The present paper is concerned with the numerical solution of a shape identification
problem for the heat equation. The goal is to determine of the shape of a void or an inclusion …

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 …

An efficient scheme for solving boundary integral equations of the heat equation based on
the Galerkin method is introduced. The parabolic fast multipole method (pFMM) is applied to …

In this paper we introduce a new parallel solver for the weakly singular space–time
boundary integral equation for the heat equation. The space–time boundary mesh is …

This paper proposes and analyzes a full discretization of the exterior transient Stokes
problem with Dirichlet boundary conditions. The method is based on a single layer boundary …

We present a family of integral equation-based solvers for the linear or semilinear heat
equation in complicated moving (or stationary) geometries. This approach has significant …

This paper is dedicated to the determination of the shape of a compactly supported constant
source in the heat equation from measurements of the heat flux through the boundary. This …

This article is concerned with the solution of a time-dependent shape identification problem.
Specifically, we consider the heat equation in a domain which contains a time-dependent …

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 …

A direct boundary integral equation method for the heat equation based on Nyström
discretization is proposed and analyzed. For problems with moving geometries, a weakly …