We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
In this paper, we construct a combined upwinding and mixed finite
element method for the numerical solution of a two-dimensional mean
field model of superconducting vortices. An advantage of our method
is that it works
for any unstructured regular triangulation. A simple convergence
analysis is given without resorting to the discrete maximum principle.
Numerical examples are also presented.
We develop a functional analytical framework for a linear
peridynamic model of a spring network system in any space dimension.
Various properties of the peridynamic operators are examined for
general micromodulus functions. These properties are utilized to
establish the well-posedness of both the stationary peridynamic
model and the Cauchy problem of the time dependent peridynamic
model. The connections to the classical elastic models are also
provided.
In this paper, we discuss the globalization of some kind of modified Levenberg-Marquardt methods for nonsmooth equations and their applications to nonlinear complementarity problems. In these modified Levenberg-Marquardt methods, only an approximate solution of a linear system at each iteration is required. Under some mild assumptions, the global convergence is shown. Finally, numerical results show that the present methods are promising.
In this paper we propose a parametrized Newton method for nonsmooth equations with finitely many maximum functions. The convergence result of this method is proved and numerical experiments are listed.
Download Results (CSV)