Related papers: Parallel solvers for virtual element discretizatio…
This paper presents the results of a preliminary experimental investigation of the performance of a stationary iterative method based on a block staircase splitting for solving singular systems of linear equations arising in Markov chain…
We present a Virtual Element Method (VEM) for possibly nonlinear elastic and inelastic problems, mainly focusing on a small deformation regime. The numerical scheme is based on a low-order approximation of the displacement field, as well as…
In this paper we review the parallel solution of sparse linear systems, usually deriving by the discretization of ODE-IVPs or ODE-BVPs. The approach is based on the concept of parallel factorization of a (block) tridiagonal matrix. This…
In this paper we construct conforming Virtual Element approximations on domains with curved boundary and/or internal curved interfaces, both in two and three dimensions. Our approach allows to impose both Dirichlet and Neumann…
We design a Mixed Virtual Element Method for the approximated solution to the first-order form of the acoustic wave equation. In absence of external load, the semi-discrete method exactly conserves the system energy. To integrate in time…
A local and parallel algorithm based on the multilevel discretization is proposed in this paper to solve the eigenvalue problem by the finite element method. With this new scheme, solving the eigenvalue problem in the finest grid is…
We propose an efficient method for the numerical approximation of a general class of two dimensional semilinear parabolic problems on polygonal meshes. The proposed approach takes advantage of the properties of the serendipity version of…
We consider the problem of minimizing block-separable convex functions subject to linear constraints. While the Alternating Direction Method of Multipliers (ADMM) for two-block linear constraints has been intensively studied both…
This article presents an immersed virtual element method for solving a class of interface problems that combines the advantages of both body-fitted mesh methods and unfitted mesh methods. A background body-fitted mesh is generated…
Diffusion models (DMs) have achieved state-of-the-art generative performance but suffer from high sampling latency due to their sequential denoising nature. Existing solver-based acceleration methods often face significant image quality…
This work concerns adaptive refinement procedures for meshes of polygonal virtual elements. Specifically, refinement procedures previously proposed by the authors for structured meshes are generalized for the challenging case of arbitrary…
The present paper has two objectives. On one side, we develop and test numerically divergence free Virtual Elements in three dimensions, for variable ``polynomial'' order. These are the natural extension of the two-dimensional divergence…
In this article, we derive fast and robust parallel-in-time preconditioned iterative methods for the all-at-once linear systems arising upon discretization of time-dependent PDEs. The discretization we employ is based on a Runge--Kutta…
In the present work we generalize the curvilinear Virtual Element technology, introduced for a simple linear scalar problem in a previous work, to generic 2D solid mechanic problems in small deformations. Such generalization also includes…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable to meshes that consist of arbitrarily-shaped polygonal and…
The goal of this paper is to propose preconditioners for the system of linear equations that arises from a discretization of fourth order elliptic problems using spectral element methods. These preconditioners are constructed using…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
In this paper, we review recent results on the conforming virtual element approximation of polyharmonic and elastodynamics problems. The structure and the content of this review is motivated by three paradigmatic examples of applications:…
The paper describes an improved parallel MPI-based implementation of VBARMS, a variable block variant of the pARMS preconditioner proposed by Li,~Saad and Sosonkina [NLAA, 2003] for solving general nonsymmetric linear systems. The parallel…