arXiv subjects

Alessandra Aimi

Publications and source records attributed to Alessandra Aimi.

6 recordsLinked to original sources

arXiv2026

Finite elements for the space approximation of a differential model for salts crystallization

This article investigates a space-time differential model related to the degradation of stone artifacts caused by exposure to air and atmospheric agents, which specifically lead to the accumulation of salt crystals in the material. A numerical method based on finite-element space discretization and implicit-explicit time marching is proposed as an extension of a one-dimensional finite-difference framework introduced in the literature. Within the same one-dimensional setting, a sensitivity analysis is performed, based on the techniques developed therein. They are also used as a comparison tool for the finite-element formulation, here introduced for more realistic simulations in higher space dimensions. Considerations about stability will be provided, together with an experimental convergence analysis highlighting the performance of the proposed approach. Numerical results in two and three space dimensions, obtained by an efficient code implementation, will be presented and discussed.

math.NA↗

arXiv2025

A space-time adaptive boundary element method for the wave equation

This article initiates the study of space-time adaptive mesh refinements for time-dependent boundary element formulations of wave equations. Based on error indicators of residual type, we formulate an adaptive boundary element procedure for acoustic soft-scattering problems with local tensor-product refinements of the space-time mesh. We discuss the algorithmic challenges and investigate the proposed method in numerical experiments. In particular, we study the performance and improved convergence rates with respect to the energy norm for problems dominated by spatial, temporal or traveling singularities of the solution. The efficiency of the considered rigorous and heuristic a posteriori error indicators is discussed.

math.NA↗

arXiv2025

Adaptive time-domain boundary element methods for the wave equation with Neumann boundary conditions

This article investigates adaptive mesh refinement procedures for the time-domain wave equation with Neumann boundary conditions, formulated as an equivalent hypersingular boundary integral equation. Space-adaptive and time-adaptive versions of a space-time boundary element method are presented, based on a reliable a posteriori error estimate of residual type. Numerical experiments illustrate the performance of the proposed approach.

math.NA↗

arXiv2024

Space-time boundary elements for frictional contact in elastodynamics

This article studies a boundary element method for dynamic frictional contact between linearly elastic bodies. We formulate these problems as a variational inequality on the boundary, involving the elastodynamic Poincar\'{e}-Steklov operator. The variational inequality is solved in a mixed formulation using boundary elements in space and time. In the model problem of unilateral Tresca friction contact with a rigid obstacle we obtain an a priori estimate for the resulting Galerkin approximations. Numerical experiments in two space dimensions demonstrate the stability, energy conservation and convergence of the proposed method for contact problems involving concrete and steel in the linearly elastic regime. They address both unilateral and two-sided dynamic contact with Tresca or Coulomb friction.

math.NA↗

arXiv2023

Time domain boundary elements for elastodynamic contact

This article proposes a boundary element method for the dynamic contact between a linearly elastic body and a rigid obstacle. The Signorini contact problem is formulated as a variational inequality for the Poincar\'{e}-Steklov operator for the elastodynamic equations on the boundary, which is solved in a mixed formulation using boundary elements in the time domain. We obtain an a priori estimate for the resulting Galerkin approximations. Numerical experiments confirm the stability and convergence of the proposed method for the contact problem in flat and curved two-dimensional geometries, as well as for moving obstacles.

math.NA↗

arXiv2023

Higher-order time domain boundary elements for elastodynamics -- graded meshes and hp versions

The solution to the elastodynamic equation in the exterior of a polyhedral domain or a screen exhibits singular behavior from the corners and edges. The detailed expansion of the singularities implies quasi-optimal estimates for piecewise polynomial approximations of the Dirichlet trace of the solution and the traction. The results are applied to hp and graded versions of the time domain boundary element method for the weakly singular and the hypersingular integral equations. Numerical examples confirm the theoretical results for the Dirichlet and Neumann problems for screens and for polygonal domains in 2d. They exhibit the expected quasi-optimal convergence rates and the singular behavior of the solutions.

math.NA↗