Boundary Element Simulation of Thermal Waves

In this paper we survey computational techniques based on boundary integral formulations for the simulation of thermal waves. Time-harmonic solutions to diffusion problems appear in many physical situations of interest and give rise to many interesting problems related to material characterization, parameter assessment or detection of defects. We review the main direct, indirect and mixed integral numerical methods for a model of scattering of thermal waves by many obstacles and discuss how multiple scattering techniques and other physical tools can be understood as iterative methods or used as preconditioners. We also deal with some transient problems that can be solved with boundary element methods using the Laplace transform and with coupled finite and boundary element schemes for non-homogeneous obstacles.