期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 12, 期 3, 页码 451-476出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127402004498
关键词
algorithm; continuation; manifold; nonlinear; numerical; union of balls
We present a new continuation method for computing implicitly defined manifolds. The manifold is represented as a set of overlapping neighborhoods, and extended by an added neighborhood of a boundary point. The boundary point is found using an expression for the boundary in terms of the vertices of a set of finite, convex polyhedra. The resulting algorithm is quite simple, allows adaptive spacing of the computed points., and deals with the problems of local and global overlap in a natural way. The algorithm is robust (the new points need only be near the boundary), and is well suited to problems with large embedding dimension, and small to moderate dimension.
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