Outline

In this chapter we will discuss how to solve a time-dependent temperature diffusion PDE for a given block of material. Within the block there is a heat source which drives the temperature diffusion. On the surface, energy can radiate into the surrounding environment. Figure  shows the configuration.

In the next Section  we will present the relevant model. A time integration scheme is introduced to calculate the temperature at given time nodes $t^{(n)}$. We will see that at each time step a Helmholtz equation must be solved. The implementation of a Helmholtz equation solver will be discussed in Section . In Section  the solver of the Helmholtz equation is used to build a solver for the temperature diffusion problem.