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Published on May 29, 2015
Although not exactly a classical big data application, the numerical treatment of partial differential equations (PDEs) has very similar characteristics: By spatial discretization, the continuous problem is translated to linear systems and the discrete solution is represented by a vector of floating point numbers. Depending on the dimensions of the domain and the granularity of the spatial discretization, the size of the arising matrices and vectors may range from a few thousands to billions of entries. Usual operations include matrix-vector multiplications, the solution of linear systems and more complicated tasks like the solution of eigenvalue problems.Due to usually large problem sizes, computational performance is certainly a main design goal of PDE solvers. However, when it comes to the implementation of complex PDEs or algorithms in general it is equally desirable to use high level programming tools that allow a concise domain-related problem definition.Recently, Python gained a lot of attention in the scientific computing community that was dominated by compiled languages as Fortran and C for a long time. The reason for this development is most likely the fulfillment of the above mentioned criteria: performance and brief syntax. While the brief syntax is a feature of the language itself, Python owes its high performance the existence of excellent third party libraries such as NumPy. Many novel scientific special purpose libraries are still written in compiled languages, but come with Python wrappers and seamlessly integrate with NumPy.The aim of this talk is to give a brief introduction to the problem domain and present a selection of Python tools and libraries for scientific computing with a focus on continuous problems.