51 citations · 263 across the 30 of their papers we have counts for
30 papers
Robust approximation error estimates for analysis-suitable isogeometric multi-patch discretizations
Fatima Hasanova, Stefan Takacs, Thomas Takacs
We prove -robust approximation error estimates for -conforming isogeometric discretizations over planar multi-patch domains. Possible applications are fourth order boundary…
The Isogeometric Fast Fourier-based Diagonalization method
Monica Montardini, Stefan Takacs, Mattia Tani
The construction of robust solvers for linear systems obtained from the discretization of partial differential equations using Isogeometric Analysis is challenging since the condit…
A robust and time-parallel preconditioner for parabolic reconstruction problems using Isogeometric Analysis
Kent-Andre Mardal, Jarle Sogn, Stefan Takacs
We consider a PDE-constrained optimization problem of tracking type with parabolic state equation. The solution to the problem is characterized by the Karush-Kuhn-Tucker (KKT) syst…
Isogeometric Tearing and Interconnecting Solvers for Linearized Elasticity in multi-patch Isogeometric Analysis
Jarle Sogn, Stefan Takacs
We consider the linearized elasticity equation, discretized with multi-patch Isogeometric Analysis. A standard discretization error analysis is based on Korn's inequality, which de…
A IETI-DP method for discontinuous Galerkin discretizations in Isogeometric Analysis with inexact local solvers
Monica Montardini, Giancarlo Sangalli, Rainer Schneckenleitner +2
We construct solvers for an isogeometric multi-patch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows the consideration of discreti…
Stable discretizations and IETI-DP solvers for the Stokes system in multi-patch Isogeometric Analysis
Jarle Sogn, Stefan Takacs
We are interested in a fast solver for the Stokes equations, discretized with multi-patch Isogeometric Analysis. In the last years, several inf-sup stable discretizations for the S…
Multigrid solvers for isogeometric discretizations of the second biharmonic problem
Jarle Sogn, Stefan Takacs
We develop a multigrid solver for the second biharmonic problem in the context of Isogeometric Analysis (IgA), where we also allow a zero-order term. In a previous paper, the autho…
Dual-Primal Isogeometric Tearing and Interconnecting methods for the Stokes problem
Jarle Sogn, Stefan Takacs
We are interested in a fast solver for linear systems obtained by discretizing the Stokes problem with multi-patch Isogeometric Analysis. We use Dual-Primal Isogeometric Tearing an…
Inexact IETI-DP for conforming isogeometric multi-patch discretizations
Rainer Schneckenleitner, Stefan Takacs
In this paper, we investigate Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for conforming Galerkin discretizations on multi-patch computational domains wi…
IETI-DP methods for discontinuous Galerkin multi-patch Isogeometric Analysis with T-junctions
Rainer Schneckenleitner, Stefan Takacs
We study Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for non-conforming multi-patch discretizations of a generalized Poisson problem. We realize the coup…
IETI-DP for conforming multi-patch Isogeometric Analysis in three dimensions
Rainer Schneckenleitner, Stefan Takacs
We consider dual-primal isogeometric tearing and interconnection (IETI-DP) solvers for multi-patch geometries in Isogeometric Analysis. Recently, the authors have published a conve…
Towards a IETI-DP solver on non-matching multi-patch domains
Rainer Schneckenleitner, Stefan Takacs
Recently, the authors have proposed and analyzed isogeometric tearing and interconnecting (IETI-DP) solvers for multi-patch discretizations in Isogeometric Analysis. Conforming and…
Robust preconditioning and error estimates for optimal control of the convection-diffusion-reaction equation with limited observation in Isogeometric analysis
Kent-Andre Mardal, Jarle Sogn, Stefan Takacs
In this paper we analyze an optimization problem with limited observation governed by a convection--diffusion--reaction equation. Motivated by a Schur complement approach, we arriv…
Convergence theory for IETI-DP solvers for discontinuous Galerkin Isogeometric Analysis that is explicit in h and p
Rainer Schneckenleitner, Stefan Takacs
In this paper, we develop a convergence theory for Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) solvers for isogeometric multi-patch discretizations of the Poisso…
Condition number bounds for IETI-DP methods that are explicit in h and p
Rainer Schneckenleitner, Stefan Takacs
We study the convergence behavior of Dual-Primal Isogeometric Tearing and Interconnecting (IETI-DP) methods for solving large-scale algebraic systems arising from multi-patch Isoge…
Fast multigrid solvers for conforming and non-conforming multi-patch Isogeometric Analysis
Stefan Takacs
Isogeometric Analysis is a high-order discretization method for boundary value problems that uses a number of degrees of freedom which is as small as for a low-order method. Standa…
A quasi-robust discretization error estimate for discontinuous Galerkin Isogeometric Analysis
Stefan Takacs
Isogeometric Analysis is a spline-based discretization method to partial differential equations which shows the approximation power of a high-order method. The number of degrees of…
Sum-factorization techniques in Isogeometric Analysis
A. Bressan, S. Takacs
The fast assembling of stiffness and mass matrices is a key issue in isogeometric analysis, particularly if the spline degree is increased. We present two algorithms based on the i…
A parallel multigrid solver for multi-patch Isogeometric Analysis
Christoph Hofer, Stefan Takacs
Isogeometric Analysis (IgA) is a framework for setting up spline-based discretizations of partial differential equations, which has been introduced around a decade ago and has gain…
Robust multigrid solvers for the biharmonic problem in isogeometric analysis
Jarle Sogn, Stefan Takacs
In this paper, we develop multigrid solvers for the biharmonic problem in the framework of isogeometric analysis (IgA). In this framework, one typically sets up B-splines on the un…
Robust approximation error estimates and multigrid solvers for isogeometric multi-patch discretizations
Stefan Takacs
In recent publications, the author and his coworkers have shown robust approximation error estimates for B-splines of maximum smoothness and have proposed multigrid methods based o…
Inexact Dual-Primal Isogeometric Tearing and Interconnecting Methods
Christoph Hofer, Ulrich Langer, Stefan Takacs
In this paper, we investigate inexact variants of dual-primal isogeometric tearing and interconnecting methods for solving large-scale systems of linear equations arising from Gale…
Robust multigrid methods for isogeometric discretizations of the Stokes equations
Stefan Takacs
In recent publications, the author and his coworkers have proposed a multigrid method for solving linear systems arizing from the discretization of partial differential equations i…
Robust Multigrid for Isogeometric Analysis Based on Stable Splittings of Spline Spaces
Clemens Hofreither, Stefan Takacs
We present a robust and efficient multigrid method for single-patch isogeometric discretizations using tensor product B-splines of maximum smoothness. Our method is based on a stab…