconditioning in isogeometric analysis: Construction and numerical studies (with K.P.S. Gahalaut and J. Kraus). Comput. Methods Appl. Mech. Engrg., 266, 40-56, 2013.
Guaranteed and sharp a posteriori error estimates in isogeometric analysis (with S.K. Kleiss). Comput. Math. Appl., 70 (3), 167-190, 2015. Also available at arXiv:1304.7712.
Condition number estimates for matrices arising in the isogeometric discretizations (with K.P.S. Gahalaut). In revision (Submitted for publication in October 2012). Available as RICAM Report, 2012-23.
Initiated by this project, Isogeometric Analysis (IGA), which was introduced by Hughes et al. in 2005, has been established as one of the main research directions of Computational Mathematics Group in RICAM, see the RICAM annual reports from 2010 to 2012 at RICAM annual reports.
Within a National Research Network project Geometry + Simulation, together with Prof. U. Langer as PI, I was a co-proposer and a participating researcher of the sub-project Discontinuous Galerkin Domain Decomposition Methods in IGA till March 2014. This project, funded by Austrian Science Fund (S117), started in March 2012 and has partners in Linz, Vienna and Bonn.