In this thesis we have sought to optimize the numerical simulation of scannig probe conudctance spectroscopy. This is a very computationally intensive problem, since, in principle, it requires as many conductance cal- culations as the number of points over which the probe is scanned.
Our target has been that of devising algorithms that reuse as much as possible inetermediate results, in order to achieve a significant speed-up.
We introduced and discussed possible strategies, both for hard-wall and soft-wall cases, and compare them to find the best suited for the task.
Finally we wrote a program using the best approach we found for the case of soft-wall system, since we wanted to cover not only ideal models, but also real-world experiments. We have then compared the performance achieved with that of available existing programs.
We also exploted the instrinsic parallelism of the conductance spec- troscopy, and showed how to take advantage of it in our simulations.
It is exactly parallelism that, in the future, can be used to further in- crease the performance of the program. CPUs are general purpose processors, with only a minor part of them dedicated to arithmetic circuits, plus their
parallelism is limited, since they cannot handle too many threads with effi- ciency. The way a CPU works is fine for general purpose applications, but it is not optimal for our needs (huge overhead for each thread and so on).
In recent years a new possibility has arisen, that allow us to take full advantage of parallel computing: programmable graphic cards. A pro- grammable graphic card can be viewed as a collection of dedicated proces- sors, specialized in mathematical computations and devised with a parallel paradigm in mind. Where a CPU can handle just a bunch of threads, a GPU is capable of running thousands of threads, with little to no overhead. There- fore an important development of the present work would be represented by the implementation of the developed algorithms on GPU-base hardware, which would allow the efficient simulation of complete scanning probe spec- troscopy experiments, with the inclusion of random dopant distributions and imperfections.