Skip to Main Content
Designing Scientific Applications on GPUs
book

Designing Scientific Applications on GPUs

by Raphael Couturier
November 2013
Intermediate to advanced content levelIntermediate to advanced
498 pages
17h 6m
English
Chapman and Hall/CRC
Content preview from Designing Scientific Applications on GPUs
88 Designing Scientific Applications on GPUs
right-hand side. For simplicity, assume that we know the exact solution, u
true
,
corresponding to (6.5). Then we use the method of manufactured solutions to
derive an expression for the corresponding right-hand side f(x, y):
f(x, y) =
2
u
true
= 2π
2
sin(πx) sin(πy). (6.9)
The spatial derivative in (6.8) is again approximated with finite differences,
similar to the example in (6.2), except boundary values are explicitly set to
zero. The discrete form of the system can now be written as a sparse linear
system of equations:
Au = f, u, f R
N
, A R
N×N
, (6.10)
where A is the sparse matrix formed by finite difference coefficients, N is the
number of unknowns, and f is given by (6.9). Equation (6.10) can be solved
in numerous ...
Become an O’Reilly member and get unlimited access to this title plus top books and audiobooks from O’Reilly and nearly 200 top publishers, thousands of courses curated by job role, 150+ live events each month,
and much more.
Start your free trial

You might also like

Introduction to Numerical Analysis and Scientific Computing

Introduction to Numerical Analysis and Scientific Computing

Nabil Nassif, Dolly Khuwayri Fayyad
Computational Electromagnetism

Computational Electromagnetism

Alain Bossavit, Isaak D. Mayergoyz

Publisher Resources

ISBN: 9781466571648