9 papers · 1 filter
Continuity estimates for Riesz potentials on polygonal boundaries
Xavier Claeys, Muhammad Hassan, Benjamin Stamm
Riesz potentials are well known objects of study in the theory of singular integrals that have been the subject of recent, increased interest from the numerical analysis community…
Guaranteed a posteriori bounds for eigenvalues and eigenvectors: multiplicities and clusters
Eric Cancès, Geneviève Dusson, Yvon Maday +2
This paper presents a posteriori error estimates for conforming numerical approximations of eigenvalue clusters of second-order self-adjoint elliptic linear operators with compact…
A Linear Scaling in Accuracy Numerical Method for Computing the Electrostatic Forces in the -Body Dielectric Spheres Problem
Muhammad Hassan, Benjamin Stamm
This article deals with the efficient and accurate computation of the electrostatic forces between charged, spherical dielectric particles undergoing mutual polarisation. We use th…
On the Scalability of the Parallel Schwarz Method in One-Dimension
Gabriele Ciaramella, Muhammad Hassan, Benjamin Stamm
In contrast with classical Schwarz theory, recent results in computational chemistry have shown that for special domain geometries, the one-level parallel Schwarz method can be sca…
An Integral Equation Formulation of the -body Dielectric Spheres Problem. Part II: Complexity Analysis
Bérenger Bramas, Muhammad Hassan, Benjamin Stamm
This article is the second in a series of two papers concerning the mathematical study of a boundary integral equation of the second kind that describes the interaction of diel…
Gradient Flow Finite Element Discretizations with Energy-Based Adaptivity for the Gross-Pitaevskii Equation
Pascal Heid, Benjamin Stamm, Thomas P. Wihler
We present an effective adaptive procedure for the numerical approximation of the steady-state Gross-Pitaevskii equation. Our approach is solely based on energy minimization, and c…