Related papers: A substructuring preconditioner with vertex-relate…
In this paper, we propose a two-level overlapping additive Schwarz domain decomposition preconditioner for the symmetric interior penalty discontinuous Galerkin method for the second order elliptic boundary value problem with highly…
A new preconditioner is developed for high order finite element approximation of linear elastic problems on triangular meshes in two dimensions. The new preconditioner results in a condition number that is bounded independently of the…
BDDC and FETI-DP algorithms are developed for three-dimensional elliptic problems with adaptively enriched coarse components. It is known that these enriched components are necessary in the development of robust preconditioners. To form the…
We propose an isogeometric solver for Poisson problems that combines i)low-rank tensor techniques to approximate the unknown solution and the system matrix, as a sum of a few terms having Kronecker product structure, ii) a Truncated…
We consider the preconditioned conjugate gradient method (PCG) with optimal preconditioner in the frame of the boundary element method (BEM) for elliptic first-kind integral equations. Our adaptive algorithm steers the termination of PCG as…
This paper introduces a new sweeping preconditioner for the iterative solution of the variable coefficient Helmholtz equation in two and three dimensions. The algorithms follow the general structure of constructing an approximate $LDL^t$…
In this paper we consider second order elliptic partial differential equations with highly varying (heterogeneous) coefficients on a two-dimensional region. The problems are discretized by a composite finite element (FE) and discontinuous…
We study preconditioning techniques for discontinuous Galerkin discretizations of isotropic linear elasticity problems in primal (displacement) formulation. We propose subspace correction methods based on a splitting of the vector valued…
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,…
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…
This work introduces nodal auxiliary space preconditioners for discretizations of mixed-dimensional partial differential equations. We first consider the continuous setting and generalize the regular decomposition to this setting. With the…
We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…
We develop a new finite element method for solving planar elasticity problems involving of heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the `broken'…
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…
A finite element method for elliptic problems with discontinuous coefficients is presented. The discontinuity is assumed to take place along a closed smooth curve. The proposed method allows to deal with meshes that are not adapted to the…
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…
Elliptic partial differential equations arise in many fields of science and engineering such as steady state distribution of heat, fluid dynamics, structural/mechanical engineering, aerospace engineering and seismology etc. In three…
We propose an augmented Lagrangian-based preconditioner to accelerate the convergence of Krylov subspace methods applied to linear systems of equations with a block three-by-three structure such as those arising from mixed finite element…
In this paper a discretization based on discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is posed on a polygonal region $\Omega$ which is a union of $N$…
The solution of the elliptic partial differential equation has interface singularity at the points which are either the intersections of interfaces or the intersections of interfaces with the boundary of the domain. The singularities that…