161 citations · 380 across the 23 of their papers we have counts for
24 papers
Tensor-product vertex patch smoothers for biharmonic problems
Julius Witte, Cu Cui, Francesca Bonizzoni +1
We discuss vertex patch smoothers as overlapping domain decomposition methods for fourth order elliptic partial differential equations. We show that they are numerically very effic…
Multigrid methods for the Stokes problem on GPU systems
Cu Cui, Guido Kanschat
This paper presents a matrix-free multigrid method for solving the Stokes problem, discretized using -conforming discontinuous Galerkin methods. We employ a Schur c…
Smoothers with localized residual computations for geometric multigrid methods
Michał Wichrowski, Peter Munch, Martin Kronbichler +1
We improve the performance of multigrid solvers on many-core architectures with cache hierarchies by reorganizing operations in the smoothing step to minimize memory transfers. We…
An implementation of tensor product patch smoothers on GPU
Cu Cui, Paul Grosse-Bley, Guido Kanschat +1
We present a GPU implementation of vertex-patch smoothers for higher order finite element methods in two and three dimensions. Analysis shows that they are not memory bound with re…
Multilevel Interior Penalty Methods on GPUs
Cu Cui, Guido Kanschat
We present a matrix-free multigrid method for high-order discontinuous Galerkin (DG) finite element methods with GPU acceleration. A performance analysis is conducted, comparing va…
Monolithic two-level Schwarz preconditioner for Biot's consolidation model in two space dimensions
Stefan Meggendorfer, Guido Kanschat, Johannes Kraus
This paper addresses the construction and analysis of a class of domain decomposition methods for the iterative solution of the quasi-static Biot problem in three-field formulation…
Homogeneous multigrid for hybrid discretizations: application to HHO methods
Daniele A. Di Pietro, Zhaonan Dong, Guido Kanschat +2
We prove the uniform convergence of the geometric multigrid V-cycle for hybrid high-order (HHO) and other discontinuous skeletal methods. Our results generalize previously establis…
Ensemble Kalman Inversion for Image Guided Guide Wire Navigation in Vascular Systems
Matei Hanu, Jürgen Hesser, Guido Kanschat +3
This paper addresses the challenging task of guide wire navigation in cardiovascular interventions, focusing on the parameter estimation of a guide wire system using Ensemble Kalma…
Discrete tensor product BGG sequences: splines and finite elements
Francesca Bonizzoni, Kaibo Hu, Guido Kanschat +1
In this paper, we provide a systematic discretization of the Bernstein-Gelfand-Gelfand (BGG) diagrams and complexes over cubical meshes of arbitrary dimension via the use of tensor…
Homogeneous multigrid method for HDG applied to the Stokes equation
Peipei Lu, Wei Wang, Guido Kanschat +1
We propose a multigrid method to solve the linear system of equations arising from a hybrid discontinuous Galerkin (in particular, a single face hybridizable, a hybrid Raviart--Tho…
The Sweep Method for radiative Transfer in Arepo
Toni Peter, Ralf S. Klessen, Guido Kanschat +2
We introduce the radiative transfer code Sweep for the cosmological simulation suite Arepo. Sweep is a discrete ordinates method in which the radiative transfer equation is solved…
Partial differential equations on hypergraphs and networks of surfaces: derivation and hybrid discretizations
Andreas Rupp, Markus Gahn, Guido Kanschat
We introduce a general, analytical framework to express and to approximate partial differential equations (PDEs) numerically on graphs and networks of surfaces---generalized by the…
Analysis of injection operators in multigrid solvers for hybridized discontinuous Galerkin methods
Peipei Lu, Andreas Rupp, Guido Kanschat
Uniform convergence of the geometric multigrid V-cycle is proven for HDG methods with a new set of assumptions on the injection operators from coarser to finer meshes. The scheme i…
Homogeneous multigrid for embedded discontinuous Galerkin methods
Peipei Lu, Andreas Rupp, Guido Kanschat
We introduce a homogeneous multigrid method in the sense that it uses the same embedded discontinuous Galerkin (EDG) discretization scheme for Poisson's equation on all levels. In…
HMG -- Homogeneous multigrid for HDG
Peipei Lu, Andreas Rupp, Guido Kanschat
We introduce a homogeneous multigrid method in the sense that it uses the same HDG discretization scheme for Poisson's equation on all levels. In particular, we construct a stable…
Fast Tensor Product Schwarz Smoothers for High-Order Discontinuous Galerkin Methods
Julius Witte, Daniel Arndt, Guido Kanschat
In this article, we discuss the efficient implementation of powerful domain decomposition smoothers for multigrid methods for high order discontinuous Galerkin (DG) finite element…
A Flexible, Parallel, Adaptive Geometric Multigrid method for FEM
Thomas C. Clevenger, Timo Heister, Guido Kanschat +1
We present the design and implementation details of a geometric multigrid method on adaptively refined meshes for massively parallel computations. The method uses local smoothing o…
Multilevel Schwarz preconditioners for singularly perturbed symmetric reaction-diffusion systems
Jose Pablo Lucero Lorca, Guido Kanschat
We present robust and highly parallel multilevel non-overlapping Schwarz preconditioners, to solve an interior penalty discontinuous Galerkin finite element discretization of a sys…
A C1-mapping based on finite elements on quadrilateral and hexahedral meshes
Daniel Arndt, Guido Kanschat
Finite elements of higher continuity, say conforming in instead of , require a mapping from reference cells to mesh cells which is continuously differentiable across cel…
A Contraction Property of an Adaptive Divergence-Conforming Discontinuous Galerkin Method for the Stokes Problem
Natasha Sharma, Guido Kanschat
We prove the contraction property for two successive loops of the adaptive algorithm for the Stokes problem reducing the error of the velocity. The problem is discretized by a dive…
A finite element method with strong mass conservation for Biot's linear consolidation model
Beatrice Riviere, Guido Kanschat
An H(div) conforming finite element method for solving the linear Biot equations is analyzed. Formulations for the standard mixed method are combined with formulation of interior p…
Geometric Multigrid for Darcy and Brinkman models of flows in highly heterogeneous porous media: A numerical study
Guido Kanschat, Raytcho Lazarov, Youli Mao
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media…
Multigrid methods for Hdiv-conforming discontinuous Galerkin methods for the Stokes equations
Guido Kanschat, Youli Mao
A multigrid method for the Stokes system discretized with an Hdiv-conforming discontinuous Galerkin method is presented. It acts on the combined velocity and pressure spaces and th…
Detecting small low emission radiating sources
Moritz Allmaras, David P. Darrow, Yulia Hristova +2
The article addresses the possibility of robust detection of geometrically small, low emission sources on a significantly stronger background. This problem is important for homelan…