Related papers: Robust multigrid solvers for the biharmonic proble…
We present an isogeometric collocation method for solving the biharmonic equation over planar bilinearly parameterized multi-patch domains. The developed approach is based on the use of the globally $C^4$-smooth isogeometric spline space…
We propose the first optimal geometric multigrid solver for hybrid high-order discretizations that can handle arbitrary polytopal agglomeration hierarchies in both two and three dimensions. The key ingredient is the use of modified skeleton…
Isogeometric Analysis (IGA) typically adopts tensor-product splines and NURBS as a basis for the approximation of the solution of PDEs. In this work, we investigate to which extent IGA solvers can benefit from the so-called sparse-grids…
Isogeometric analysis (IgA) offers enhanced approximation capabilities for the discretization of elliptic boundary-value problems, yet it results in large, sparse, and increasingly ill-conditioned linear systems due to higher…
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…
Unfitted mesh formulations for interface problems generally adopt two distinct methodologies: (i) penalty-based approaches and (ii) explicit enrichment space techniques. While Stable Generalized Finite Element Method (SGFEM) has been…
In this paper, we propose a $W$-cycle $p$-multigrid method for solving the $p$-version symmetric interior penalty discontinuous Galerkin (SIPDG) discretization of elliptic problems. This SIPDG discretization employs hierarchical Legendre…
We present the analysis of interior penalty discontinuous Galerkin Isogeometric Analysis (dGIGA) for the biharmonic problem on orientable surfaces $\Omega \subset \mathbb{R}^3.$ Here, we consider a surface consisting of several…
Multigrid is a powerful solver for large-scale linear systems arising from discretized partial differential equations. The convergence theory of multigrid methods for symmetric positive definite problems has been well developed over the…
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 present work develops hybrid multigrid methods for high-order discontinuous Galerkin discretizations of elliptic problems. Fast matrix-free operator evaluation on tensor product elements is used to devise a computationally efficient PDE…
We have developed an efficient algorithm for steady axisymmetrical 2D fluid equations. The algorithm employs multigrid method as well as standard implicit discretization schemes for systems of partial differential equations. Linearity of…
This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when…
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 presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…
Isogeometric Analysis (IgA) has become a viable alternative to the Finite Element Method (FEM) and is typically combined with a time integration scheme within the method of lines for time-dependent problems. However, due to a stagnation of…
Over the years, Isogeometric Analysis has shown to be a successful alternative to the Finite Element Method (FEM). However, solving the resulting linear systems of equations efficiently remains a challenging task. In this paper, we consider…
We present an isogeometric framework based on collocation to construct a $C^2$-smooth approximation of the solution of the Poisson's equation over planar bilinearly parameterized multi-patch domains. The construction of the used globally…
We propose and analyze a domain decomposition solver for the biharmonic problem. The problem is discretized in a conforming way using multi-patch Isogeometric Analysis. As first step, we discuss the setup of a sufficiently smooth…
We consider and discretize a mixed formulation for linear elasticity with weakly imposed symmetry in two and three dimensions. Whereas existing methods mainly deal with simplicial or polygonal meshes, we take advantage of isogeometric…