VSB – Technical University of Ostrava
Faculty of Electrical Engineering and Computer Science
Department of Applied Mathematics
Diploma Thesis Assignment
Student:
Ing. Jakub Homola
Study Programme:
N0541A170007 Computational and Applied Mathematics
Specialization:
S02 Computational Methods and HPC
Title:
Acceleration of the space-time boundary element method using GPUs Akcelerace prostoro-časové metody hraničních prvků pomocí GPU
The thesis language:
Description:
The thesis deals with the acceleration of the space-time boundary element method (BEM) for the heat equation [1] using GPU accelerator cards. Application of BEM to solution of partial differential equations has several advantages. One only has to discretize the boundary of the computational domain, which makes it well suited for problems stated on unbounded domains. Moreover, it makes the mesh generation much easier. On the other hand, the system matrices generated by the method are mostly dense, thus requiring O (N^2) operations to assemble and memory to store. Next, singularities occurring during integration process require special treatment.
However, the high computational intensity of BEM makes it well suited for current and future
heterogeneous computer architectures equipped with CPUs with wide vector registers and accelerator cards with large number of vector processors. Furthermore, the space-time formulation leads to large matrices which enables parallelisation both in space and time concurrently. This is currently a hot topic, since the parallel-in-time approaches improve scalability of the scientific code on current multi-petascale and future exascale clusters.
The main topic of the thesis is on-the-fly acceleration of the BEM matrices application using GPUs. The student will analyze the existing CPU code and design a suitable approach to accelerate it using GPUs without a need to explicitly assemble the system matrices. The thesis will consist of these parts:
1) Introduction,
2) A short introduction to space-time boundary element method for the heat equation, 3) GPUs and CUDA/OpenACC/OpenCL,
4) Analysis of the current CPU code, 5) GPU acceleration [2],
6) Numerical experiments, 7) Conclusion.
If needed, the thesis can be further extended by the acceleration of the fast multipole method. The student will learn basics of the space-time boundary element method, but the main focus and contribution will be optimisation and acceleration of existing scientific code. He will base his implementation on the existing BESTHEA code created within the Czech-Science-Foundation-supported project Space-Time Boundary Element Methods for the Heat Equation [3]. If successful, the thesis will be a significant contribution to the project.
References:
Extent and terms of a thesis are specified in directions for its elaboration that are opened to the public on the web sites of the faculty.
Supervisor: Ing. Michal Merta, Ph.D.
Date of issue: 01.09.2020 Date of submission: 30.04.2021
prof. RNDr. Jiří Bouchala, Ph.D. prof. Ing. Pavel Brandštetter, CSc.
Head of Department Dean
