相关论文: Adaptive boundary element methods for the computat…

We formulate and analyze an adaptive algorithm for isogeometric analysis with hierarchical B-splines for weakly-singular boundary integral equations. We prove that the employed weighted-residual error estimator is reliable and converges at…

In this paper, we are concerned with the numerical treatment of boundary integral equations by means of the adaptive wavelet boundary element method (BEM). In particular, we consider the second kind Fredholm integral equation for the double…

Present work presents a code written in the very simple programming language MATLAB, for three dimensional linear elastostatics, using constant boundary elements. The code, in full or in part, is not a translation or a copy of any of the…

We develop a boundary integral equation-based numerical method to solve for the electrostatic potential in two dimensions, inside a medium with piecewise constant conductivity, where the boundary condition is given by the complete electrode…

Accurate triangulation of the domain plays a pivotal role in computing the numerical approximation of the differential operators. A good triangulation is the one which aids in reducing discretization errors. In a standard collocation…

We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…

This article deals with the adaptive and approximative computation of the Lam\'e equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM).…

A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…

The Poisson-Boltzmann equation is a widely used model to study the electrostatics in molecular solvation. Its numerical solution using a boundary integral formulation requires a mesh on the molecular surface only, yielding accurate…

In this paper we have derived explicitly computable bounds on the error in energy norms for the fully nonlinear Poisson-Boltzmann equation. Together with the computable bounds, we have also obtained efficient error indicators which can…

We present a boundary integral method for numerical computation of the capacity of generalized condensers. The presented method applies to a wide variety of generalized condenser geometry including the cases when the plates of the…

In this paper we propose a novel methodology for static analysis of binary code using abstract interpretation. We use an abstract domain based on polyhedra and two mapping functions that associate polyhedra variables with registers and…

Semidefinite programming (SDP) is a fundamental class of convex optimization problems with diverse applications in mathematics, engineering, machine learning, and related disciplines. This paper investigates the application of the…

We are interested in numerical algorithms for computing the electrical field generated by a charge distribution localized on scale $\ell$ in an infinite heterogeneous medium, in a situation where the medium is only known in a box of…

A method for finding the exact analytical solutions for the bulk and edge energy levels and corresponding eigenstates for all commensurate Aubry-Andr\'e/Harper single-particle models under open boundary conditions is presented here, both…

A stationary free boundary problem modeling a three-dimensional electrostatic MEMS device is investigated. The device is made of a rigid ground plate and an elastic top plate which is hinged at its boundary, the plates being held at…

We give a survey of computation of the conformal capacity of planar condensers, generalized capacity, and logarithmic capacity with emphasis on our recent work 2020-2025. We also discuss some applications of our method based on the boundary…

Accurately predicting wave-structure interactions is critical for the effective design and analysis of marine structures. This is typically achieved using solvers that employ the boundary element method (BEM), which relies on linear…

This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense…

The continuum theory applied to bimolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like…