399 research outputs found
Solving the planar p-median problem by variable neighborhood and concentric searches
Two new approaches for the solution of the p-median problem
in the plane are proposed. One is a Variable Neighborhood Search (VNS)
and the other one is a concentric search. Both approaches are enhanced by a
front-end procedure for finding good starting solutions and a decomposition
heuristic acting as a post optimization procedure. Computational results
confirm the effectiveness of the proposed algorithms
A numerical method for mass conservative coupling between fluid flow and solute transport
We present a new coupled discretization approach for species transport
in an incompressible fluid. The Navier-Stokes equations for the flow are
discretized by the divergence-free Scott-Vogelius element on barycentrically
refined meshes guaranteeing LBB stability. The convection-diffusion equation
for species transport is discretized by the Voronoi finite volume method. In
accordance to the continuous setting, due to the exact integration of the
normal component of the flow through the Voronoi surfaces, the species
concentration fulfills discrete global and local maximum principles. Besides
of the the numerical scheme itself, we present important aspects of its
implementation. Further, for the case of homogeneous Dirichlet boundary
conditions, we give a convergence proof for the coupled scheme. We report
results of the application of the scheme to the interpretation of limiting
current measurements in an electrochemical flow cell with cylindrical shape
A Characterization Theorem and An Algorithm for A Convex Hull Problem
Given and , testing if , the convex hull of , is a fundamental
problem in computational geometry and linear programming. First, we prove a
Euclidean {\it distance duality}, distinct from classical separation theorems
such as Farkas Lemma: lies in if and only if for each there exists a {\it pivot}, satisfying . Equivalently, if and only if there exists a
{\it witness}, whose Voronoi cell relative to contains
. A witness separates from and approximate to
within a factor of two. Next, we describe the {\it Triangle Algorithm}: given
, an {\it iterate}, , and , if
, it stops. Otherwise, if there exists a pivot
, it replace with and with the projection of onto the
line . Repeating this process, the algorithm terminates in arithmetic operations, where
is the {\it visibility factor}, a constant satisfying and
, over all iterates . Additionally,
(i) we prove a {\it strict distance duality} and a related minimax theorem,
resulting in more effective pivots; (ii) describe -time algorithms that may compute a witness or a good
approximate solution; (iii) prove {\it generalized distance duality} and
describe a corresponding generalized Triangle Algorithm; (iv) prove a {\it
sensitivity theorem} to analyze the complexity of solving LP feasibility via
the Triangle Algorithm. The Triangle Algorithm is practical and competitive
with the simplex method, sparse greedy approximation and first-order methods.Comment: 42 pages, 17 figures, 2 tables. This revision only corrects minor
typo
A numerical method for mass conservative coupling between fluid flow and solute transport
We present a new coupled discretization approach for species transport in an incompressible fluid. The Navier-Stokes equations for the flow are discretized by the divergence-free Scott-Vogelius element on barycentrically refined meshes guaranteeing LBB stability. The convection-diffusion equation for species transport is discretized by the Voronoi finite volume method. In accordance to the continuous setting, due to the exact integration of the normal component of the flow through the Voronoi surfaces, the species concentration fulfills discrete global and local maximum principles. Besides of the the numerical scheme itself, we present important aspects of its implementation. Further, for the case of homogeneous Dirichlet boundary conditions, we give a convergence proof for the coupled scheme. We report results of the application of the scheme to the interpretation of limiting current measurements in an electrochemical flow cell with cylindrical shape
- …