Parallel programming in problems of mathematical physics

1.

Parallel
programming in
problems of
mathematical physics
Dmitry Bogoslovsky
Voronezh State University

2.

The Dirichlet problem
Solution
Software implementation on the CPU
Software implementation on the GPU

3.

The Dirichlet problem
Find an unknown function u(x,y)
2u 2u
2 0,
2
x
y
{( x, y | 0 x a,0 y b)}

4.

Solution
Approximate partial derivatives:
ui , j
ui 1, j ui 1, j ui , j 1 ui , j 1
4
i 1,..., n 1, j 1,..., m 1.
,

5.

Solution

6.

01
Software implementation
on the CPU
02
03
Implementation in C++
Single-threated
Implementation in C++
OpenMP
Implementation in Python
Single-threated

7.

Software implementation on the CPU

8.

Software implementation
on the GPU
Tesla K80

9.

Software implementation
on the GPU
Tesla K80 accelerator features:
4992 cores
Performance up to 8.73 teraflops
CUDA

10.

Software implementation on the GPU

11.

12.

Pluses
High performance.
Lots of ready made solutions.
Great documentation.
Minuses
Need a supercomputer.
Expensive.
Slow development of technology.

13.

Parallel
programming in
problems of
mathematical physics
Dmitry Bogoslovsky
Voronezh State University