Numerično reševanje valovne enačbe z grafično procesno enoto : diplomsko delo

Tribušon, Matic (author), Lotrič, Uroš (mentor)

Cilj diplomske naloge je implementacija algoritma za numerično reševanje valovne enačbe na grafični procesni enoti. Diferencialno enačbo smo reševali z Eulerjevo metodo in metodo Runge-Kutta 4. reda. Metodi se razlikujeta po računski zahtevnosti, točnosti in numerični stabilnosti. Algoritma smo implementirali na platformah CUDA in OpenCL. Konkurenčni platformi smo med seboj primerjali in predstavili rezultate. Na koncu smo rezultate algoritmov v vsakem koraku vizualizirali z uporabo OpenGL in ocenili, kakšen vpliv na hitrost ima vizualizacija. Rezultati potrjujejo hipotezo, da sta si platformi po zmogljivosti zelo podobni. CUDA je vendrale nekoliko hitrejša predvsem pri izračunih na nekoliko manjših matrikah, OpenCL pa je malce hitrejši pri večjih količinah podatkov. Vizualizacija v primerjavi z izračunom porabi ogromno časa. Zato ob vizualizaciji izbira platforme za programiranje na grafični procesni enoti ni ključnega pomena.

• Language: Slovenian
• Keywords: valovna enačba, Eulerjeva metoda, metoda Runge-Kutta, CUDA, OpenCL, OpenGL, računalništvo, računalništvo in informatika, univerzitetni študij, diplomske naloge
• Work type: Bachelor thesis/paper
• Typology: 2.11 - Undergraduate Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Publisher: M. Tribušon
• Year: 2014
• Number of pages: 54 str.
• PID: 20.500.12556/RUL-29493
• COBISS.SI-ID: 1536072643
• Publication date in RUL: 18.09.2014

Secondary language

• Language: English
• Title: Solving the wave equation on graphics processing unit

Abstract

The aim of this thesis is implementation of algorithm for numerical solution of the wave equation on graphics processing unit. We used Euler and 4th order Runge-Kutta method. The methods differ in calculation complexity, numerical accuracy and numerical stability. Algorithms were implemented on CUDA and OpenCL platforms. Competitive platforms were compared with each other. Results of each step of the calculation were also visualized using OpenGL standard with the purpose of assessing the impact visualization has on time spent by algorithms. Results confirm the hypothesis that the two GPGPU platforms are very similar in performance. CUDA is slightly faster on smaller matrices, OpenCL performs better on larger matrices. Visualization takes a lot of time compared to the calculation. Therefore, in the case of visualization, the choice of platform is not crucial.

• Keywords: wave equation, Euler method, Runge-Kutta method, GPGPU, CUDA, OpenCL, OpenGL, computer science, computer and information science, diploma