We describe a modified Nyström method for the discretization of the weakly singular boundary integral operators which arise from the formulation of linear elliptic boundary value problems as integral equations. Standard Nyström and collocation schemes proceed by representing functions via their values at a collection of quadrature nodes. Our method uses appropriately scaled function values in l...

This paper presents our research and development of system interfaces between Building Information Modeling (BIM) and Building Energy Modeling (BEM), for supporting integrated architectural design and energy simulation. Our methods utilize the BIM authoring tools’ Application Programming Interface (API) to translate BIM into Object-Oriented Physical Models (in Modelica) for building thermal sim...

The interface problem describing the scattering of time-harmonic electromagnetic waves by a dielectric body is often formulated as a pair of coupled boundary integral equations for the electric and magnetic current densities on the interface Γ. In this paper, following an idea developed by Kleinman and Martin [19] for acoustic scattering problems, we consider methods for solving the dielectric ...

We explore global existence and stability of planar solutions to a multi-dimensional Case II polymer diffusion model which takes the form of a one-phase free boundary problem with phase onset. Due to a particular boundary condition, convergence can not be expected on the whole domain. A boundary integral formulation derived in [16] is shown to remain valid in the present context and allows us t...

The integration of building information modelling (BIM) and geographic information system (GIS) in construction management is a new and fast developing trend in recent years, from research to industrial practice. BIM has advantages on rich geometric and semantic information through the building life cycle, while GIS is a broad field covering geovisualization-based decision making and geospatial...

Multitrace formulations (MTF) for boundary integral equations (BIE) were developed over the last few years in [4] and [1, 2] for the simulation of electromagnetic problems in piecewise constant media, see also [3] for associated boundary integral methods. The MTFs are naturally adapted to the developments of new block preconditioners, as indicated in [5], but very little is known so far about s...

In this paper we report on a non-overlapping and an overlapping domain decomposition method as preconditioners for the boundary element approximation of an indefinite hypersingular integral equation on a surface. The equation arises from an integral reformulation of the Neumann screen problem with the Helmholtz equation in the exterior of a screen in R. It is well-known that the linear algebrai...