Parallel Iterative solution of the Hermite Collocation Equations on GPUs Emmanuel N. Mathioudakis Co-Authors : Elena Papadopoulou – Yiannis Saridakis – Nikolaos Vilanakis TECHNICAL UNIVERSITY OF CRETE DEPARTMENT OF SCIENCES APPLIED MATHEMATICS AND COMPUTERS LABORATORY 73100 CHANIA - CRETE - GREECE
38
Embed
Parallel iterative solution of the hermite collocation equations on gpus
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Parallel Iterative solution of the
Hermite Collocation Equations
on GPUs
Emmanuel N. Mathioudakis
Co-Authors : Elena Papadopoulou – Yiannis Saridakis – Nikolaos Vilanakis
TECHNICAL UNIVERSITY OF CRETE
DEPARTMENT OF SCIENCES
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
73100 CHANIA - CRETE - GREECE
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Talk Overview
Hermite Collocation for elliptic BVPs &
Derivation of the Collocation linear system
Development of a parallel algorithm for the
Schur Complement method on Shared
Memory Parallel Architectures
Parallel implementation on multicore computers
with GPUs
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
( , ) ( , ) , ( , )
( , ) ( , ) , ( , )
u x y f x y x y
u x y g x y x y
L
BBV
P
( , ) ( , ) 0 , ( , ):
( , ) ( , ) 0 , (,
, )
y y yx x xi j i j i j
y y yx x xi j i j i j
ai j
u f
u g
L
B
Hermite Collocation Method
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Hermite Collocation Method…
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Hermite Collocation Method…
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Red – Black Collocation Linear system
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Red – Black Collocation Linear system
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Red – Black Collocation Linear system
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Red – Black Collocation Linear system
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Red – Black Collocation Linear system
with 0
( , ) ( , ) ( , ) , ( , )
( , ) ( , ) , ( , )
u x y u x y f x y x y
u x y g x y x y
2M
od
el
Pro
ble
m
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Helmholtz Collocation
Matrix
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Red – Black Collocation Linear system
The collocation matrix is large, sparse and enjoys no pleasant
properties (e.g. symmetric, definite)
Iterative
+
Parallel
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Iterative Solution
with
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Iterative Solution
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Eigenvalues of Collocation matrix
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Schur Complement Iterative Solution
TECHNICAL UNIVERSITY OF CRETE
APPLIED MATHEMATICS AND COMPUTERS LABORATORY
Parallel Iterative Solution of Collocation Linear system