@MISC{Wohlever96symmetry,nonlinear, author = {J.C. Wohlever}, title = {Symmetry, Nonlinear Bifurcation Analysis, and Parallel Computation}, year = {1996} }

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Abstract

In the natural and engineering sciences the equations which model physical systems with symmetry often exhibit an invariance with respect to a particular group G of linear transformations. G is typically a linear representation of a symmetry group G which characterizes the symmetry of the physical system. In this work, we will discuss the natural parallelism which arises while seeking families of solutions to a specific class of nonlinear vector equations which display a special type of group invariance, referred to as equivariance. The inherent parallelism stems from a global de-coupling, due to symmetry, of the full nonlinear equations which effectively splits the original problem into a set of smaller problems. Numerical results from a symmetry-adapted numerical procedure, (MMcontcm.m), written in MultiMATLAB 1 are discussed. 1 Introduction Consider the task of finding solutions to the following vector equilibrium equation f (u; ) = 0; f : R n \Theta R 7! R n : (1) In eq: ...