Developing a general software framework for RBF approximation methods

We have a flexible software for solving time-independent partial differential equations using radial basis function approximation which we wish to develop further. In a previous master thesis by Danhua Xiang (1), the design of this software was reworked, and this new master thesis project is about continuing the work on the design and also to see how some of the ideas could be implemented.

One of the most interesting parts is a module currently called the "Workflow manager". The software offers a set of common building blocks for working with radial basis function approximations, and this module helps a user to combine these building blocks by determining how to assemble them together in an efficient way. That is, the workflow manager takes as input a number of predefined operations, such as composing certain matrices and solving equation systems, and finds a good order to perform these operations. This includes:

• Finding which operations can be run in parallel, and scheduling these operations to different cores on multicore architectures.
• When operations are performed inside loops or nested loops, find out in which order to perform the loops by trying to minimize memory usage and maximize parallelism.
• Handling of data dependencies between the operations.

The implementation should preferably be done in Fortran 90, since this is the language used in the existing code. For the parallelization, we can make use of a task library that has already been developed. This task library is in C++, so this would include connecting the Fortran 90 code to the C++ code.

Applicants will be asked to take a programming test.

Contact: Elisabeth Larsson

References

1. Designing a Flexible Software Tool for RBF Approximations Applied to PDEs. Danhua Xiang. Student thesis (Master Programme in Computational Science), supervisor: Elisabeth Larsson, Martin Tillenius, examiner: Michael Thuné, Anders Jansson, IT nr 10 058, 2010. (fulltext).