Basic HTML version of Foils prepared February 25 2000

Foil 11 Matrices and Graphs I

From Parallel Programming for Particle Dynamics Extra Foils Computational Science CPS615 -- Spring 2000 Semester. by Geoffrey C. Fox


1 Especially in cases where the "force" is linear in the ?i(t) , it is convenient to think of force being specified by a matrix M whose elements mij are nonzero if and only if the force between i and j is nonzero. A typical force law is: Fi = ? mij ?i(t)
2 In Laplace example, the matrix M is sparse ( most elements are zero) and this is a specially common case where one can and needs to develop efficient algorithms
3 We will return to the matrix formulation in the case of partial differential solvers

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