Related papers: High-order Multiscale Preconditioner for Elasticit…
In this paper, based on the overlapping domain decomposition method (DDM) proposed in \cite{Leng2015}, an one step preconditioner is proposed to solve 2D high frequency Helmholtz equation. The computation domain is decomposed in both $x$…
Convergence of domain decomposition methods rely heavily on the efficiency of the coarse space used in the second level. The GenEO coarse space has been shown to lead to a fully robust two-level Schwarz preconditioner which scales well over…
Two non-overlapping domain decomposition methods are presented for the mixed finite element formulation of linear elasticity with weakly enforced stress symmetry. The methods utilize either displacement or normal stress Lagrange multiplier…
Folding grid value vectors of size $2^L$ into $L$th order tensors of mode sizes $2\times \cdots\times 2$, combined with low-rank representation in the tensor train format, has been shown to lead to highly efficient approximations for…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
We introduce a preconditioner based on a hierarchical low-rank compression scheme of Schur complements. The construction is inspired by standard nested dissection, and relies on the assumption that the Schur complements can be approximated,…
In this paper, we propose a domain decomposition method for multiscale second order elliptic partial differential equations with highly varying coefficients. The method is based on a discontinuous Galerkin formulation. We present both a…
The purpose of this paper is to discuss representations of high order $C^0$ finite element spaces on simplicial meshes in any dimension. When computing with high order piecewise polynomials the conditioning of the basis is likely to be…
This paper investigates model-order reduction methods for geometrically nonlinear structures. The parametrisation method of invariant manifolds is used and adapted to the case of mechanical systems expressed in the physical basis, so that…
We propose a multiscale method for elliptic problems on complex domains, e.g. domains with cracks or complicated boundary. For local singularities this paper also offers a discrete alternative to enrichment techniques such as XFEM. We…
Although some preconditioners are available for solving dense linear systems, there are still many matrices for which preconditioners are lacking, in particular in cases where the size of the matrix $N$ becomes very large. There remains…
Peridynamics provides a versatile tool for fracture modelling in materials where fracture pathways cannot be predicted beforehand, but must be envisaged as an emergent features of the deformation process. One class of materials where this…
We devise a Hybrid High-Order (HHO) method for highly oscillatory elliptic problems that is capable of handling general meshes. The method hinges on discrete unknowns that are polynomials attached to the faces and cells of a coarse mesh;…
This paper studies and analyzes a preconditioned Krylov solver for Helmholtz problems that are formulated with absorbing boundary layers based on complex coordinate stretching. The preconditioner problem is a Helmholtz problem where not…
The purpose of this research is to describe an efficient iterative method suitable for obtaining high accuracy solutions to high frequency time-harmonic scattering problems. The method allows for both refinement of local polynomial degree…
We deal with the numerical solution of linear elliptic problems with varying diffusion coefficient by the $hp$-discontinuous Galerkin method. We develop a two-level hybrid Schwarz preconditioner for the arising linear algebraic systems. The…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
A balancing domain decomposition by constraints (BDDC) algorithm with adaptive primal constraints in variational form is introduced and analyzed for high-order mortar discretization of two-dimensional elliptic problems with high varying and…
We consider a strongly heterogeneous medium saturated by an incompressible viscous fluid as it appears in geomechanical modeling. This poroelasticity problem suffers from rapidly oscillating material parameters, which calls for a thorough…
Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed-dimensional…