Related papers: Robust and scalable domain decomposition solvers f…
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 propose a new discretization method for PDEs on moving domains in the setting of unfitted finite element methods, which is provably higher-order accurate in space and time. In the considered setting, the physical domain that evolves…
This paper presents and studies an approach for constructing auxiliary space preconditioners for finite element problems using a constrained nonconforming reformulation, that is based on a proposed modified version of the mortar method. The…
Domain decomposition (DD) methods are widely used as preconditioner techniques. Their effectiveness relies on the choice of a locally constructed coarse space. Thus far, this construction was mostly achieved using non-assembled matrices…
We present a domain decomposition method (DDM) devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation (EFIE) for the…
In this work, we consider unfitted finite element methods for the numerical approximation of the Stokes problem. It is well-known that this kind of methods lead to arbitrarily ill-conditioned systems. In order to solve this issue, we…
The balancing domain decomposition methods (BDDC) are originally introduced for symmetric positive definite systems and have been extended to the nonsymmetric positive definite system from the linear finite element discretization of…
In this paper we propose a variant of the substructuring preconditioner for solving three-dimensional elliptic-type equations with strongly discontinuous coefficients. In the proposed preconditioner, we use the simplest coarse solver…
This paper provides the first provable $\mathcal{O}(N \log N)$ algorithms for the linear system arising from the direct finite element discretization of the fourth-order equation with different boundary conditions on unstructured grids of…
We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by…
In this paper, a parallel overlapping domain decomposition preconditioner is proposed to solve the linear system of equations arising from the extended finite element discretization of elastic crack problems. The algorithm partitions the…
Domain decomposition methods are used for approximate solving boundary problems for partial differential equations on parallel computing systems. Specific features of unsteady problems are taken into account in the most complete way in…
Biot's consolidation model in poroelasticity has a number of applications in science, medicine, and engineering. The model depends on various parameters, and in practical applications these parameters ranges over several orders of…
We present a two-level preconditioner for solving linear systems arising from the discretization of the elliptic, linear-elastic deformation equation, in displacement unknowns, over domains that have arbitrary geometric and topological…
This article addresses the research question if and how the finite cell method, an embedded domain finite element method of high order, may be used in the simulation of metal deposition to harvest its computational efficiency. This…
The efficient solution of discretisations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov…
The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…
We present a fully discrete stability analysis of the domain-of-dependence stabilization for hyperbolic problems. The method aims to address issues caused by small cut cells by redistributing mass around the neighborhood of a small cut cell…
The discretization of constrained nonlinear optimization problems arising in the field of topology optimization yields algebraic systems which are challenging to solve in practice, due to pathological ill-conditioning, strong nonlinearity…
Unfitted finite element methods, like CutFEM, have traditionally been implemented in a matrix-based fashion, where a sparse matrix is assembled and later applied to vectors while solving the resulting linear system. With the goal of…