1,411 research outputs found
Grid generation using classical techniques
A brief historical review of conformal mapping and its applications to problems in fluid mechanics and electromagnetism is presented. The use of conformal mapping as a grid generator is described. The philosophy of the 'closed form' approach and its application to a Neumann problem is discussed. Karman-Trefftz mappings and grids for ablated, three dimensional bodies are also discussed
A modified Christoffel function and its asymptotic properties
We introduce a certain variant (or regularization) of
the standard Christoffel function associated with a measure
on a compact set . Its reciprocal is now a
sum-of-squares polynomial in the variables , .
It shares the same dichotomy property of the standard Christoffel function,
that is, the growth with of its inverse is at most polynomial inside and
exponential outside the support of the measure. Its distinguishing and crucial
feature states that for fixed , and under weak assumptions,
where (assumed to be continuous) is the unknown density of w.r.t.
Lebesgue measure on , and
(and so
when is small). This is in
contrast with the standard Christoffel function where if exists, it is of the form where
is the density of the equilibrium measure of , usually
unknown. At last but not least, the additional computational burden (when
compared to computing ) is just integrating symbolically the
monomial basis on the box , so that is
obtained as an explicit polynomial of .Comment: Rapport LAAS n 2300
- …