In this work, a novel true meshless numerical technique is
proposed. It is termed the Hermite–Cloud
method and is
based on the classical reproducing kernel particle method
except that a fixed reproducing kernel approximation is
used instead. Another distinction is that the point
collocation technique is used for the discretization of the
governing partial differential equations. In this method,
the Hermite theorem is employed for the construction of the
interpolation
functions. Through the constructed Hermite-
type interpolation functions, we are able to generate the
expressions of
approximate solutions of both the unknown
functions and the first-
order derivatives, in a direct
manner. A set of auxiliary
conditions have also been
developed so as to construct a complete set of PDEs with
mixed Dirichlet and Neumann boundary conditions. Through
several structural analysis examples, it is shown that the
numerical results at the scattered discrete points
generated by the Hermite–Cloud method are distinctly
improved, for both the approximate solutions as well as the
first-order derivatives.
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