Related papers: Parallel solvers for virtual element discretizatio…
This paper focuses on the analysis of conforming virtual element methods for general second-order linear elliptic problems with rough source terms and applies it to a Poisson inverse source problem with rough measurements. For the forward…
We present a family of Virtual Element Methods for three-dimensional linear elasticity problems based on the Hellinger-Reissner variational principle. A convergence and stability analysis is developed. Moreover, using the hybridization…
We present a new solver for coupled nonlinear elliptic partial differential equations (PDEs). The solver is based on pseudo-spectral collocation with domain decomposition and can handle one- to three-dimensional problems. It has three…
A characteristic feature of the state-of-the-art of real-space methods in electronic structure calculations is the diversity of the techniques used in the discretization of the relevant partial differential equations. In this context, the…
In the present paper we describe the computational implementation of some integral terms that arise from mixed virtual element methods (mixed-VEM) in two-dimensional pseudostress-velocity formulations. The implementation presented here…
This paper introduces a discretization-accurate stopping criterion of symmetric iterative methods for solving systems of algebraic equations resulting from the finite element approximation. The stopping criterion consists of the evaluations…
The Virtual Element Method (VEM) is a Galerkin approximation method that extends the Finite Element Method (FEM) to polytopal meshes. In this paper, we present a conforming formulation that generalizes the Scott-Vogelius finite element…
In view of the existing limitations of sequential computing, parallelization has emerged as an alternative in order to improve the speedup of numerical simulations. In the framework of evolutionary problems, space-time parallel methods…
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 work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…
In this paper, we propose a robust solver for the finite element discrete problem of the stationary incompressible magnetohydrodynamic (MHD) equations in three dimensions. By the mixed finite element method, both the velocity and the…
We consider systems of nonlinear magnetostatics and quasistatics that typically arise in the modeling and simulation of electric machines. The nonlinear problems, eventually obtained after time discretization, are usually solved by…
A new method for solving systems of linear algebraic equations of a special type arising in solving problems of image reconstruction has been proposed. This method, due to a certain symmetry of the matrix and the choice of the voxel…
In this paper, we present a family of new mixed finite element methods for linear elasticity for both spatial dimensions $n=2,3$, which yields a conforming and strongly symmetric approximation for stress. Applying…
The DD-CPM software library provides a set of tools for the discretization and solution of problems arising from the closest point method (CPM) for partial differential equations on surfaces. The solvers are built on top of the well-known…
We present a distributed parallel mesh curving method for virtual geometry. The main application is to generate large-scale curved meshes on complex geometry suitable for analysis with unstructured high-order methods. Accordingly, we devise…
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their…
In the present contribution we develop a sharper error analysis for the Virtual Element Method, applied to a model elliptic problem, that separates the element boundary and element interior contributions to the error. As a consequence we…
We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid schemes, we…