We present an active cloaking method for the parabolic heat (and mass or light diffusion)
equation that can hide both objects and sources. By active, we mean that it relies on …

In this chapter, we describe a space-time boundary element method for the numerical
solution of the time-dependent heat equation. As model problem, we consider the initial …

In this paper, we recast the variational formulation corresponding to the single layer
boundary integral operator $\operatorname {V} $ for the wave equation as a minimization …

We analyze the mathematical model that describes the heat generated by electromagnetic
nanoparticles. We use the known optical properties of the nanoparticles to control the …

The presented paper concentrates on the boundary element method (BEM) for the heat
equation in three spatial dimensions. In particular, we deal with tensor product space-time …

While an integration by parts formula for the bilinear form of the hypersingular boundary
integral operator for the transient heat equation in three spatial dimensions is available in …

We develop couplings of a recent space-time first-order system least-squares (FOSLS)
method for parabolic problems and space-time boundary element methods (BEM) for the …

We consider the space-time boundary element method (BEM) for the heat equation with
prescribed initial and Dirichlet data. We propose a residual-type a posteriori error estimator …

This article provides a functional analytical framework for boundary integral equations of the
heat equation in time-dependent domains. More specifically, we consider a non-cylindrical …

Partial differential equations are used for the modeling of a wide variety of (natural)
phenomena appearing in biology, physics, chemistry, engineering, finance and many more …