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Page 12
Journal of Biotechnology and Phytochemistry
Volume 1, Issue 2
Notes:
Plasma Chemistry 2017
November 13-14, 2017 Paris, France
5th International Conference on
PLASMA CHEMISTRY AND
PLASMA PROCESSING
Edward J Kansa, J Biot Phyt 2017
Overview of meshless radial basis functions of
solve multi-dimensional problems
Aradial distance, rab is the shortest path between a
pair of points in a curved space, ℜn; a radial basis
function (RBF), φ(rab), is a univariate function of rab. The
C∞ (infinite differentiability) RBFs are non-orthonormal
wavelets that converge exponentially, and faster as the
spatial dimensions increases making them the best tools
for plasma simulations and multi-dimensional quantum
mechanics. Since nomesh is involved, strictly hyperbolic
PDEs can be very accurately modelled by allowing
each interior point, xi in the interior, Ω\∂Ω to move at
a velocity, vi , such that a complicated nonlinear PDE
becomes an exact differential in a moving frame, vi . Strict
conservation of specie, mass, momentum components,
and total energy are enforced by integrating the RBFs
over space. The solution space can be enriched by
including discontinuous RBFs; these are products
of a Heaviside function in the normal propagation
direction, and a RBF in ℜ(n-1) in the tangential directions.
RBFs are either very broad-banded or global; domain
decomposition , pre-conditioners, regularization, global
optimization are used to control ill-conditioning. Recent
computer science developments in extended arithmetic
precision permit the control of ill-conditioning to produce
extremely accurate numerical results. In both accuracy
and the minimization of execution time, the total number
of discretization points can be minimized compared to
finite element methods.
Biography
Edward J Kansa is the president of Convergent Solutions, LLC and principal
investigator in computational sciences, LLC. He received his Ph D from Vanderbilt
University; He has an experience of road background in solving multi-disciplinary
problems in physics, and engineering with emphasis on analysis and computational
modeling.
Edward J Kansa
Convergent Solutions, USA