Projects in Sparse Grids and High Dimensional Approximation
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Possible topics are listed below. Crossed topics indicate topics already assigned to students. It might however be possible to continue the work of past students or to extend the scope of a topic. Therefore, do not hesitate to ask about crossed out topics if you are interested in one of them.
Topic | Description | Contact |
Developping and Evaluating a stable Asynchronous Combination Technique | In a previous thesis we have made first progress in implementing an asynchronous Combination Technique. Here we delay the combination step until the next combination point and apply the results then. This approach worked for some of the test scenarios but also showed instabilities in certain cases. In this thesis a more robust variant will be developed that incorporates more knowledge of the PDE into the asynchronous method. Finally this method will be evaluated and analyzed using different PDEs. Good knowledge of numerical methods, PDEs and C++ is helpful. | Michael Obersteiner; Master or Bachelor thesis |
Optimizing Communication Volume for the Combination Technique | One of the critical parts of an HPC implementation of the Combination Technique is the large amount of data that needs to be communicated. Such a full volume reduction usually does not scale to large process counts and problem sizes. Therefore, this thesis will cover more efficient communication schemes that optimize the placement of component grid onto the different process groups to minimize the overlap that needs to be communicated. For this the theoretical background will be developed and implemented in an C++ framework. MPI and C++ knowledge is helpful. | Michael Obersteiner; Master or Bachelor thesis |
Towards exascale-ready PDE solvers | We will soon reach the era of exascale: 10^18 floating point operations per second on high-end supercomputers. This will allow scientists to explore new research fields, but the sheer complexity of these systems brings along many issues. Among the most difficult ones is fault tolerance. A supercomputer with hundreds of thousands of computing elements will inevitably suffer from faults of different types, and algorithm designers should take this into consideration. We have developed a PDE solver that can run on large HPC systems and respond to simulated hardware faults. The objective of this thesis will be to test the exascale emulator GREMLINS on a high-dimensional PDE solver. Several test scenarios will be studied to understand how the solver could perform in future exascale systems, including fault emulation, power caps, thermal caps, and limited bandwidth, among others. This thesis involves C++ programming, parallel programming, performance analysis, and numerics. | Michael Obersteiner; Master thesis |
Michael Obersteiner; Bachelor or Master thesis | ||
Michael Obersteiner; Bachelor thesis or student project | ||
Michael Obersteiner; Master thesis or IDP | ||
Michael Obersteiner; (Bachelor thesis), IDP, Master thesis | ||
The work will include a comprehensive literature study and a comparison of existing PDE solver frameworks, their coupling to the existing combination technique framework written in Python, and a study of the numerical errors introduced by the combination technique for each PDE problem. |
Michael Obersteiner; Bachelor thesis | |
The work includes the implementation of a solver of the Schroedinger equation on varying non-equidistant meshes. After its validation it will be used with the various traditional and new combination techniques for eigenvalue problems. The existing results will be compared with this new method. |
Michael Obersteiner; Master thesis |