Related papers: An efficient multigrid solver for isogeometric ana…
For uncertainty propagation of highly complex and/or nonlinear problems, one must resort to sample-based non-intrusive approaches [1]. In such cases, minimizing the number of function evaluations required to evaluate the response surface is…
We develop multilevel methods for interface-driven multiphysics problems that can be coupled across dimensions and where complexity and strength of the interface coupling deteriorates the performance of standard methods. We focus on solvers…
We propose a robust, adaptive coarse-grid correction scheme for matrix-free geometric multigrid targeting PDEs with strongly varying coefficients. The method combines uniform geometric coarsening of the underlying grid with heterogeneous…
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 established results for HDG methods, and our multigrid method uses…
This paper deals with a special class of parametrizations for Isogeometric Analysis (IGA). The so-called scaled boundary parametrizations are easy to construct and particularly attractive if only a boundary description of the computational…
One of the important aspects of IsoGeometric Analysis (IGA) is the strong link between Computer Aided Design and analysis. Two of IGA'a major challenge are the assembly of patches (Constructive Solid Geometry geometries made of Boolean…
This work presents a novel agglomeration-based multilevel preconditioner designed to accelerate the convergence of iterative solvers for linear systems arising from the discontinuous Galerkin discretization of the monodomain model in…
Convolution-type integral equations commonly occur in signal processing and image processing. Discretizing these equations yields large and ill-conditioned linear systems. While the classic multigrid method is effective for solving linear…
We study multilevel techniques, commonly used in PDE multigrid literature, to solve structured optimization problems. For a given hierarchy of levels, we formulate a coarse model that approximates the problem at each level and provides a…
In this article we suggest two discretization methods based on isogeometric analysis (IGA) for planar linear elasticity. On the one hand, we apply the well-known ansatz of weakly imposed symmetry for the stress tensor and obtain a…
We present a geometric multigrid solver based on adaptive smoothed aggregation suitable for Discontinuous Galerkin (DG) discretisations. Mesh hierarchies are formed via domain decomposition techniques, and the method is applicable to fully…
The matrix formation associated to high-order discretizations is known to be numerically demanding. Based on the existing procedure of interpolation and lookup, we design a multiscale assembly procedure to reduce the exorbitant assembly…
In this paper, we develop a local Fourier analysis of multigrid methods based on block-structured relaxation schemes for stable and stabilized mixed finite-element discretizations of the Stokes equations, to analyze their convergence…
Numerical simulation of incompressible viscous flow, in particular in three space dimensions, continues to remain a challenging task. Space-time finite element methods feature the natural construction of higher order discretization schemes.…
The Riesz maps of the $L^2$ de Rham complex frequently arise as subproblems in the construction of fast preconditioners for more complicated problems. In this work we present multigrid solvers for high-order finite element discretizations…
We construct solvers for an isogeometric multi-patch discretization, where the patches are coupled via a discontinuous Galerkin approach, which allows the consideration of discretizations that do not match on the interfaces. We solve the…
We provide an alternative Fourier analysis for multigrid applied to the Poisson problem in 1D, based on explicit derivation of spectra of the iteration matrix. The new Fourier analysis has advantages over the existing one. It is easy to…
During the last decade, Neural Networks (NNs) have proved to be extremely effective tools in many fields of engineering, including autonomous vehicles, medical diagnosis and search engines, and even in art creation. Indeed, NNs often…
Numerical simulation of incompressible fluid flows has been an active topic of research in Scientific Computing for many years, with many contributions to both discretizations and linear and nonlinear solvers. In this work, we propose an…
We study efficient simulation of steady state for rarefied gas flow, which is modeled by the Boltzmann equation with BGK-type collision term. A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following…