This monograph focuses on the numerical methods needed in the context of developing a reliable
simulation tool to promote the use of renewable energy. One very promising source of energy is
the heat stored in the Earth's crust which is harnessed by so-called geothermal facilities.
Scientists from fields like geology geo-engineering geophysics and especially geomathematics
are called upon to help make geothermics a reliable and safe energy production method. One of
the challenges they face involves modeling the mechanical stresses at work in a reservoir. The
aim of this thesis is to develop a numerical solution scheme by means of which the fluid
pressure and rock stresses in a geothermal reservoir can be determined prior to well drilling
and during production. For this purpose the method should (i) include poroelastic effects
(ii) provide a means of including thermoelastic effects (iii) be inexpensive in terms of
memory and computational power and (iv) be flexible with regard to the locations of data
points. After introducing the basic equations and their relations to more familiar ones (the
heat equation Stokes equations Cauchy-Navier equation) the method of fundamental solutions
and its potential value concerning our task are discussed. Based on the properties of the
fundamental solutions theoretical results are established and numerical examples of stress
field simulations are presented to assess the method's performance. The first-ever 3D graphics
calculated for these topics which neither requiring meshing of the domain nor involving a
time-stepping scheme make this a pioneering volume.
