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1554 IEEE TRANSACTIONS ON COMPUTERS, VOL. 37, NO. 12. DECEMBER 19x8 Iterative Algorithms for Solution of Large Sparse
 

Summary: 1554 IEEE TRANSACTIONS ON COMPUTERS, VOL. 37, NO. 12. DECEMBER 19x8
Iterative Algorithms for Solution of Large Sparse
Systems of Linear Equations on Hypercubes
CEVDET AYKANAT, FUSUN OZGUNER, MEMBER, IEEE, FIKRET ERCAL, STUDENT MEMBER, IEEE, AND
PONNUSWAMY SADAYAPPAN, MEMBER, IEEE
Abstract-Solution of many scientific and engineering prob-
lems requires large amounts of computing power. The finite
element method [l]is a powerful numerical technique for solving
boundary value problems involving partial differential equations
in engineering fields such as heat flow analysis, metal forming,
and others. As a result of finite element discretization, linear
equations in the form A x = b are obtained where A is large,
sparse, and banded with proper ordering of the variables x. In
this paper, solution of such equations on distributed-memory
message-passing multiprocessors implementing the hypercube [2]
topology is addressed. Iterative algorithms based on the Conju-
gate Gradient method are developed for hypercubes designed for
coarse grain parallelism. Communication requirements of differ-
ent schemes for mapping finite element meshes onto the proces-
sors of a hypercube are analyzed with respect to the effect of

  

Source: Aykanat, Cevdet - Department of Computer Engineering, Bilkent University

 

Collections: Computer Technologies and Information Sciences