
Accession Number : ADA207517
Title : On a Computational Method for the Second Fundamental Tensor and Its Application to Bifurcation Problems.
Descriptive Note : Technical rept.,
Corporate Author : PITTSBURGH UNIV PA INST FOR COMPUTATIONAL MATHEMATICS AND APPLICATIONS
Personal Author(s) : Rheinboldt, Werner C ; Rabier, Patrick J
PDF Url : ADA207517
Report Date : Feb 1989
Pagination or Media Count : 25
Abstract : An algorithm is presented for the computation of the second fundamental tensor V of a Riemannian submanifold M of R superscript n. From V the Riemann curvature tensor of M is easily obtained. Moreover, V has a close relation to the second derivative of certain functionals on M which, in turn, provides a powerful new tool for the computational determination of multiple bifurcation directions. Frequently, in applications, the manifold M is defined implicitly as the zero set of a submersion F on R superscript n. In this case, the principal cost of algorithm for computing V (p) at a given point p an element of M involves only the decomposition of the Jacobian DF (p) of F at p and the projection of d(d+1) neighboring points onto M by means of a local iterative process using DF(p). Several numerical examples are given which show the efficiency and dependability of the method. (jhd)
Descriptors : *TENSORS, ALGORITHMS, COMPUTATIONS, COSTS, CURVATURE, DECOMPOSITION, DETERMINATION, ITERATIONS
Subject Categories : Theoretical Mathematics
Distribution Statement : APPROVED FOR PUBLIC RELEASE